In PKanalix, a dataset should be loaded in the Data tab to create a project. Once the dataset accepted, it is possible to specify units and filter the dataset, so units and filtering information should not be included in the file loaded in the Data tab.

The data set format used in PKanalix is the same as for the entire MonolixSuite, to allow smooth transitions between applications. In this format:

• Each line corresponds to one individual and one time point.
• Each line can include a single measurement (also called observation), or a dose amount (or both a measurement and a dose amount).
• Dosing information should be indicated for each individual in a specific column, even if it is the same treatment for all individuals.
• Headers are free but there can be only one header line.
• Different types of information (dose, observation, covariate, etc) are recorded in different columns, which must be tagged with a column type (see below).

If your dataset is not in this format, in most cases, it is possible to format it in a few steps in the data formatting tab, to incorporate the missing information.

• Overview of most common column types
• Example datasets
  • Plasma concentration data
    • extravascular
    • IV infusion
    • IV bolus
  • Steady-state data
  • BLQ data
  • Urine data
  • Occasions (“Sort” variables)
  • Covariates (“Carry” variables)
  • Other useful column-types
• Description of all possible column types

Overview of most common column-types

A data set typically contains only the following columns: ID (mandatory), TIME (mandatory), OBSERVATION (mandatiry), AMOUNT (optional). The main rules for interpreting the dataset are:

• Cells that do not contain information (e.g AMOUNT column on a line recording a measurement) should have a dot.
• Headers are free but there can be only one header line and the columns must be assigned to one of the available column-types. The full list of column-types is available at the end of this page and a detailed description is given on the dataset documentation website.

The most common column types in addition to ID, TIME, OBSERVATION and AMOUNT are:

• For IV infusion data, an additional INFUSION RATE or INFUSION DURATION is necessary.
• For steady-state data, either an INTERDOSE INTERVAL column is added, or the interdose interval tau is specified in the NCA settings.
• If a dose and a measurement occur at the same time, they can be encoded on the same line or on different lines.
• Sort and carry variables can be defined using the OCCASION, and CATEGORICAL COVARIATE and CONTINUOUS COVARIATE column-types.
• BLQ data are defined using the CENSORING and LIMIT column-types.

In addition to the typical cases presented above, a few additional column-types may also be convenient:

• ignoring a line: with the IGNORED OBSERVATION (ignores the measurement only) or IGNORED LINE (ignores the entire line, including regressor and dose information). However it is more convenient to filter lines of your dataset without modifying it by using filters (available once your dataset is accepted).
• working with several types of observations: If several observation types are present in the dataset (for example parent and metabolite), all measurements should still appear in the same OBSERVATION column, and another column should be used to distinguish the observation types. If this is not the case in your dataset, data formatting enables to merge several observation columns. To run NCA for several observations at the same time for the same id, tag the column listing the observation types as OCCASION . To run CA for several observations with a model including several outputs (for example PK and PD), tag the column listing the observation types as OBSERVATION ID. In this case, only one observation type will be available for NCA. It can be selected in the “NCA” section to perform the calculations.
• working with several types of administrations: a single data set can contain different types of administrations, for instance IV bolus and extravascular, distinguished using the ADMINISTRATION ID column-type. The setting “administration type” in “Tasks>Run” can be chosen separately for each administration id, and the appropriate parameter calculations will be performed.

Example datasets

Below we show how to encode the dataset for most typical situations.

Plasma concentration data

Extravascular

For extravascular administration, the mandatory column-types are ID (individual identifiers as integers or strings), OBSERVATION (measured concentrations), AMOUNT (dose amount administered, mandatory for 2023 and previous versions) and TIME (time of dose or measurement). Since version 2024, datasets that do not contain an AMOUNT column or no information in the AMOUT column are accepted for single dose or multiple dose administrations.

To distinguish the extravascular from the IV bolus case, in “Tasks>Run” the administration type must be set to “extravascular”.

If no measurement is recorded at the time of the dose, a concentration of zero is added for single dose data, the minimum concentration observed during the dose interval for steady-state data.

Example:

• demo project_extravascular.pkx

This data set records the drug concentration measured after single oral administration of 150 mg of drug in 20 patients. For each individual, the first line records the dose (in the “Amount” column tagged as AMOUNT column-type) while the following lines record the measured concentrations (in the “Conc” column tagged as OBSERVATION). Cells of the “Amount” column on measurement lines contain a dot, and respectively for the concentration column. The column containing the times of measurements or doses is tagged as TIME column-type and the subject identifiers, which we will use as sort variable, are tagged as ID. Check the OCCASION section if more sort variables are needed. After accepting the dataset, the data is automatically assigned as “Plasma”.

In the “Tasks/Run” tab, the user must indicate that this is extravascular data. In the “Check lambda_z”, on linear scale for the y-axis, measurements originally present in the data are shown with full circles. Added data points, such as a zero concentration at the dose time, are represented with empty circles. Points included in the \(\lambda_z\) calculation are highlighted in blue.

After running the NCA analysis, PK parameters relevant to extravascular administration are displayed in the “Results” tab.

IV infusion

Intravenous infusions are indicated in the data set via the presence of an INFUSION RATE or INFUSION DURATION column-type, in addition to the ID (individual identifiers as integers or strings), OBSERVATION (measured concentrations), AMOUNT (dose amount administered, mandatory for 2023 and previous versions) and TIME (time of dose or measurement). The infusion duration (or rate) can be identical or different between individuals. Since version 2024, datasets that do not contain an AMOUNT column or no information in the AMOUT column are accepted for single dose or multiple dose administrations.

In “Tasks>Run” the administration type must be set to “intravenous”.

If no measurement is recorded at the time of the dose, a concentration of zero is added for single dose data, the minimum concentration observed during the dose interval for steady-state data.

Example:

• demo project_ivinfusion.pkx:

In this example, the patients receive an iv infusion over 3 hours. The infusion duration is recorded in the column called “TINF” in this example, and tagged as INFUSION DURATION.

In the “Tasks/Run” tab, the user must indicate that this is intravenous data.

IV bolus

For IV bolus administration, the mandatory column-types are ID (individual identifiers as integers or strings), OBSERVATION (measured concentrations), AMOUNT (dose amount administered, mandatory for 2023 and previous versions) and TIME (time of dose or measurement). Since version 2024, datasets that do not contain an AMOUNT column or no information in the AMOUT column are accepted for single dose or multiple dose administrations.

To distinguish the IV bolus from the extravascular case, in “Tasks>Run” the administration type must be set to “intravenous”.

If no measurement is recorded at the time of the dose, the concentration of at time zero is extrapolated using a log-linear regression of the first two data points, or is taken to be the first observed measurement if the regression yields a slope >= 0. See the calculation details for more information.

Example:

• demo project_ivbolus.pkx:

In this data set, 25 individuals have received an iv bolus and their plasma concentration have been recorded over 12 hours. For each individual (indicated in the column “Subj” tagged as ID column-type), we record the dose amount in a column “Dose”, tagged as AMOUNT column-type. The measured concentrations are tagged as OBSERVATION and the times as TIME. Check the OCCASION section if more sort variables are needed in addition to ID. After accepting the dataset, the data is automatically assigned as “plasma”.

In the “Tasks/Run” tab, the user must indicate that this is intravenous data. In the “Check lambda_z”, measurements originally present in the data are shown with full circles. Added data points, such as the C0 at the dose time, are represented with empty circles. Points included in the \(\lambda_z\) calculation are highlighted in blue.

After running the NCA analysis, PK parameters relevant to iv bolus administration are displayed in the “Results” tab.

Steady-state

Starting from version 2024, the interdose interval tau used to calculate NCA parameters specific to steady-state can be specified either in the dataset column tagged as INTERDOSE INTERVAL, or directly as part of the NCA settings.

In the 2023 and previous versions, it was necessary to indicate steady-state using the STEADY STATE column-type: SS=1 indicates that the individual is already at steady-state when receiving the dose. This implicitly assumes that the individual has received many doses before this one. SS=0 or ‘.’ indicates a single dose. Starting from version 2024, the SS column is accepted but not mandatory anymore.

The dosing interval (also called tau) is indicated in the INTERDOSE INTERVAL column on the lines defining the doses, or as part of the NCA settings.

Steady state calculation formulas will be applied for individuals having a dose with INTERDOSE INTERVAL = double. A data set can contain individuals which are at steady-state and some which are not. If the NCA setting “Interdose interval for single dose profiles” is selected, steady-state parameters are calculated for all individuals.

If no measurement is recorded at the time of the dose, the minimum concentration observed during the dose interval is added at the time of the dose for extravascular and infusion data. For iv bolus, a regression using the two first data points is performed. Only measurements between the dose time and dose time + interdose interval will be used.

Examples:

• demo project_steadystate.pkx:

In this example, the individuals are already at steady-state when they receive the dose. This is indicated in the data set via the column “SteadyState” tagged as STEADY STATE column-type, which contains a “1” on lines recording doses. The interdose interval is noted on those same line in the column “tau” tagged as INTERDOSE INTERVAL. When accepting the data set, a “Settings” section appears, which allows to define the number of steady-state doses. This information is relevant when exporting to Monolix, but not used in PKanalix directly.

After running the NCA estimation task, steady-state specific parameters are displayed in the “Results” tab.

BLQ data

Below the limit of quantification (BLQ) data can be recorded in the data set using the CENSORING column:

• “0” indicates that the value in the OBSERVATION column is the measurement.
• “1” indicates that the observation is BLQ.

The lower limit of quantification (LOQ) must be indicated in the OBSERVATION column when CENSORING = “1”. Note that strings are not allowed in the OBSERVATION column (except dots). A different LOQ value can be used for each BLQ data.

When performing an NCA analysis, the BLQ data before and after the Tmax are distinguished. They can be replaced by:

• zero
• the LOQ value
• the LOQ value divided by 2
• or considered as missing

For a CA analysis, the same options are available, but no distinction is done between before and after Tmax. Once replaced, the BLQ data are handled as any other observation.

A LIMIT column can be added to record the other limit of the interval (in general zero). This value will not be used by PKanalix but can facilitate the transition from an NCA/CA analysis PKanalix to a population model with Monolix.

To easily encode BLQ data in a dataset that only has BLQ tags in the observation column, you can use Data formatting.

Examples:

• demo project_censoring.pkx: two studies with BLQ data with two different LOQ

In this dataset, the measurements of two different studies (indicated in the STUDY column, tagged as CATEGORICAL COVARIATE in order to be carried over) are recorded. For the study 101, the LOQ is 1.8 ug/mL, while it is 1 ug/mL for study 102. The BLQ data are marked with a “1” in the BLQ column, which is tagged as CENSORING. The LOQ values are indicated for each BLQ in the CONC column of measurements, tagged as OBSERVATION.

In the “Task>NCA>Run” tab, the user can choose how to handle the BLQ data. For the BLQ data before and after the Tmax, the BLQ data can be considered as missing (as if this data set row would not exist), or replaced by zero (default before Tmax), the LOQ value or the LOQ value divided by 2 (default after Tmax). In the “Check lambda_z” tab, the BLQ data are shown in green and displayed according to the replacement value.

For the CA analysis, the replacement value for all BLQ can be chosen in the settings of the “Run” tab (default is Missing). In the “Check init.” tab, the BLQ are again displayed in green, at the LOQ value (irrespective of the chosen method for the calculations).

Urine data

To work with urine data, it is necessary to record the time and amount administered, the volume of urine collected for each time interval, the start and end time of the intervals and the drug concentration in a urine sample of each interval. The time intervals must be continuous (no gaps allowed).

In PKanalix, the start and end times of the intervals are recorded in a single column, tagged as TIME column-type. In this way, the end time of an interval automatically acts as start time for the next interval. The concentrations are recorded in the OBSERVATION column. The volume column must be tagged as REGRESSOR column type. This general column-type of MonolixSuite data sets allows to easily transition to the other applications of the Suite. As several REGRESSOR columns are allowed, the user can select which REGRESSOR column should be used as volume. The concentration and volume measured for the interval [t1,t2] are noted on the t2 line. The volume value on the dose line is meaningless, but it cannot be a dot. We thus recommend to set it to zero.

A typical urine data set has the following structure. A dose of 150 ng has been administered at time 0. The first sampling interval spans from the dose at time 0 to 4h post-dose. During this time, 410 mL of urine have been collected. In this sample, the drug concentration is 112 ng/mL. The second interval spans from 4h to 8h, the collected urine volume is 280 mL and its concentration is 92 ng/mL. The third interval is marked on the figure: 390mL of uring have been collected from 8h to 12h.

The given data is used to calculate the intervals midpoints, and the excretion rates for each interval. This information is then used to calculate the \(\lambda_z\) and calculate urine-specific parameters. In “Tasks/Check lambda_z”, we display the midpoints and excretion rates. However, in the “Plots>Data viewer”, we display the measured concentrations at the end time of the interval.

Example:

• demo project_urine.pkx: urine PK dataset

In this urine PK data set, we record the consecutive time intervals in the “TIME” column tagged as TIME. The collected volumes and measured concentration are in the columns “VOL” and “CONC”, respectively tagged as REGRESSOR and OBSERVATION. Note that the volume and concentration are indicated on the line of the interval end time. The volume on the first line (start time of the first interval, as well as dose line) is set to zero as it must be a double. This value will not be used in the calculations. Once the dataset is accepted, the observation type must be set to “urine” and the regressor column corresponding to the volume defined.

In “Tasks>Check lambda_z”, the excretion rate are plotted on the midpoints time for each individual. The choice of the lambda_z works as usual.

Once the NCA task has run, urine-specific PK parameters are displayed in the “Results” tab.

Occasions (“Sort” variables)

The main sort level are the individuals indicated in the ID column. Additional sort levels can be encoded using one or several OCCASION column(s). OCCASION columns contain integer values that permit to distinguish different time periods for a given individual. The time values can restart at zero or continue when switching from one occasion to the next one. The variables differing between periods, such as the treatment for a crossover study, are tagged as CATEGORICAL or CONTINUOUS COVARIATES (see below). The NCA and CA calculations will be performed on each ID-OCCASION combination. Each occasion is considered independent of the other occasions (i.e a washout is applied between each occasion).

Note: occasions columns encoding the sort variables as integers can easily be added to an existing data set using Excel or R.
With R, the “OCC” column can be added to an existing “data” data frame with a column “TREAT” using data$OCC <- ifelse(data$TREAT=="ref", 1, 2).
With Excel, assuming the sort variable is encoded in the column E with values “ref” and “test”, type =IF(E2="ref",1,2) to generate the first value of the “OCC” column and then propagate to the entire column:

Examples:

• demo project_occasions1.pkx: crossover study with two treatments

The subject column is tagged as ID, the treatment column as CATEGORICAL COVARIATE and an additional column encoding the two periods with integers “1” and “2” as OCCASION column.

In the “Check lambda_z” (for the NCA) and the “Check init.” (for CA), each occasion of each individual is displayed. The syntax “1#2” indicates individual 1, occasion 2, according to the values defined in the ID and OCCASION columns.

In the “Individual estimates” output tables, the first columns indicate the ID and OCCASION (reusing the data set headers). The covariates are indicated at the end of the table. Note that it is possible to sort the table by any column, including, ID, OCCASION and COVARIATES.

The OCCASION values are available in the plots for stratification, in addition to possible CATEGORICAL or CONTINUOUS COVARIATES (here “TREAT”).

• demo project_occasions2.pkx: study with two treatments and with/without food

In this example, we have three sorting variables: ID, TREAT and FOOD. The TREAT and FOOD columns are duplicated: once with strings to be used as CATEGORICAL COVARIATE (TREAT and FOOD) and once with integers to be used as OCCASION (occT and occF).

In the individual parameters tables and plots, three levels are visible. In the “Individual parameters vs covariates”, we can plot Cmax versus FOOD, split by TREAT for instance (Cmax versus TREAT split by FOOD is also possible).

Covariates (“Carry” variables)

Individual information that need to be carried over to output tables and plots must be tagged as CATEGORICAL or CONTINUOUS COVARIATES. Categorical covariates define variables with a few categories, such as treatment or sex, and are encoded as strings. Continuous covariates define variables on a continuous scale, such as weight or age, and are encoded as numbers. Covariates will not automatically be used as “Sort” variables. A dedicated OCCASION column is necessary (see above).

Covariates will automatically appear in the output tables. Plots of estimated NCA and/or CA parameters versus covariate values will also be generated. In addition, covariates can be used to stratify (split, color or filter) any plot. Statistics about the covariates distributions are available in table format in “Results > Cov. stat.” and in graphical format in “Plots > Covariate viewer”.

Note: It is preferable to avoid spaces and special characters (stars, etc) in the strings for the categories of the categorical covariates. Underscores are allowed.

Example:

• demo project_covariates.pkx

In this data set, “SEX” is tagged as CATEGORICAL COVARIATE and “WEIGHT” as CONTINUOUS COVARIATE.

The “cov stat” table permits to see a few statistics of the covariate values in the data set. In the plot “Covariate viewer”, we see that the distribution of weight is similar for males and females.

After running the NCA and CA tasks, both covariates appear in the table of individual estimated parameters estimated.

In the plot “parameters versus covariates”, the parameters values are plotted as scatter plot with the parameter value (here Cmax and AUCINF_pred) on on y-axis and the weight value on the x-axis, and as boxplots for sex female and sex male.

All plots can be stratified using the covariates. For instance, the “Data viewer” can be colored by weight after having created 3 weight groups. Below we also show the plot “Distribution of the parameters” split by sex with selection of the AUCINF_pred parameter.

Description of all possible column types

Column-types used for all types of lines:

• ID (mandatory): identifier of the individual
• OCCASION (formerly OCC): identifier (index) of the occasion
• TIME (mandatory): time of the dose or observation record
• NOMINAL TIME: time at which doses and observations were expected to occur
• DATE/DAT1/DAT2/DAT3: date of the dose or observation record, to be used in combination with the TIME column
• EVENT ID (formerly EVID): identifier to indicate if the line is a dose-line or a response-line
• IGNORED OBSERVATION (formerly MDV): identifier to ignore the OBSERVATION information of that line
• IGNORED LINE (from 2019 version): identifier to ignore all the informations of that line
• CONTINUOUS COVARIATE (formerly COV): continuous covariates (which can take values on a continuous scale)
• CATEGORICAL COVARIATE (formerly CAT): categorical covariate (which can only take a finite number of values)
• REGRESSOR (formerly X): defines a regression variable, i.e a variable that can be used in the structural model (used e.g for time-varying covariates)
• IGNORE: ignores the information of that column for all lines

Column-types used for response-lines:

• OBSERVATION (mandatory, formerly Y): records the measurement/observation for continuous, count, categorical or time-to-event data
• OBSERVATION ID (formerly YTYPE): identifier for the observation type (to distinguish different types of observations, e.g PK and PD)
• CENSORING (formerly CENS): marks censored data, below the lower limit or above the upper limit of quantification
• LIMIT: upper or lower boundary for the censoring interval in case of CENSORING column

Column-types used for dose-lines:

• AMOUNT (mandatory, formerly AMT): dose amount (with version 2024 only mandatory if dataset contains STEADY STATE, ADDITIONAL DOSES, INFUSIONRATE or INFUSION DURATION columns)
• ADMINISTRATION ID (formerly ADM): identifier for the type of dose (given via different routes for instance)
• INFUSION RATE (formerly RATE): rate of the dose administration (used in particular for infusions)
• INFUSION DURATION (formerly TINF): duration of the dose administration (used in particular for infusions)
• ADDITIONAL DOSES (formerly ADDL): number of doses to add in addition to the defined dose, at intervals INTERDOSE INTERVAL
• INTERDOSE INTERVAL (formerly II): interdose interval for doses added using ADDITIONAL DOSES or STEADY-STATE column types
• STEADY STATE (formerly SS): marks that steady-state has been achieved, and will add a predefined number of doses before the actual dose, at interval INTERDOSE INTERVAL, in order to achieve steady-state

Starting on the 2020 version, filtering a data set to only take a subpart into account in your modelization is possible. It allows to make filters on some specific IDs, times, measurement values,… It is also possible to define complementary filters and also filters of filters. It is accessible through the filters item on the data tab.

• Creation of a filter
• Filtering actions
• Filters with several actions
• Other filers: filter of filter and complementary filters

Creation of a filter

To create a filter, you need to click on the data set name. You can then create a “child”. It corresponds to a subpart of the data set where you will define your filtering actions.

You can see on the top (in the green rectangle) the action that you will complete and you can CANCEL, ACCEPT, or ACCEPT & APPLY with the bottoms on the bottom.

Filtering a data set: actions

In all the filtering actions, you need to define

• An action: it corresponds to one of the following possibilities: select ids, remove ids, select lines, remove lines.
• A header: it corresponds to the column of the data set you wish to have an action on. Notice that it corresponds to a column of the data set that was tagged with a header.
• An operator: it corresponds to the operator of choice (=, ≠, < ≤, >, or ≥).
• A value. When the header contains numerical values, the user can define it. When the header contains strings, a list is proposed.

For example, you can

• Remove the ID 1 from your study:
  
  In that case, all the IDs except ID = 1 will be used for the study.
• Select all the lines where the time is less or equal 24:
  
  In that case, all lines with time strictly greater that 24 will be removed. If a subject has no measurement anymore, it will be removed from the study.
• Select all the ids where SEX equals F:
  
  In that case, all the male will be removed of the study.
• Remove all Ids where WEIGHT less or equal 65:
  
  In that case, only the subjects with a weight over 65 will be kept for the study.

In any case, the interpreted filter data set will be displayed in the data tab.

Filters with several actions

In the previous examples, we only did one action. It is also possible to do several actions to define a filter. We have the possibility to define UNION and/or INTERSECTION of actions.

INTERSECTION

By clicking by the + and – button on the right, you can define an intersection of actions. For example, by clicking on the +, you can define a filter corresponding to intersection of

• The IDs that are different to 1.
• The lines with the time values less than 24.

Thus in that case, all the lines with a time less than 24 and corresponding to an ID different than 1 will be used in the study. If we look at the following data set as an example

Initial data set	Resulting data set after action: select IDs ≠ 1	Considered data set for the study as the intersection of the two actions
	Resulting data set after action: select lines with time ≤ 24

UNION

By clicking by the + and – button on the bottom, you can define an union of actions. For example, in a  data set with a multi dose, I can focus on the first and the last dose. Thus, by clicking on the +, you can define a filter corresponding to union of

• The lines where the time is strictly less than 12.
• The lines where the time is greater than 72.

Initial data set	Resulting data set after action: select lines where the time is strictly less than 12	Considered data set for the study as the union of the three actions
	Resulting data set after action: select lines where the time is greater than 72
	Resulting data set after action: select lines where amt equals 40

Notice that, if just define the first two actions, all the dose lines at a time in ]12, 72[ will also be removed. Thus, to keep having all the doses, we need to add the condition of selecting the lines where the dose is defined.

In addition, it is possible to do any combination of INTERSECTION and UNION.

Other filers: filter of filter and complementary filters

Filtering a data set can be nested. Based on the definition of a filter, by clicking on the filter, it is possible to create:

• A child: it corresponds to a new filter with the initial filter as the source data set.
• A complement: corresponds to the complement of the filter. For example, if you defined a filter with only the IDs where the SEX is F, then the complement corresponds to the IDs where the SEX is not F.

MonolixSuite applications are interconnected and projects can be exported/imported between different applications. This interconnection is guaranteed by using the same model syntax (mlxtran language) and the same dataset format.

There are two options to create a PKanalix project from a Monolix or Simulx project*

• Import a Monolix project to PKanalix to run NCA or CA on the original dataset in the Monolix project
• Export from Monolix to PKanalix to run NCA or CA on the original dataset, or on the VPC simulations or individual fits
  • Export with individual fits dataset.
  • Export with VPC simulations
• Export from Simulx to PKanalix to run NCA or CA on simulations

*Note: Import and export to PKanalix is available starting from the 2023 version. In the previous versions, you can only export a PKanalix project to Monolix.

To import a Monolix project, open PKanalix application and in the home page select IMPORT FROM:

 

In PKanalix, it is possible to import only a Monolix project with its original dataset. When you select in the home screen IMPORT FROM > Monolix, then PKanalix will create a new, untitled, project with:

• Dataset tagging and formatting steps if present as in the Monolix project.
• Dataset filters if applied as in the Monolix project.
• NCA settings: “administration type” set to intravenous or extravascular depending on the administration in a model selected in the Monolix project.
• NCA settings: “observation ID to use” set to the first one alphabetically (if obsid are strings) or numerically (if obsid are integers).
• NCA settings: default PKanalix settings for the integral method, treatment of BLQ values, parameters.
• Acceptance criteria: not selected.
• Bioequivalence: default PKanalix settings
• CA model: set to the same structural model and the same mapping between observation ids and model outputs as in the Monolix project
• CA initial parameter values: equal to the initial estimates of the Monolix project
• CA parameters constraints: none for normally distributed parameters, positive for log-normally distributed parameters; bounded with limits imported from the Monolix project for logit-normally and probit-normally distributed parameters.
• CA calculations settings: default PKanalix settings

After the import, you can save the PKanalix project as usual, edit it and run the analysis.

Remark: Importing a Monolix project to PKanalix is only with the original dataset used to create a Monolix project. Export from Monolix to PKanalix has more options. You can choose to import a Monolix project with its original dataset, vpc dataset or with individual fits dataset, see the next section. Import from Simulx is currently unavailable.

To export a Monolix project to PKanalix click EXPORT PROJECT TO in the top menu “Export”:

When you export a Monolix project, in the export pop-up window you can choose:

• to which application you want to export your current project: PKanalix or Simulx: select “PKanalix”
• which dataset you want to use in the export: original dataset, vpc dataset, individual fits dataset

By default, Monolix will copy all files, e.g. dataset and model, next to the new PKanalix project. To keep current location of these files, switch the toggle “Generated files next to project” off. Click the “EXPORT” button at the bottom to confirm. PKanalix application will open automatically with a predefined project called “untitled”. It will contain the same pre-defined elements as during the import, see the description above. If you selected export with vpc dataset or individual fits dataset, then Monolix creates a .csv files with vpc simulations or individual model predictions in the MonolixSuite data format. These dataset will be automatically loaded in the new PKanalix project.

Export with individual fits dataset

The .csv generated file contains model predictions on a fine time grid (specified in the Plots tasks settings in Monolix) obtained with different individual parameters:

• popPred: model predictions with individual parameters corresponding to the population parameters estimated by Monolix and the impact of the individual covariates, but random effects set to zero. For instance,\( V_i = V_{pop} \times exp^{\beta_{V,WT}\times WT_i} \)
• popPred_medianCOV: model predictions with individual parameters corresponding to the population parameters and the impact of the covariates using the population median for continuous covariates and reference category for categorical covariates, and random effects set to zero. For instance, \( V_i = V_{pop} \times exp^{\beta_{V,WT}\times WT_{med}} \)
• indivPred_mode: [when EBEs task has run] model predictions with individual parameters corresponding to the EBEs (conditional mode) estimated by Monolix (as displayed in Monolix Results > Indiv. param > Cond. mode.). Tagged as OBSERVATION by default.
• indivPred_mean: [when COND. DISTRIB. task has run] model predictions with individual parameters corresponding to the conditional mean estimated by Monolix (as displayed in in Monolix Results > Indiv. param > Cond. mean.)

The dataset contains also the individual design: doses, occasions, regressors, covariates.

Export with vpc dataset

The .csv generated dataset in the Monolix format constructed from the VPC simulations and individual design (doses, occasions, regressors, covariates)

• rep: simulation replicate. Tagged as stratification categorical covariate
• uid: unique id obtained by concatenation of “rep” and “id”. Tagged as ID by default.
• time/timeAfterLastDose: observation times or times after last dose
• doseid: administration id
• y1/observation: simulated observation values. Default header is “y1” if a model has only one output, and “observation” in case of several outputs (obsid column is created automatically). Tagged automatically as OBSERVATION

The following page describes all the parameters computed by the non compartmental analysis. Parameter names are fixed and cannot be changed.

• Parameters related to \(\lambda_z\)
• Parameters related to plasma/blood measurements
• Parameters related to plasma/blood measurements specific to steady state dosing regimen
• Parameters related to urine measurements
• Parameters related to sparse NCA
• Parameter renamings
• Custom (user-defined) NCA parameters

Name	PKPARMCD CDISC	PKPARM CDISC	UNITS	DESCRIPTION
Rsq	R2	R Squared	no unit	Goodness of fit statistic for the terminal (log-linear) phase between the linear regression and the data
Rsq_adjusted	R2ADJ	R Squared Adjusted	no unit	Goodness of fit statistic for the terminal elimination phase, adjusted for the number of points used in the estimation of \(\lambda_z\)
Corr_XY	CORRXY	Correlation Between TimeX and Log ConcY	no unit	Correlation between time (X) and log concentration (Y) for the points used in the estimation of \(\lambda_z\)
No_points_lambda_z	LAMZNPT	Number of Points for Lambda z	no unit	Number of points considered in the \(\lambda_z\) regression
Lambda_z	LAMZ	Lambda z	1/time	First order rate constant associated with the terminal (log-linear) portion of the curve. Estimated by linear regression of time vs. log concentration
Lambda_z_lower	LAMZLL	Lambda z Lower Limit	time	Lower limit on time for values to be included in the \(\lambda_z\) calculation
Lambda_z_upper	LAMZUL	Lambda z Upper Limit	time	Upperlimit on time for values to be included in the \(\lambda_z\) calculation
HL_Lambda_z	LAMZHL	Half-Life Lambda z	time	Terminal half-life = ln(2)/Lambda_z
Lambda_z_intercept	–	–	no unit	Intercept found during the regression for (\lambda_z\), i.e. value of the regression (in log-scale) at time 0, i.e. the regression writes log(Concentration) = -Lambda_z*t+Lambda_z_intercept
Span	–	–	no unit	Ratio between the sampling interval of the measurements used for the \(\lambda_z\) and the terminal half-life = (Lambda_z_upper – Lambda_z_lower)*Lambda_z/ln(2)

Name	PKPARMCD CDISC	PKPARM CDISC	UNITS	DESCRIPTION
Tlag	TLAG	Time Until First Nonzero Conc	time	Tlag is the time prior to the first measurable (non-zero) concentration. Tlag is 0 if the first observation after the last dose is not 0 or LOQ. The value is set to 0 for non extravascular input.
T0			time	Time of the dose
Dose			amount	Amount of the dose
N_Samples	–	–	no unit	Number of samples in the individuals.
C0	C0	Initial Conc	amount/volume	If a PK profile does not contain an observation at dose time (C0), the following value is added Extravascular and Infusion data. For single dose data, a concentration of zero.  For steady-state, the minimum observed during the dose interval. IV Bolus data. Log-linear regression of first two data points to back-extrapolate C0.
Tmax	TMAX	Time of CMAX	time	Time of maximum observed concentration. – For non-steady-state data, the entire curve is considered. – For steady-state data, Tmax corresponds to points collected during a dosing interval. If the maximum observed concentration is not unique, then the first maximum is used.
Cmax	CMAX	Max Conc	amount/volume	Maximum observed concentration, occurring at Tmax. If not unique, then the first maximum is used.
Cmax_D	CMAXD	Max Conc Norm by Dose	1/volume	Maximum observed concentration divided by dose. Cmax_D = Cmax/Dose
Tlast	TLST	Time of Last Nonzero Conc	time	Last time point with measurable concentration
Clast	CLST	Last Nonzero Conc	amount/volume	Concentration of last time point with measurable concentration
AUClast	AUCLST	AUC to Last Nonzero Conc	time.amount/volume	Area under the curve from the time of dosing to the last measurable positive concentration. The calculation depends on the Integral method setting.
AUClast_D	AUCLSTD	AUC to Last Nonzero Conc Norm by Dose	time/volume	Area under the curve from the time of dosing to the last measurable concentration divided by the dose. AUClast_D = AUClast/Dose
AUMClast	AUMCLST	AUMC to Last Nonzero Conc	time2.amount/volume	Area under the moment curve (area under a plot of the product of concentration and time versus time) from the time of dosing to the last measurable concentration.
MRTlast	MRTIVLST	MRT Intravasc to Last Nonzero Conc	time	[if intravascular] Mean residence time from the time of dosing to the time of the last measurable concentration, for a substance administered by intravascular dosing. MRTlast_iv = AUMClast/AUClast – TI/2, where TI represents infusion duration.
MRTlast	MRTEVLST	MRT Extravasc to Last Nonzero Conc	time	[if extravascular] Mean residence time from the time of dosing to the time of the last measurable concentration for a substance administered by extravascular dosing. MRTlast_ev = AUMClast/AUClast – TI/2, where TI represents infusion duration.
AUCall	AUCALL	AUC All	time.amount/volume	Area under the curve from the time of dosing to the time of the last observation. If the last concentration is positive AUClast=AUCall. Otherwise, AUCall will not be equal to AUClast as it includes the additional area from the last measurable concentration down to zero or negative observations.
AUCINF_obs	AUCIFO	AUC Infinity Obs	time.amount/volume	AUC from Dosing_time extrapolated to infinity, based on the last observed concentration. AUCINF_obs = AUClast + Clast/Lambda_z
AUCINF_D_obs	AUCIFOD	AUC Infinity Obs Norm by Dose	time/volume	AUCINF_obs divided by dose AUCINF_D_obs = AUCINF_obs/Dose
AUC_PerCentExtrap_obs	AUCPEO	AUC %Extrapolation Obs	%	Percentage of AUCINF_obs due to extrapolation from Tlast to infinity. AUC_%Extrap_obs = 100*(1- AUClast / AUCINF_obs)
AUC_PerCentBack_Ext_obs	AUCPBEO	AUC %Back Extrapolation Obs	%	Applies only for intravascular bolus dosing. the percentage of AUCINF_obs that was due to back extrapolation to estimate C(0).
AUMCINF_obs	AUMCIFO	AUMC Infinity Obs	time2.amount/volume	Area under the first moment curve to infinity using observed Clast AUMCINF_obs = AUMClast + (Clast/Lambda_z)*(Tlast + 1.0/Lambda_z)
AUMC_PerCentExtrap_obs	AUMCPEO	AUMC % Extrapolation Obs	%	Extrapolated (% or total) area under the first moment curve to infinity using observed Clast AUMC_%Extrap_obs = 100*(1- AUMClast / AUMCINF_obs)
MRTINF_obs	MRTIVIFO	MRT Intravasc Infinity Obs	time	[if intravascular] Mean Residence Time extrapolated to infinity for a substance administered by intravascular dosing using observed Clast MRTINF_obs_iv = AUMCINF_obs/AUCINF_obs- TI/2, where TI represents infusion duration.
MRTINF_obs	MRTEVIFO	MRT Extravasc Infinity Obs	time	[if extravascular] Mean Residence Time extrapolated to infinity for a substance administered by extravascular dosing using observed Clast MRTINF_obs_ev = AUMCINF_obs/AUCINF_obs
Vz_F_obs	VZFO	Vz Obs by F	volume	[if extravascular] Volume of distribution associated with the terminal phase divided by F (bioavailability) Vz_F_obs = Dose/Lambda_z/AUCINF_obs
Cl_F_obs	CLFO	Total CL Obs by F	volume/time	[if extravascular] Clearance over F (based on observed Clast) Cl_F_obs = Dose/AUCINF_obs
Vz_obs	VZO	Vz Obs	volume	[if intravascular] Volume of distribution associated with the terminal phase Vz_obs= Dose/Lambda_z/AUCINF_obs
Cl_obs	CLO	Total CL Obs	volume/time	[if intravascular] Clearance (based on observed Clast) Cl_obs = Dose/AUCINF_obs
Vss_obs	VSSO	Vol Dist Steady State Obs	volume	[if intravascular] An estimate of the volume of distribution at steady state based last observed concentration. Vss_obs = MRTINF_obs*Cl_obs
Clast_pred	–	–	amount/volume	Clast_pred = exp(Lambda_z_intercept- Lambda_z* Tlast) The values alpha (corresponding to the y-intercept obtained when calculating \(\lambda_z\)) and lambda_z are those values found during the regression for \(\lambda_z\)
AUCINF_pred	AUCIFP	AUC Infinity Pred	time.amount/volume	Area under the curve from the dose time extrapolated to infinity, based on the last predicted concentration, i.e., concentration at the final observation time estimated using the linear regression performed to estimate \(\lambda_z\) . AUCINF_pred = AUClast + Clast_pred/Lambda_z
AUCINF_D_pred	AUCIFPD	AUC Infinity Pred Norm by Dose	time/volume	AUCINF_pred divided by dose = AUCINF_pred/Dose
AUC_PerCentExtrap_pred	AUCPEP	AUC %Extrapolation Pred	%	Percentage of AUCINF_pred due to extrapolation from Tlast to infinity AUC_%Extrap_pred = 100*(1- AUClast / AUCINF_pred)
AUC_PerCentBack_Ext_pred	AUCPBEP	AUC %Back Extrapolation Pred	%	Applies only for intravascular bolus dosing. The percentage of AUCINF_pred that was due to back extrapolation to estimate C(0).
AUMCINF_pred	AUMCIFP	AUMC Infinity Pred	time2.amount/volume	Area under the first moment curve to infinity using predicted Clast AUMCINF_pred = AUMClast + (Clast_pred/Lambda_z)*(Tlast+1/Lambda_z)
AUMC_PerCentExtrap_pred	AUMCPEP	AUMC % Extrapolation Pred	%	Extrapolated (% or total) area under the first moment curve to infinity using predicted Clast AUMC_%Extrap_pred = 100*(1- AUMClast / AUMCINF_pred)
MRTINF_pred	MRTIVIFP	MRT Intravasc Infinity Pred	time	[if intravascular] Mean Residence Time extrapolated to infinity for a substance administered by intravascular dosing using predicted Clast
MRTINF_pred	MRTEVIFP	MRT Extravasc Infinity Pred	time	[if extravascular] Mean Residence Time extrapolated to infinity for a substance administered by extravascular dosing using predicted Clast
Vz_F_pred	VZFP	Vz Pred by F	volume	[if extravascular] Volume of distribution associated with the terminal phase divided by F (bioavailability) = Dose/Lambda_z/AUCINF_pred
Cl_F_pred	CLFP	Total CL Pred by F	volume/time	[if extravascular] Clearance over F (using predicted Clast) Cl_F_pred = Dose/AUCINF_pred
Vz_pred	VZP	Vz Pred	volume	[if intravascular] Volume of distribution associated with the terminal phas Vz_pred = Dose/Lambda_z/AUCINF_pred
Cl_pred	CLP	Total CL Pred	volume/time	[if intravascular] Clearance (using predicted Clast) = Dose/AUCINF_pred
Vss_pred	VSSP	Vol Dist Steady State Pred	volume	[if intravascular] An estimate of the volume of distribution at steady state based on the last predicted concentration. Vss_pred = MRTINF_pred*Cl_pred
AUC_lower_upper	AUCINT	AUC from T1 to T2	time.amount/volume	AUC from T1 to T2 (partial AUC)
AUC_lower_upper_D	AUCINTD	AUC from T1 to T2 Norm by Dose	time/volume	AUC from T1 to T2 (partial AUC) divided by Dose
CAVG_lower_upper	CAVGINT	Average Conc from T1 to T2	amount/volume	Average concentration from T1 to T2

In the case of repeated doses, dedicated parameters are used to define the steady state parameters and some specific formula should be considered for the clearance and the volume for example. Notice that all the calculation dedicated to the area under the first moment curve (AUMC) are not relevant.

Name	PKPARMCD CDISC	PKPARM CDISC	UNITS	DESCRIPTION
Tau	–		time	The (assumed equal) dosing interval for steady-state data.
Ctau	CTAU	Conc Trough	amount/volume	Concentration at end of dosing interval. If the observed concentration does not exist, the value is interpolated. It it cannot be interpolated, it is extrapolated using lambda_z. If lambda_z has not been computed, it is extrapolated as the last observed value.
Ctrough	CTROUGH	Conc Trough	amount/volume	Concentration at end of dosing interval. If the observed concentration does not exist, the value is NaN.
AUC_TAU	AUCTAU	AUC Over Dosing Interval	time.amount/volume	The area under the curve (AUC) for the defined interval between doses (TAU). The calculation depends on the Integral method setting.
AUC_TAU_D	AUCTAUD	AUC Over Dosing Interval Norm by Dose	time/volume	The area under the curve (AUC) for the defined interval between doses (TAU) divided by the dose. AUC_TAU_D = AUC_TAU/Dose
AUC_TAU_PerCentExtrap	–	–	%	Percentage of AUC due to extrapolation in steady state.  AUC_TAU_%Extrap = 100*(AUC [Tlast, tau] if Tlast<=tau)/AUC_TAU;
AUMC_TAU	AUMCTAU	AUMC Over Dosing Interval	time2.amount/volume	The area under the first moment curve (AUMC) for the defined interval between doses (TAU).
Vz_F	VZFTAU	Vz for Dose Int by F	volume	[if extravascular] The volume of distribution associated with the terminal slope following extravascular administration divided by the fraction of dose absorbed, calculated using AUC_TAU. Vz_F =  Dose/Lambda_z/AUC_TAU
Vz	VZTAU	Vz for Dose Int	volume	[if intravascular] The volume of distribution associated with the terminal slope following intravascular administration, calculated using AUC_TAU. Vz =  Dose/Lambda_z/AUC_TAU
CLss_F	CLFTAU	Total CL by F for Dose Int	volume/time	[if extravascular] The total body clearance for extravascular administration divided by the fraction of dose absorbed, calculated using AUC_TAU . CLss_F =  Dose/AUC_TAU
CLss	CLTAU	Total CL for Dose Int	volume/time	[if intravascular] The total body clearance for intravascular administration, calculated using AUC_TAU. CLss =  Dose/AUC_TAU
Cavg	CAVG	Average Concentration	amount/volume	AUCTAU divided by Tau. Cavg = AUC_TAU /Tau
FluctuationPerCent	FLUCP	Fluctuation%	%	The difference between Cmin and Cmax standardized to Cavg, between dose time and Tau. Fluctuation%  = 100.0* (Cmax -Cmin)/Cavg
FluctuationPerCent_Tau	–	–	%	The difference between Ctau and Cmax standardized to Cavg, between dose time and Tau. Fluctuation% _Tau  = 100.0* (Cmax -Ctau)/Cavg
Accumulation_Index	AILAMZ	Accumulation Index using Lambda z	no unit	Theoretical accumulation ratio: Predicted accumulation ratio for area under the curve (AUC) calculated using the Lambda z estimated from single dose data. Accumulation_Index = 1.0/(1.0 -exp(-Lambda_z*Tau))
Swing	–	–	no unit	The degree of fluctuation over one dosing interval at steady state Swing = (Cmax -Cmin)/Cmin
Swing_Tau	–	–	no unit	Swing_Tau = (Cmax -Ctau)/Ctau
Tmin	TMIN	Time of CMIN observation.	time	Time of minimum concentration sampled during a dosing interval.
Cmin	CMIN	Min Conc	amount/volume	Minimum observed concentration between dose time and dose time + Tau.
Cmax	CMAX	Max Conc	amount/volume	Maximum observed concentration between dose time and dose time + Tau.
MRTINF_obs	MRTIVIFO or MRTEVIFO	MRT Intravasc Infinity Obs or MRT Extravasc Infinity Obs	time	Mean Residence Time extrapolated to infinity using predicted Clast, calculated using AUC_TAU.

Name	PKPARMCD CDISC	PKPARM CDISC	UNITS	DESCRIPTION
T0			time	Time of the last administered dose (assumed to be zero unless otherwise specified).
Dose	–	–	amount	Amount of the dose
N_Samples	–	–	no unit	Number of samples in the individuals.
Tlag	TLAG	Time Until First Nonzero Conc	time	Midpoint prior to the first measurable (non-zero) rate.
Tmax_Rate	ERTMAX	Midpoint of Interval of Maximum ER	time	Midpoint of collection interval associated with the maximum observed excretion rate.
Max_Rate	ERMAX	Max Excretion Rate	amount/time	Maximum observed excretion rate.
Mid_Pt_last	ERTLST	Midpoint of Interval of Last Nonzero ER	time	Midpoint of collection interval associated with Rate_last.
Rate_last	ERLST	Last Meas Excretion Rate	amount/time	Last measurable (positive) rate.
AURC_last	AURCLST	AURC to Last Nonzero Rate	amount	Area under the urinary excretion rate curve from time 0 to the last measurable rate.
AURC_last_D	AURCLSTD	AURC to Last Nonzero Rate Norm by Dose	no unit	The area under the urinary excretion rate curve (AURC) from time zero to the last measurable rate, divided by the dose.
Vol_UR	VOLPK	Sum of Urine Vol	volume	Sum of Urine Volumes
Amount_Recovered			amount	Cumulative amount eliminated.
Percent_Recovered			%	100*Amount_Recovered/Dose
AURC_all	AURCALL	AURC All	amount	Area under the urinary excretion rate curve from time 0 to the last rate. This equals AURC_last if the last rate is measurable.
AURC_INF_obs	AURCIFO	AURC Infinity Obs	amount	Area under the urinary excretion rate curve extrapolated to infinity, based on the last observed excretion rate.
AURC_PerCentExtrap_obs	AURCPEO	AURC % Extrapolation Obs	%	Percent of AURC_INF_obs that is extrapolated
AURC_INF_pred	AURCIFP	AURC Infinity Pred	amount	Area under the urinary excretion rate curve extrapolated to infinity, based on the last predicted excretion rate.
AURC_PerCentExtrap_pred	AURCPEP	AURC % Extrapolation Pred	%	Percent of AURC_INF_pred that is extrapolated
AURC_lower_upper	AURCINT	AURC from T1 to T2 (partial AUC)	amount	The area under the urinary excretion rate curve (AURC) over the interval from T1 to T2.
AURC_lower_upper_D	AURCINTD	AURC from T1 to T2 Norm by Dose	no unit	The area under the urinary excretion rate curve (AURC) over the interval from T1 to T2 divided by Dose
Rate_last_pred	–	–	amount/time	The values alpha and Lambda_z are those values found during the regression for lambda_z

Name	UNITS	DESCRIPTION
SE_Cmax	amount/volume	Sample standard error of the concentration values at Tmax (standard deviation of the y-values at time Tmax divided by the square root of the number of observations at Tmax)
SE_AUClast	time.amount/volume	SE_AUClast = \(\sqrt{Var(\hat{AUC})} = \sqrt{\sum_{i=0}^{m} \frac{w_i^2s_i^2}{n_i}+2 \sum_{i<j} \frac{w_i w_j n_{ij} s_{ij}}{n_i n_j}}\)with \( w_{i} = \begin{cases} \frac{t_1-t_0}{2}, & \text{if i=0}\\ \frac{t_{i+1}-t_{i-1}}{2}, & \text{if i=1, …, m}\\ \frac{t_m-t_{m-1}}{2}, & \text{if i=m} \end{cases} \) and \( s_{ij} = \sum_{k=1}^{n_{ij}} \frac{(C_{ik}-\bar{C_i})(C_{jk}-\bar{C_j})}{(n_{ij}-1)+(1-\frac{n_{ij}}{n_i})(1-\frac{n_{ij}}{n_j})}\) where: \(m\) = time of last measurable (positive) mean concentration \(n_{ij}\) = number of individuals sampled at both times i and j \(n_i\) = number of individuals sampled at time i \(s_i^2\) = sample variance of concentrations at time i \(s_{ij}\) = sample covariance between concentrations \(C_{ik}\) and \(C_{jk}\) for all individuals k that are sampled at both times i and j
SE_AUCall	time.amount/volume	Same as SE_AUClast with m = last observation time
SE_Max_Rate	amount/time	Same as SE_Cmax with excretion rates
SE_AURC_last	amount	Same as SE_AUClast with excretion rates
SE_AURC_all	amount	Same as SE_AUCall with excretion rates

SE_AUClast, SE_AUCall, SE_AURC_last, SE_AURC_all are available only if the integral method is “linear trapezoidal linear” or “linear trapezoidal linear/log” (because the formula is based on linear calculation of AUC).

Parameter renamings

Starting from the 2023 version of MonolixSuite, default parameter names used in results tables and plots in the graphical user interface and reports do not match the names present in the Name column of the tables above. The names that are used can be customized in the NCA parameters renamings section of Preferences. The section contains two columns:

• Parameter – this column contains parameter names from the tables above,
• Alias – this column contains parameter names used in the interface and the values in cells can be changed.

The Alias column is prefilled with default aliases. By clicking on an alias, PKanalix allows users to input characters. There are several options present, when in the input mode:

• Undo – reverse the last action,
• Redo – redo an undone action,
• Subscript – formats selected text and subsequently entered characters as subscript,
• Superscript – formats selected text and subsequently entered characters as superscript,
• CF – clears formatting of a selected text,
• Cancel – cancels the changes and restores the alias,
• Accept – accepts the changes (changes can be accepted by clicking anywhere in the interface as well).

This pages provides the information on the statistics used for the summary of the individual parameters for both NCA tasks and CA tasks. All the statistics are made with respect to the NOBS individuals where the parameter has value. For example, in the NCA task, the parameter \(\lambda_z\) might not be possible to compute. Thus, the value associated to these subjects will be missing and not taken into account in the statistics.

• MIN: Minimum of the parameter over the NOBS individuals
• Q1: First quartile of the parameter over the NOBS individuals
• MEDIAN: Median of the parameter over the NOBS individuals
• Q3: Third quartile of the parameter over the NOBS individuals
• MAX: Maximum of the parameter over the NOBS individuals
• MEAN: Arithmetic mean of the parameter over the NOBS individuals
• SD: Standard deviation of the parameter over the NOBS individuals
• SE: Standard error of the parameter over the NOBS individuals
• CV: Coefficient of variation of the parameter over the NOBS individuals
• NTOT: Total number of individuals
• NOBS: Number of individuals with a valid value
• NMISS: Number of individuals with no valid value
• GEOMEAN: Geometric mean of the parameter over the NOBS individuals
• GEOSD: Geometric standard deviation of the parameter over the NOBS individuals
• GEOCV: Geometric coefficient of variation over the NOBS individuals
• HARMMEAN: Harmonic mean of the parameter over the NOBS individuals

Starting from the version 2024R1, it is possible to define custom NCA parameters as formulas of existing parameters and covariates. User defined NCA parameters can be defined via Preferences or for a specific project:

1. Definition via Preferences: user defined NCA parameters defined via Preferences can be used in any project with which they are compatible (if parameters that are used in the formula can be calculated in a project and if covariates used in the formula are present in the data set used in a project).
2. Project-specific definition: user defined NCA parameters defined in a project will be used just in that particular project. However, when or after creating a project-specific NCA parameter, user can send the parameter to Preferences.

Definition of parameters

To define a parameter in Preferences, users can choose Settings > Preferences and define parameters in the section “NCA custom parameters”. To define project-specific parameters, users can click on the button “+” in the list of parameters in the Tasks tab. In both cases, a parameter can be defined using a form that contains for fields: The fields are the following:

1. Name: contains the name of the parameter used in the list of Parameters in the Tasks tab. This field can only start with a letter and cannot contain any special characters except “_”.
2. Alias: parameter name used in results tables and plots in the graphical user interface and reports. Can contain special characters and can be stylized with subscripts and superscripts.
3. Formula: mathematical expression used to define the parameter. The expression can contain NCA parameters calculated by PKanalix (list) and names of the covariates present in the data set. Operators +, –, *, /, and ^ can be used in the definition, as well as parentheses and functions abs, sqrt, exp, log, log10, logit, invlogit, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, floor, ceil, factorial, min, max, atan2, rem (definitions of those functions can be found here).
   Partial AUC parameters can also be used in formulas, with slightly changed names – when start or end time contain a decimal point, it needs to be replaced by “d” (e.g., AUC_0_0.5 becomes AUC_0_0d5), and if they are in a scientific notation, a minus sign needs to be replaced by “m” (e.g., AUC_0_2e-10 becomes AUC_0_2em10).
   When writing parameter names, an autocomplete panel will show up to help users write the name. If covariates are present in the project, instead of writing their names, users can click on the buttons available above the formula input field.
4. Units: contains the unit definition for the parameter. If a unit of a custom parameter depends on a project, generalized strings TIME, AMOUNT, VOLUME, CONC and GRADING can be used for time, amount, volume, concentration and dose normalization units defined in the project (these strings can be entered in a field via buttons above the field). Superscripts can be used with the syntax “^x” where x is a positive or a negative number (superscripts ^2 and ^-1 are also available via buttons). Different units can be concatenated using the character “.” (also available via a button). When defining a project-specific parameter, preview of the unit will be shown (the preview will replace the generalized strings with the units defined in the project). Note that “/” sign cannot be used. To define for instance “mg/L”, use “mg.L^-1”.

If definition is project-specific, form contains an additional checkbox “Add to preferences”, which if ticked will save the parameter in Preferences, in addition to adding it to the project.

Custom parameter usage

The parameters defined via Preferences will appear in the dropdown of the Parameters section of the Tasks tab, if they are compatible with the current project (i.e if they use parameters that can be calculated for the current project and covariates present in the data set). They can be added to the project by clicking on them in the dropdown. If clicked on, they will appear on the parameter list and calculated if the checkbox in the NCA column is ticked. Next to the custom parameter names in the Parameters section three options are available:

1. Save in preferences () – available when a parameter is available in the project, but is not saved in the preferences (for example, the parameter was created in the project and the “Add to preferences” checkbox was not ticked, or the project was shared with a user that does not have the custom parameter in the preferences).
2. Edit () – allows to edit the name, alias, formula and unit of a parameter. If a parameter is saved in the preferences, users will be asked if they want to update the parameter only in the current project, or also in the preferences.
3. Delete () – removes the parameter from the project (but not from the preferences, if the parameter is saved in preferences).

Sparse data are data that have few observations per individual or per occasion, and that may not allow to estimate individual pharmacokinetic parameters reliably. Sparse data require specific handling in NCA analysis to get the most informative metrics from the data. PKanalix offers a dedicated mode to perform NCA analysis on sparse data, based on the calculation of mean profiles and standard errors of NCA parameters.

• Set up of sparse NCA
• Calculation of mean profiles
• NCA parameters specific to sparse data
• Sparse NCA results

Set up of sparse NCA

To specify a sparse dataset, you need to go to the NCA tab and select the “Sparse NCA” toggle below the NCA task. This will enable the calculation of mean profiles based on the individual data.

Sparse NCA is available for plasma and urine datasets.

Stratified sparse data

With the “Sparse data stratification” in NCA calculation settings, you can select one or more stratification covariates to group the data by different categories. For example, if you have a categorical covariate indicating the treatment group, you can select it to calculate a mean profile for each treatment group. The stratification covariates must be of type “categorical covariate” or “stratification categorical covariate” in the dataset tagging.

BLQ samples

If you have censored data, you can also click on the “BLQ method” button to select a censoring rule to handle the below limit of quantification (BLQ) samples.

The available rules are:

• Single rule: Replace all BLQ samples by [missing/zero/LOQ/(LOQ/2)]
  
• Two rules based on absolute number of BLQ samples:
  if Nblq >= [number]:
  • then:
    • either replace BLQ samples by [missing/zero/LOQ/(LOQ/2)]
    • or replace the mean sample by [missing/zero/LOQ/(LOQ/2)]
  • else replace BLQ samples by [missing/zero/LOQ/(LOQ/2)]
    
• Two rules based on fraction of total number of samples:
  if Nblq >= [number] % of Ntot
  • then:
    • either replace BLQ samples by [missing/zero/LOQ/(LOQ/2)]
    • or replace the mean sample by [missing/zero/LOQ/(LOQ/2)]
  • else replace BLQ samples by [missing/zero/LOQ/(LOQ/2)]
    

In addition, it is possible to check if the mean is below a LOQ value and add a special handling is it is the case:

• Check that mean samples stay above the LOQ:
  If the mean sample is below [number] (LOQ usually), replace the mean sample by [missing/zero/LOQ/(LOQ/2)] before Tmax and [missing/zero/LOQ/(LOQ/2)] after Tmax.
  

Calculation of mean profiles

When “Sparse NCA” is selected, one or several mean profiles are calculated:

• One mean profile per stratification group is calculated (one group for each combination of modalities from the covariates selected in “Sparse stratification”).
• The mean profile is calculated by taking the mean concentration value across all subject-occasions for each unique time value for plasma data, or the mean rate value for each unique midpoint for urine data.
• If a column of type NOMINAL TIME is selected, the mean profiles are calculated based on nominal time, otherwise they are calculated based on TIME.
• If the individuals used to calculate a mean profile have different dosing regimen (different dosing time or dosing amount), only the dosing regimen from the first individual is kept for the mean profile.
• For urine data, if the individuals used to calculate a mean profile have different volumes for some interval, only the volumes from the first individual are kept for the mean profile.
• Subject-occasions are handled independently for the calculation of mean profiles.

The mean profiles do not appear in the Observed data plot, but they appear in Check lambda_z and NCA individual fits

NCA parameters specific to sparse data

All usual NCA parameters are available in the list of parameters to compute, and in addition the following NCA parameters are available:

• For plasma data: SE_Cmax, SE_AUClast, SE_AUCall
• For urine data: SE_Max_Rate, SE_AURC_last, SE_AURC_all

See the page on NCA parameters for more details.

These parameters are not selected by default. SE_AUClast, SE_AUCall, SE_AURC_last, SE_AURC_all are available only if the integral method is “linear trapezoidal linear” or “linear trapezoidal linear/log” (because the formula is based on linear calculation of AUC).

Sparse NCA results

The results of the NCA analysis on sparse data are displayed in the Results and Plots tabs. The table below summarizes the availability of the results in sparse NCAmode.

Result	Based on
Tables of NCA parameters	mean profiles
Table of concentrations	individual data + mean profiles
NCA data plot	individual data + mean profiles
NCA individual fits	mean profiles
Other NCA plots	disabled

The parameters calculated on the mean profiles appear in the table of individual NCA parameters and the NCA summary table.

The table of concentrations displays both the individual concentration data, and the mean profiles on the “mean” rows. The table is stratified by the covariates selected for sparse data.

The NCA data plot is a new plot that shows the mean profiles and the individual data points on the same plot, with different colors for the different mean profiles.

The NCA individual fits plot shows the mean profiles and the NCA parameters calculated on them. The other NCA plots are disabled because they are not relevant for sparse data analysis.

The first step to run the compartmental analysis task in PKanalix is selecting a model. Models in PKanalix are .txt files and are loaded in the Model sub tab of the Task tab. You can:

• Load a custom model from your directory by clicking the BROWSE button.
• Load a model from PKanalix library by clicking the LOAD FROM LIBRARY button.
• Write a new model from scratch in the mlxtran language by clicking the NEW MODEL button.

Note: In PKanalix versions before 2023, only models from the PK library are available.

After loading a model, PKanalix switches automatically the MODEL sub-tab to the CHECK INIT. sub-tab for parameters initialization. To view the model file go back to the MODEL sub-tab. The left section shows the model file content. Clicking on the EDIT MODEL button allows to edit the model, save and apply it to the current project. For more details, see the custom model documentation page.The right hand side shows the mapping between the data set observations ids and the model outputs. For more details, see the mapping in Monolix documentation page. This feature is the same in PKanalix and Monolix.

Saving model information in the PKanalix project file

In PKanalix, a model file is a .txt file and its name is displayed on top of the MODEL sub-tab. If a model is from the PKanalix library, then the file name contains a prefix “lib:”. For custom models there is the full path to the file.

Remark on using custom models. Be careful when you change a location of a model file. If it was used in any PKanalix project, then you will not be able to re-open this project. You will see an error “Missing model file at ‘original_path_to_modelFile/model_filename.txt’.”. To avoid such situation, use a project settings (In the top menu “Settings”) and switch on the toggle “Save the dataset and the model beside the project”.

Next section: library of models

PKanalix provides libraries of ready-to-use models for compartmental analysis. This simplifies the use of the software by decreasing the necessity of coding. You can pick models from the libraries, use them directly or edit. They are accessible in the Model sub-tab of the CA task by clicking the button “LOAD FROM LIBRARY“.

Libraries are organized into several categories:

• PK model library includes standard compartmental models. It is possible to select different administration routes (bolus, infusion, first-order absorption, zero-order absorption, with or without Tlag), different number of compartments (1, 2 or 3 compartments), and different types of eliminations (linear or Michaelis-Menten). The PK library models can be used with single or multiple doses data, and with two different types of administration in the same data set (oral and bolus for instance).
• PD model library includes direct response models such as Emax and Imax with various baseline models, and turnover response models. These models are PD models only and the drug concentration over time must be defined in the data set and passed as a regressor.
• PK/PD model library provides all standard combinations of pharmacokinetic and pharmacodynamic models.
• PK double absorption model library includes double absorption models. They take into account all the combinations of absorption types and delays for two absorptions. The absorptions can be specified as simultaneous or sequential, and with a pre-defined or independent order.
• Parent-Metabolite model library includes models describing parent drug and one metabolite, with or without the first pass effect, uni and bidirectional transformation and up to three compartments for parent and metabolite.
• Target-mediated drug disposition (TMDD) model library – includes a large number of TMDD models corresponding to different approximations, different administration routes, different parametrizations, and different outputs.
• Tumor growth inhibition (TGI) library – includes a wide range of models for tumour growth (TG) and tumour growth inhibition (TGI) that are available in the literature. Models correspond to different hypotheses on the tumor or treatment dynamics.

In each library, available models are displayed as a list. With the top filtering panel you can easily selected a model based on its characteristics such as administration type, number of compartments or elimination mechanism.

To select a model click on its corresponding line – when all filters are used, only one model is shown. The model will be automatically loaded and displayed in the Model tab. Model filename is displayed on top of the “Model file” section, and has a prefix “lib” to distinguish it from custom models.

Next section: Custom model

 

The following page describes how compartmental analysis calculates individual parameters of a model selected in the MODEL tab. Three elements impact this calculation:

• Initialization of model parameters and their constrains on their values
• Cost function used in the optimization algorithm
• Estimation algorithm

 

The estimation of model parameters is the key function of the compartmental analysis task. In PKanalix it is performed in the framework of generalized least squares estimation. The optimization algorithm consists in minimizing a cost function with an improved version of the Nelder-Mead simplex algorithm, starting from multiple guesses in addition to the initial values provided. To run the algorithm click on the button COMPARTMENTAL ANALYSIS in the RUN tab.

The goal of the optimization is to find model parameters that give the best model fit to the observed data – minimize the objective (cost) function.

• The optimization algorithm performs well in general. However, even if it tries to explore the parameter space, the core algorithm (Nelder-Mead) is local. Therefore proper initialization of parameters is crucial.
• The cost function is described in this documentation page.
• In case of censored data, you can choose a method to treat BLQ data during the optimization:  missing, equal to zero, equal to LOQ or equal to LOQ/2.
• By default, the optimization is performed for each individual independently.  Switching on the toggle “Pooled fit” in the calculation settings will fit the same parameters to all individuals (data from all individuals is analysed together).
• If occasions are present and pooled fit is not selected, parameters are all considered occasion-dependent so the optimization for every individual includes \( N_{param} \times N_{occ}\) parameters (with \( N_{param} \) the number of parameters in the structural model and \(N_{occ}\) the number of occasions for this individual).

Cost function and likelihood

 

Cost function

The cost function that is minimized in the optimization performed during CA is described here. The cost is reported in the result tables after running CA, as individual cost in the table of individual parameters, and as total cost in a separate table, together with the likelihood and additional criteria.

Formulas for the cost function used in PKanalix are derived in the framework of generalized least squares described in the publication Banks, H. T., & Joyner, M. L. (2017). AIC under the framework of least squares estimation. Applied Mathematics Letters, 74, 33-45, with an additional scaling to put the same weight on different observation types.

The total cost function, shown in the COST table in the results, is a sum of individual cost per each occasion (sum over id-occ):

where in the above formula:

• \( N_{obs}(id\#occ, obsType) \) denotes the number of observations for one individual, one occasion and one observation type (ie one model output mapped to data, eg parent and metabolite, or PK and PD, see here).
• \( res_j = Y_{pred}(t_j) – Y_{obs}(t_j) \) are residuals at measurement times \( t_j \), where \(Y_{pred}\) are the predictions for every time point  \(t_j\) , and \(Y_{obs}\) the observations read from the dataset.
• \( w_j \) are weights \(1, Y_{obs}, Y_{pred}, \sqrt{|Y_{obs}|}, \sqrt{|Y_{pred}|}, \sqrt{|Y_{obs}|\cdot |Y_{pred}|} \) depending on the choice in the CA task > Settings > Calculations, as explained in this tutorial video.

\( X_{scaling} \) is a scaling parameter given by:

with \( n_{obsTypes}(id\#occ) \) number of observation IDs mapped to a model output for one individual and one occasion. Note that if there is only one observation type (model output mapped to an observation ID), \( X_{scaling} =1\) and the cost function is a simple sum of squares over all observations, weighted by the \(w_j\) .

 

Likelihood

 

The likelihood is not directly used for the optimization in CA, but it is possible to derive it based on the optimal cost obtained with the following formula (details in Banks et al):

where

• -2LL stands for -2 x ln(Likelihood)
• \( N_{tot} \) is the total number of observations for all individuals, all occasions and all mapped model outputs
• \(w_j\) are the weights as defined above

 

 

Additional Criteria

 

Additional information criteria are the Akaike Information Criteria (AIC) and the Bayesian Information Criteria (BIC). They are used to compare models. They penalize -2LL by the number of model parameters used for the optimization \( N_{param} \), and the number of observations: \( N_{tot} \), total number of observations, and \(N_{obs}(id\#occ)\), number of observations for every subject-occasion. This penalization enables to compare models with different levels of complexity. Indeed, with more parameters, a model can easily give a better fit (lower -2LL), but with too many parameters, a model loses predictive power and confidence in the parameter estimates. If not only the -2LL, but also AIC and BIC criteria decrease after changing a model, it means that the increased likelihood is worth increasing the model complexity.

This formula simplifies if the “pooled fit” option is selected in the calculation settings of the CA task:

 

AIC derivation in the case of individual fits

The total AIC for all individuals penalizes -2LL with 2x the number of parameters used in the optimization. For the structural model, we use \(N_{param} N_{id\#occ}\), where \(N_{param}\) is the number of parameters in the structural model and \(N_{id\#occ}\) is the number of subject-occasions (since there is a set of parameters of each id#occ). For the statistical model, we also calculate implicitly one parameter \(\sigma^2\), which is the variance of the residual error model shared by all the individuals (it is derived using the sum of squares of residuals as described in Banks et al). Therefore, AIC penalizes -2LL by \(2(N_{param} N_{idocc} + 1)\).

 

BIC derivation in the case of individual fits

The total BIC should penalize -2LL by (nb of parameters) x ln(nb of data points). In this case, we should distinguish between the data for each id#occ, which is used to optimize N_param parameters, and the data for all individuals, which is used all together to calculate the residual variance σ². To penalize each individual’s data in the optimization with N_param, we add the term \(N_{param} \times ln(N_{obs}(id\#occ))\) for each id#occ. To penalize the calculation of the error model parameter with all the observations (substitution of \(\sigma\) as described in Banks et al), we add the term \(1\times ln(N_{tot})\).

 

• Export to Monolix
• Export to Simulx
• Sharing a PKanalix project

Export a PKanalix to Monolix/Simulx

MonolixSuite applications are interconnected and you can export & import a PKanalix project between different applications. This interconnection is guaranteed by using the same model syntax (mlxtran language) and the same dataset format. There are two options to export a PKanalix project*

• Export to Monolix for population model development, estimation and diagnosis. See Monolix documentation.
• Export to Simulx for simulations of new scenarios, e.g. new dosing regimens. It requires loading a model in CA. See Simulx documentation.

*Note: Export of a PKanalix project to Simulx is available starting from the 2023 version. In the previous versions, you can only export a PKanalix project only to Monolix. To export a PKanalix project to Monolix or Simulx click EXPORT PROJECT TO in the top menu “Export”, select the target software (Monolix or Simulx), and confirm the process by clicking on the button EXPORT at the bottom. By default, generated files, e.g. dataset and model file, will be saved next to the target project.

Share a PKanalix project

The 2024 version of MonolixSuite introduces a highly convenient method for sharing projects. Simply click on “Share Project” in the export menu, and a zip folder is generated containing all the required files to re-open the project (dataset, model for CA if not from library, pkx file, result folder). By default, the suggested location for the zipped shared project matches that of the original, but this can be easily modified to any other location on the computer.

After having run the “NCA” task to calculate the NCA PK parameters, the “Bioequivalence” task can be launched to compare the calculated PK parameters between two groups, usually one receiving the “test” formulation and one the “reference” formulation.

• Bioequivalence task
• Bioequivalence results
• Bioequivalence plots
• Bioequivalence outputs

Bioequivalence task

The task “Bioequivalence” is available if at least one categorical covariate column has been tagged in the “Data” tab. The “Bioequivalence” task can only be run after having run the “NCA” task. It can be run by clicking on the “Bioequivalence” task button (pink highlight below) or by selecting it as part of the scenario (tickbox in the upper right corner of the “Bioequivalence” button) and clicking the “Run” button. The parameters to be included in the bioequivalence analysis are selected in the box “Parameters to compute / BE” (orange highlight), where the user can also indicate if the parameter should be log-transformed or not. The fixed effect included in the linear model can be chosen in the box “Bioequivalence design” (blue highlight).

Bioequivalence results

The results of the bioequivalence analysis are presented in the “Results” tab, in the “BE” subtab. Three tables are proposed.

Confidence intervals

The table of confidence intervals is the key bioequivalence table that allows to conclude if the two formulations are equivalent or not. For each parameter selected for bioequivalence analysis, the following information is given:

• the adjusted means (i.e least square means) for each formulation,
• the number of individuals for each formulation,
• the formulation difference (see calculation rules) and the corresponding confidence interval,
• the formulation ratio (see calculation rules) and the corresponding confidence interval.

If N formulations are present in the dataset, N-1 tables are shown.

Coefficient of variation

This table gives for each parameter selected for bioequivalence analysis the standard deviation of the residuals and the intra-subject coefficient of variation (CV).

ANOVA

This table presents the analysis of variance (ANOVA) for the factors included in the linear model, for each parameter selected for the bioequivalence analysis. For each factor, the degrees of freedom (DF), sum of squares (SUMSQ), mean squares (MEANSQ), F-value (FVALUE) and the p-value (PR(>F)) are given. A small p-value indicates a significant effect of the corresponding factor.
For the residuals, only the degrees of freedom (DF), sum of squares (SUMSQ), and mean squares (MEANSQ) are given.

In the “Plots” tab, several plots are displayed:

• Sequence by period: This plot allows to visualize, for each parameter, the mean and standard deviation for each period, sequence and formulation.
• Subject by formulation: This plot allows to visualize, for each parameter, the subject-by-formulation interaction and the inter-subject variability.
• Confidence intervals: This plot gives a visual representation of the confidence intervals of the ratio of each parameter.
• NCA individual fits: This plot can also be used to display the individual concentration data with one subplot per individual with all its periods.

 

Bioequivalence outputs

After running the Bioequivalence task, the following files are available in the result folder <result folder>/PKanalix/IndividualParameters/be:

• anova_XXX.txt: these is one such file for each NCA parameter included in the bioequivalence analysis. It contains the ANOVA table with columns ‘Factor’ (factors included in the linear model), ‘Df’ (degrees of freedom), ‘SumSq’ (sum of squares), ‘MeanSq’ (mean squares), ‘FValue’ (F-value), ‘Pr(>F)’ (p-value). For the residuals (last line), the two last columns are empty.
• confidenceInterval_XXX.txt: these is one such file per non-reference formulation. It contains the confidence interval table with columns ‘Parameter’ (parameter name), ‘AdjustedMeanTest’ (adjusted mean for the test formulation), ‘NTest’ (number of individuals for the test formulation), ‘AdjustedMeanRef’ (adjusted mean for the reference formulation), ‘NRef’ (number of individuals for the ref formulation), ‘Difference’ (formulation difference – see calculation rules), ‘CIRawLower’ (lower confidence interval bound for the difference), ‘CIRawUpper’ (upper confidence interval bound for the difference), ‘Ratio’ (formulation ratio – see calculation rules), ‘CILower’ (lower confidence interval bound for the ratio), ‘CIUpper’ (upper confidence interval bound for the ratio), ‘Bioequivalence’ (1 if the CI for the ratio falls within the BE limits, 0 otherwise)
• estimatedCoefficients_XXX.txt: these is one such file for each NCA parameter included in the bioequivalence analysis. It contains the estimated coefficient for each category of each factor included in the linear model, as well as the intercept. This information is only available as an output table and is not displayed in the GUI. The table columns are ‘name’ (factor followed by the category), ‘estimate’ (estimated coefficient), ‘se’ (standard error), ‘tValue’ (estimate divided by the SE), and ‘Pr(>|t|)’ (p-value).
• variationCoef.txt: This file contains the standard deviation and coefficient of variation from each NCA parameter. Columns are ‘Parameter’, ‘SD’ and ‘CV(%)’

Detection of “crossover” versus “parallel” design

In PKanalix, the design is detected based on the data set columns. If no OCCASION column is present, the design is detected as “parallel”. On the opposite, if one or several columns have been tagged as OCCASION, the design is detected as “crossover” (repeated or non-repeated). The detected design is displayed in the bioequivalence settings for the users information and cannot be changed. Depending on the detected design, the factors selected by default for the linear model are different.

Linear model

The linear model can only include fixed effects, as recommended by the FDA for parallel and non-repeated crossover design (see Statistical Approaches to Establishing Bioequivalence, page 10) and by the EMA for parallel, non-repeated crossover and repeated crossover designs (see Guideline On The Investigation Of Bioequivalence, page 15). In addition, “id” is automatically considered as nested in “sequence” and no additional nesting can be defined. Interaction terms and random effects are not supported.

According to the regulatory guidelines, the default models are:

• parallel design:
  \(\log(\textrm{NCAparam}) \sim \textrm{FORM}\)
  which can also be written as
  \(\log(\textrm{NCAparam})=\textrm{intercept} + \beta_{test} \textrm{[ if FORM=test]} + \varepsilon\)
  in case of two formulations “ref” and “test”, with \(\varepsilon\) a normal random variable (i.e the residuals).
• crossover design:
  \(\log(\textrm{NCAparam}) \sim \textrm{SEQ + ID + PERIOD + FORM}\)
  which can also be written as
  \(\log(\textrm{NCAparam})=\textrm{intercept} + \beta_{test} \textrm{[ if FORM=test]} + \beta_{period2} \textrm{[ if PERIOD=2]} + \beta_{seqTR} \textrm{[ if SEQ=TR]} + \beta_{id2} \textrm{[ if ID=id2]} + \beta_{id3} \textrm{[ if ID=id3]} + … + \varepsilon\)
  in case of several individuals (id1, id2, etc), two sequences (“RT” and “TR”), two periods (“1” and “2”) and two formulations (“ref” and “test”).

The model parameters are calculated using a QR factorization.

The \(\beta\) parameters are called the coefficients. They are saved in the output file estimatedCoefficients_XXX.txt. We are interested in the coefficient representing the formulation effect \(\beta_{test}\), which is also called the point estimate.

Difference and ratio

In the Results > Confidence intervals table, the “difference” corresponds to the point estimate \(\beta_{test}\) (see above). The “ratio” is calculated depending on the log-transformation choice:

• without log-transformation: \(\textrm{Ratio}=\textrm{LSM}_{test}/\textrm{LSM}_{ref}\times 100\)  with \(LSM\) the least square mean (also called adjusted mean, see below).
• with log-transformation: \(\textrm{Ratio}=\exp (\beta_{test}) \times 100\)

Confidence intervals

The confidence interval is first calculated for the difference (\(CI_{diff}\)) and then for the ratio (\(CI_{ratio}\)).

\(CI_{diff}=\beta_{test} \pm t(1-\alpha,df) \times SE \)

with \(\beta_{test}\) the point estimate (“difference”, see above), \(t(1-\alpha,df)\) the quantiles of a Student t-distribution at the \(\alpha\) level and \(df\) degrees of freedom, and \(SE\) the standard error of the point estimate.

In case of a parallel design with the Welch-Satterthwaite correction (see Bioequivalence settings), the formula is different:

\(CI_{diff}=\beta_{test} \pm t(1-\alpha,df) \times \sqrt{\frac{S_R^2}{n_R}+\frac{S_T^2}{n_T}} \)

with \(S_X\) the samples standard deviation of the individuals and \(n_X\) the number of individuals having received formulation X. A correction is also applied to the degrees of freedom, which are calculated as:

\(df=\frac{\left(\frac{S_T^2}{n_T}+\frac{S_R^2}{n_R}\right)^2}{\frac{(S_T^2/n_T)^2}{n_T – 1}+\frac{(S_R^2/n_R)^2}{n_R – 1}}\)

The confidence interval for the ratio is then calculated using the following formula:

• without log-transformation: \(CI_{ratio}=(1+CI_{diff}/\textrm{LSM}_{ref})\times100\) with \(\textrm{LSM}_{ref}\) the least square mean for the reference formulation (see below).
• with log-transformation: \(CI_{ratio}=\exp(CI_{diff})\times 100\)

Adjusted means (least square means)

The model NCAparam ~ SEQ + ID + PERIOD + FORM allows to calculate the expected value (mathematical expectation) for any value of SEQ, ID, PERIOD and FORM. The least square mean for the reference represents the expected value for the reference formulation leaving the value for the other factors undefined. To calculate it, we average the model-predicted values across the levels of ID, PERIOD and SEQ.

The weights assigned to each combination of levels depend if the factors are nested or not. A factor A is said nested in factor B if each level of A appears in only one level of B. By design, in crossover bioequivalence studies, ID is nested in SEQUENCE (i.e each individual belongs to only one sequence). Thus, in PKanalix, when ID and SEQUENCE are defined as factors in the linear model, we assume that ID is nested in SEQUENCE when calculating the least square means. No further nesting is assumed, nor can be specified. Note that the nesting definition only affects the adjusted means and not the point estimate (ratio) and its confidence interval.

Excluded individuals

In case of a parallel design, individuals for which the NCA parameter cannot be calculated are excluded.

In case of a crossover design, incomplete individuals are excluded. Incomplete individual are those that do not have a value for each period, either because these were no concentration data for this period (period missing in the data set) or because the computed NCA parameter could not be calculated for this period (e.g because the data were insufficient to calculate the terminal slope). In case of a non-repeated crossover design, excluding the individuals with missing data or not has no impact on the calculation of the point estimate and confidence interval. In case of a repeated crossover design (i.e when the individuals receive several times the same formulation), excluding the individuals for which the NCA parameter for one or more periods is missing has an impact on the point estimate calculation and confidence interval. The common practice is to exclude incomplete individuals (see also the EMA Guideline On The Investigation Of Bioequivalence, page 14).

Excluded individuals are calculated for each NCA parameter separately, as some individuals may have values for all periods for the Cmax but not the AUCINF_obs for instance.

In the Results > Confidence intervals, the number of individuals “N” does not count the excluded individuals. Thus, in case of a crossover design, the number of individuals contributing to ref and to test is the same. In the BE plots, only the individuals included in the bioequivalence analysis are shown.

ANOVA

The sum of squares presented in the ANOVA table of the Results tab are type-I sequential sum of squares. In case of an unbalanced design (i.e not the same number of individuals receiving RT versus TR), the type-I sum of squares depends on the order of the included factors. In PKanalix, the enforced order is SEQUENCE + ID + PERIOD + FORMULATION (+ ADDITIONAL), following the SAS sample codes provided by the FDA (see Statistical Approaches to Establishing Bioequivalence, 2001, Appendix E) and EMA (see Questions & Answers: positions on specific questions addressed to the Pharmacokinetics Working Party, 2015, question 8).

Coefficient of variation

In Results > Coefficients of variation, the SD corresponds to the standard deviation of the residuals, i.e to the standard deviation of the normal random variable \(\varepsilon\) in the linear model \(\log(\textrm{NCAparam})=\textrm{intercept} + \beta_{test} \textrm{[ if FORM=test]} + \varepsilon\) (for the typical model of a parallel design for instance).

The coefficient of variation is then calculated as:

• without log-transformation: \(CV = SD / LSM_{ref}\)  (with \(LSM_{ref}\) the least square mean for the reference formulation, see above)
• with log-transformation: \(CV = 100 \times \sqrt{\exp{(SD^2)}-1}\)

 

This page describes the settings of the bioequivalence calculations.

Parameters to compute

In the section “Parameters to compute”, the user can move the parameters from the “Parameters” column (list of all available parameters) to the “Computed parameters” column to select them for the NCA calculations. Among the parameters selected for the NCA calculations, the user can choose which parameters should be included in the bioequivalence analysis by ticking the box in the “BE” column. Regulatory guidelines usually recommend to perform the bioequivalence on the log-transformed NCA parameters. This can be set using the toggles in the “log-transform” column.

• BE: parameters on which to perform the bioequivalence analysis. Defaults: Cmax, AUClast, and AUCINF_obs if plasma single-dose, or AUCtau and Cmax if plasma steady-state, or AURC_last and Max_Rate if urine data.
• log-transform: whether the bioequivalence should be computed on the log-transformed NCA parameter (toggle on) or on the NCA parameter directly (toggle off). Default: log-transform toggle on, except for Tmax.

Bioequivalence design

The study design, parallel or crossover (repeated or not), is detected automatically based on the structure of the ID and OCCASION columns of the data set, see the Calculation rules for more details. The user can then select one or several fixed effect factors to be included in the linear model. By default, for a parallel design, only the formulation is included. For a crossover design, the factors ID, PERIOD, FORMULATION and SEQUENCE are included by default, if present in the data set. When both ID and SEQUENCE are given, ID is considered as nested in SEQUENCE. Additional factors can also be added, to be chosen among the (STRATIFICATION) CATEGORICAL and CONTINUOUS COVARIATES columns of the data set. All factors are considered as fixed effects and random effects are not available. Nesting of ID in SEQUENCE is considered automatically, but further nesting cannot be specified. Note that the nesting affects the calculation of the adjusted means but not of the bioequivalence ratio.

• Study design: parallel or crossover (repeated or not-repeated). Detected automatically based on the structure of the ID and OCCASION columns of the data set (see Calculation rules). Cannot be changed by the user.
• Factors in the linear model:
  • id [if crossover]: data set column representing the ID of the individuals. Default: the column tagged as ID in the data set. This can be set to “none” if the ID should not be used as a factor in the linear model. When a “sequence” column is defined, “id” is considered as nested in “sequence”.
  • period [if crossover]: data set column representing the different periods for each individual. Default: the first column tagged as OCCASION in the data set. This setting can be set to “none” if the period should not be used as a factor in the linear model.
  • formulation: data set column representing the different groups for which the bioequivalence is calculated, typically the different formulations of the drug products. Default: the column with header ‘trt’, ‘treatment’, ‘form’, or ‘formulation’ (case insensitive) if it exists, otherwise first CATEGORICAL COVARIATE column. It is mandatory to include the formulation in the linear model.
    • reference: among the categories of the categorical covariate selected as formulation, the one considered as the reference. The bioequivalence will be computed for all categories compared to the reference category. Default: ‘r’ or ‘ref’ or ‘reference’ (case insensitive), otherwise the category of the first occasion of the first indiv of the data set.
  • sequence [if crossover]: data set column representing the different sequences. Default: the column with header ‘seq’, or ‘sequence’ (case insensitive) if it exist, otherwise “none”. This setting can be set to “none” if the sequence should not be used as a factor in the linear model.
  • additional: data set columns tagged as CATEGORICAL or CONTINUOUS covariates, which have not already been selected above, can be added as additional factors in the linear model.

Confidence interval

Several settings are more specific to the calculation of the confidence interval. They can be changed in the pop-up settings window of the Bioequivalence task.

• Level: level of the confidence interval. Default: 90% confidence interval. This means that there is a 90% probability that the true ratio is included in the calculated confidence interval.
• Bioequivalence limits: limits within which the confidence interval should be in order to conclude for bioequivalence. Default: [80,125].
• Degrees of freedom [if parallel design]: method to calculate the degrees of freedom involved in the confidence interval calculations, either using the residuals (this assumes equal variance between the groups or using the Welch-Satterthwaite formula (this assumes possibly unequal variances). Default: Welch-Satterthwaite

For the CA task, PKanalix generates automatically specific plots to help in model diagnosis. Plots are interactive for better data exploration. You can modify display options (lin/log scales, axis limits, etc), stratify (split, color, filter) them using covariates from a dataset, and change the graphical preferences (font size, colors etc).

In the PLOTS tab you will find the following plots:

• Individual fits This plot displays the individual predictions using the individual estimated parameters (or one set of common parameters if you enable the “pooled fit” option)  w.r.t. time on a continuous grid, with the observed data overlaid.
• Individual parameters vs covariates This plot displays estimated individual parameters w.r.t. the covariates in the dataset.
• Distribution of the individual parameters. This plot displays the estimated population distributions of the individual parameters.
• Correlation between individual parameters This plot displays scatter plots for each pair of individual parameters.
• Observations vs predictions This plot displays observations w.r.t. the predictions computed using the individual parameters (or one set of common parameters if you enable the “pooled fit” option).

Stratification & Preferences

Stratification of plots in PKanalix works in the same way as in Monolix. Complete description of available options and examples is in the Monolix documentation here.

Save/Export plots and charts data

You can export each single plot as an image (png or svg) using an icon on top of each plot. They are saved in the results folder > PKanalix > ChartsFigures.

To export all plots at once use the top menu option: “Export > Export Plots”. You can also export plots data as tables (in .txt files), for example to re-generate them with external tools, with “Export > Export charts data”.

In addition, you can export plots automatically after each CA run. To select this option enable the toggle buttons in the PKanalix Preferences: top menu > Settings > Preferences:

Next section: CA Individual fits plot

 

Purpose

This plot can be used for two purposes:

• show the terminal slope (lambdaZ) linear regression for each occasion of each individual (default)
• show the individual concentration data with one individual per subplot and all occasions

LambdaZ terminal slope

By default, the settings let you see each occasion of each individual on a subplot, in y log-scale with the lambdaZ linear regression. Note that the NCA parameters Lambda_z and Lambda_z_intercept need to be selected in the “Computed parameters” of NCA settings in order to display the lambdaZ regression line.

Selecting the “Information” toggle allows you to display information about the rule used to calculated the lambdaZ (“Adjusted R2”, “R2”, “Interval”, “Points” or “custom” – when points have been manually selected), the number of points included in the calculation and the R2 or adjusted R2 criteria. Again, the NCA parameters Rsq_adjusted, Rsq, and No_points_lambda_z must be selected in “Computed parameters” in the NCA settings in order to appear in the information box.

Individual concentration data

The plot can also be used to visualize the individual concentration data with one individual per subplot and occasions all together. For a crossover study with two periods and two formulations for instance, one can:

• display the “Lines”
• display the “unused data” as “colored”
• hide the “LambdaZ regression”
• untick the “split occasions”
• set the y axis in linear scale
• color by the Formulation in the stratify tab

Settings

• Grid arrange (top left above the plot): The user can define the number of subplots displayed, as well as the number of rows and the number of columns. This choice is not saved. See below the “Default number of individuals per page” for a setting that is saved.
• General
  • Legend: hide/show the legend. The legends adapts automatically to the elements displayed on the plot. The same legend box applies to all subplots and it is possible to drag and drop the legend at the desired place.
  • Grid : hide/show the grid in the background of the plots.
  • Information: hide/show
    • the continuous covariates: continuous covariates values are displayed for each individual
    • the goodness of fit: the rule used to calculate the lambdaZ (“Adjusted R2”, “R2”, “Interval”, “Points” or “custom” – when points have been manually selected), the number of points used to calculate the lambdaZ and the R2 value (if rule=R2) or the adjusted R2 (if rule different from R2). Note that the NCA parameters Rsq_adjusted, Rsq, and No_points_lambda_z must be selected as “Computed parameters” in the NCA settings in order to appear in the information box.
  • Units: hide/show the units next to the NCA parameter names. The color and surrounding characters for the units can be chosen in the plot “Preferences”.
  • Dosing times: hide/show dosing times as vertical lines for each subject.
  • Link zoom between plots: activate the linked zoom for all subplots. The same zooming region can be applied on all individuals only on the x-axis, only on the Y-axis or on both (option “none” in the “zoom constraint”).
• Display
  • Dots: hide/show the observed data as dots
  • Lines: hide/show the connecting lines between the observed data points
  • Censored data [if censored data present]: hide/show the data marked as censored (BLQ), shown as a red dot according to the “BLQ method before/after Tmax” choice in the NCA settings.
  • Unused data: hide/show the data points not used for the lambdaZ calculation
    • greyed: display the data points not used in the lambdaZ calculation as greyed
    • colored: display the data points not used in the lambdaZ calculation with the default color (set in the plot “Preferences”)
  • Split occasions [if occasions present]: Split the individual subplots by occasions or group occasions on a single subplot for each individual.
  • Default number of individuals per page: Set the number of subplots to display. This setting can be saved, whereas the “grid arrange” on the top left corner is not.
  • LambdaZ regression: hide/show the lambdaZ linear regression
• Sorting: Sort the subjects by ID, goodness of fit (R2 or adjusted R2 value) or continuous covariate value in ascending or descending order.

Purpose

This figure can be used to see the empirical distribution of the NCA parameters. Further analysis such as stratification by covariate  can be performed and will be detailed below.

PDF and CDF

It is possible to display the theoretical distribution and the histogram of the empirical distribution as proposed below.

The distributions are represented as histograms for the probability density function (PDF). Hovering on the histogram also reveals the density value of each bin as shown on the figure below

Cumulative distribution functions (CDF) is proposed too.

Example of stratification

It is possible to stratify the population by some covariate values and obtain the distributions of the individual parameters in each group. This can be useful to check covariate effect, in particular when the distribution of a parameter exhibits two or more peaks for the whole population. On the following example, the distribution of the parameter k from the same example as above has been split for two groups of individuals according to the value of the sex, allowing to visualize two clearly different distributions.

Settings

• General: add/remove the legend, and the grid
• Display
  • Distribution function: The user can choose to display either the probability density function (PDF) as histogram or the cumulative distribution function (CDF).

Purpose

The figure displays the individual parameters as a function of the covariates. It allows to identify correlation effects between the individual parameters and the covariates.

Identifying correlation effects

In the example below, we can see the parameters Cl_obs and Cmax with respect to the covariates: the weight WT, the age AGE and the sex category.

Visual guidelines

In order to help identifying correlations, regression lines, spline interpolations and correlation coefficients can be overlaid on the plots for continuous covariates. Here we can see a strong correlation between the parameter Cl_obs and the age and the weight.

Overlay of values on top of the boxplot

The NCA parameter values used to generate the boxplots for the categorical covariates can be overlayed on top of the boxplots, which enables to better visualize the distribution in case of a small number of individuals.

Highlight

Hovering on a point reveals the corresponding individual and, if multiple individual parameters have been simulated from the conditional distribution for each individual, highlights all the points points from the same individual. This is useful to identify possible outliers and subsequently check their behavior in the observed data.

Selection

It is possible to select a subset of covariates or parameters, as shown below. In the selection panel, tick the items you would like to see and click “Accept”. This is useful when there are many parameters or covariates. 

Stratification

Stratification can be applied by creating groups of covariate values. As can be seen below, these groups can then be split, colored or filtered, allowing to check the effect of the covariate on the correlation between two parameters. The correlation coefficient is updated according to the split or filtering.

 Settings

• General
  • Legend: add/remove the legend. There is only one legend for all plots.
  • Grid: add/remove the grid.
  • Information: display/hide the correlation coefficient associated with each scatter plot.
  • Units: display/hide the units of the NCA parameters on the y axis
• Display
  • Individual parameters: Selects the NCA parameters to display as subplot on rows. Tick  the items you would like to see and click “accept”.
  • Covariates: Selects the NCA parameters to display as subplot on columns. Tick  the items you would like to see and click “accept”.
  • Boxplots data: overlay the NCA parameters as dots on top of the boxplots for categorical covariates, either aligned on a vertical line (“aligned”), spread over the boxplot width (“spread”) or not at all (“none”).
  • Regression line: Add/remove the linear regression line corresponding to the correlation coefficient.
  • Spline: Add/remove the spline. Spline settings cannot be changed.

Purpose

This plot displays scatter plots for each pair of parameters. It allows to identify correlations between parameters, which can be used to see the results of your analysis and see the coherence of the parameters for each individuals.

Example

In the following example, one can see pairs of parameters estimated for all parameters.

Visual guidelines

In addition to regression lines, correlation coefficients can been added to see the correlation between random effects, as well as spline interpolations.

Selection

It is possible to select a subset of parameters, whose pairs of correlations are then displayed, as shown below. In the selection panel, a set of contiguous rows can be selected with a single extended click, or a set of non-contiguous rows can be selected with several clicks while holding the Ctrl key.

Highlight

Similarly to other plots, hovering on a point provides information on the corresponding subject id, and highlights other points corresponding to the same individual.

Stratification: coloring and filtering

Stratification can be applied by creating groups of covariate values. As can be seen below, these groups can then be split, colored and/or filtered allowing to check the effect of the covariate on the correlation between two parameters. The correlation coefficient is updated according to the stratifying action. In the following case, We split by the covariate SEX and color bay 2 categories of AGE.

Settings

• General
  • Legend and grid : add/remove the legend or the grid. There is only one legend for all plots.
  • Information: display/hide the correlation coefficient associated with each scatter plot.
• Display
  • Selection. The user can select some of the parameters to display only the corresponding scatter plots. A simple click selects one parameter, whereas multiple clicks while holding the Ctrl key selects a set of parameters.
  • Visual cues. Add/remove the regression line or the spline interpolation.

Purpose

This plot, available with version 2024, enables the interpreted data for NCA to be displayed in the same way as the observed data. The interpreted data in the plot takes into account exclusions, filters and censoring rules.

While executing the NCA task, the NCA plot is automatically generated alongside the standard set of plots.

Compared to the Observed data plot, the following data processing rules have been applied:

• additional points at dose time (if not present in original dataset)
• points before the last dose of each profile (i.e occasion or subject) are removed
• BLQ data is replaced according to the chosen NCA settings (BLQ after Tmax and BLQ before Tmax)

Besides these two mentioned differences from the observed data plot, the NCA data plot offers the same plot settings and stratification properties. Note the option to display the x-axis as nominal time.

Sparse data

The NCA plot for sparse data differs in certain points from the one for dense data.

• Stratification

Due to the enforced stratification in the calculation settings, the data also appears according to this stratification in the plots tab. No further stratification settings are possible in the plots tab that deviate from the stratification specified in the calculations panel in the NCA tasks tab.

 

• Trend line

The data is summarized using the arithmetic mean, which is represented by a trend line in the plot. Unlike for dense data in the NCA plot or in the observed data plot, there is no option to select an alternative mean value formula. However, it is possible to display or hide these metrics, arithmetic mean and standard deviation, in the plot using their associated toggles.

• Censored data

The rules defined in the NCA task tab for handling censored data are also considered in the calculation and therefore also in the display of the mean curve and the associated error bars in the in plot.

 

• Nominal time

If nominal time is present in the dataset, it serves as the time variable in calculations and is consequently enforced as the x-axis in the plot, with no option of changing it.

Purpose

The figure displays the observed data for each subject, as well as prediction using the individual parameters.

Individual parameters

Information on individual parameters can be used in two ways, as shown below. By clicking on Information (marked in green on the figure) in the General panel, individual parameter values can be displayed on each individual plot. Moreover, the plots can be sorted according to the values for a given parameter, in ascending or descending order (Sorting panel marked in blue). By default, the individual plots are sorted by subject id, with the same order as in the data set.

Special zoom

User-defined constraints for the zoom are available. They allow to zoom in according to one axis only instead of both axes. Moreover, a link between plots can be set in order to perform a linked zoom on all individual plots at once. This is shown on the figure below with observations from the remifentanil example, and individual fits from a two-compartment model. It is thus possible to focus on the same time range or observation values for all individuals. In this example it is used to zoom on time on the elimination phase for all individuals, while keeping the Y axis in log scale unchanged for each plot.

• Censored data

When a data is censored, this data is different to a “classical” observation and has thus a different representation. We represent it as a bar from the censored value specified in the data set and the associated limit.

Settings

• Grid arrange. The user can define the number of subjects that are displayed, as well as the number of rows and the number of columns. Moreover, a slider is present to be able to change the subjects under consideration.
• General
  • Legend: hide/show the legend. The legends adapts automatically to the elements displayed on the plot. The same legend box applies to all subplots and it is possible to drag and drop the legend at the desired place.
  • Grid : hide/show the grid in the background of the plots.
  • Information: hide/show the individual parameter values for each subject (conditional mode or conditional mean depending on the “Individual estimates” choice is the setting section “Display”).
  • Dosing times: hide/show dosing times as vertical lines for each subject.
  • Link between plots: activate the linked zoom for all subplots. The same zooming region can be applied on all individuals only on the x-axis, only on the Y-axis or on both (option “none”).
• Display
  • Observed data: hide/show the observed data.
  • Censored intervals [if censored data present]: hide/show the data marked as censored (BLQ), shown as a rectangle representing the censoring interval (for instance [0, LOQ]).
  • Split occasions [if IOV present]: Split the individual subplots by occasions in case of IOV.
  • Number of points of the calculation for the prediction
• Sorting: Sort the subjects by ID or individual parameter values in ascending or descending order.

By default, only the observed data and the individual fits are displayed.

Purpose

This figure can be used to see the empirical distribution of the CA parameters. Further analysis such as stratification by covariate can be performed and will be detailed below.

PDF and CDF

It is possible to display the theoretical distribution and the histogram of the empirical distribution as proposed below.

The distributions are represented as histograms for the probability density function (PDF). Hovering on the histogram also reveals the density value of each bin as shown on the figure below

Cumulative distribution functions (CDF) is proposed too.

Example of stratification

It is possible to stratify the population by some covariate values and obtain the distributions of the individual parameters in each group. This can be useful to check covariate effect, in particular when the distribution of a parameter exhibits two or more peaks for the whole population. On the following example, the distribution of the parameter k from the same example as above has been split for two groups of individuals according to the value of the SEX, allowing to visualize two clearly different distributions.

Settings

• General: add/remove the legend, and the grid
• Display
  • Distribution function: The user can choose to display either the probability density function (PDF) as histogram or the cumulative distribution function (CDF).

Purpose

The figure displays the individual parameters as a function of the covariates. It allows to identify correlation effects between the individual parameters and the covariates.

Identifying correlation effects

In the example below, we can see the parameters Cl and V1 with respect to the covariates: the weight WT, the age AGE and the sex category.

Visual guidelines

In order to help identifying correlations, regression lines, spline interpolations and correlation coefficients can be overlaid on the plots for continuous covariates. Here we can see a strong correlation between the parameter Cl and the age and the weight. This is the same with V1.

Highlight

Hovering on a point reveals the corresponding individual and, if multiple individual parameters have been simulated from the conditional distribution for each individual, highlights all the points points from the same individual. This is useful to identify possible outliers and subsequently check their behavior in the observed data.

Selection

It is possible to select a subset of covariates or parameters, as shown below. In the selection panel, a set of contiguous rows can be selected with a single extended click, or a set of non-contiguous rows can be selected with several clicks while holding the Ctrl key. This is useful when there are many parameters or covariates.

Stratification

Stratification can be applied by creating groups of covariate values. As can be seen below, these groups can then be split, colored or filtered, allowing to check the effect of the covariate on the correlation between two parameters. The correlation coefficient is updated according to the split or filtering.

Settings

• General
  • Legend and grid : add/remove the legend or the grid. There is only one legend for all plots.
  • Information: display/hide the correlation coefficient associated with each scatter plot.
• Display
  • Selection. The user can select some of the parameters or covariates to display only the corresponding plots. A simple click selects one parameter (or covariate), whereas multiple clicks while holding the Ctrl key selects a set of parameters.
  • Visual cues. Add/remove a regression line or a spline interpolation.

The observations vs predictions plot displays observations (\(y_{ij}\)) versus the corresponding predictions (\(\hat{y}_{ij}\)) estimated by the CA task. It is a useful tool to detect misspecifications in the structural model. The points shall scatter as close as possible along the y = x line (black solid line). If a large amount of points are not scattered close to the identity line, then this might be due to the chosen structural model not capturing certain kinetics. Moreover, the distribution of the dots should be symmetrical around the y=x line, meaning that the model prediction is sometimes abve and sometimes below the observed data.

This plot is generated automatically when you run the compartmental analysis task. You can access it from the CA section in the plots list.

Visual Guides

In addition to the observed data, in the DISPLAY settings panel you can add: the identity line y = x and spline interpolation.

Highlight

Hovering on any point of observed data shows:

• the subject id and time corresponding to this point
• highlights all the points corresponding to this subject
• segments linking all points corresponding to the same individual to visualize the time chronology.

Highlighting works across plots. An individual data highlighted in this plot, will be highlighted in every other plot to help you in the model diagnosis.

Log scale

A log scale allows to focus on low observation values. You can set it in the AXIS section of the settings panel for each axis separately or for both together.

The example below displays the predicted concentrations of remifentanil, modeled via a two-compartments model with a linear elimination. In this case, the log-log scale reveals a misspecification of the model: the small observations are under-predicted. These observations correspond to late time points, meaning that the last phase of elimination is not properly captured by the two-compartment model. A three-compartment model might give better results.

Settings

• General
  • Legend and grid : add/remove the legend or the grid.
•  Display
  • BLQ data : show and put in a different color the data that are BLQ (Below the Limit of Quantification)
  • Visual cues: add/remove visual guidelines such as the line y = x or a spline interpolation.
• Axis
  • Use log scale
  • Set automatic or manual (user – defined step) tick values
  • Edit axis labels

Stratification

You can split, color or filter the plot as described for the observed data.

Purpose

This plot displays scatter plots for each pair of parameters. It allows to identify correlations between parameters, which can be used to see the results of your analysis and see the coherence of the parameters for each individuals.

Example

In the following example, one can see pairs of parameters estimated for all parameters.

Visual guidelines

In addition to regression lines, correlation coefficients can been added to see the correlation between random effects, as well as spline interpolations.

Selection

It is possible to select a subset of parameters, whose pairs of correlations are then displayed, as shown below. In the selection panel, a set of contiguous rows can be selected with a single extended click, or a set of non-contiguous rows can be selected with several clicks while holding the Ctrl key.

Highlight

Similarly to other plots, hovering on a point provides information on the corresponding subject id, and highlights other points corresponding to the same individual.

Stratification: coloring and filtering

Stratification can be applied by creating groups of covariate values. As can be seen below, these groups can then be split, colored and/or filtered allowing to check the effect of the covariate on the correlation between two parameters. The correlation coefficient is updated according to the stratifying action. In the following case, We split by the covariate SEX and color bay 2 categories of AGE.

Settings

• General
  • Legend and grid : add/remove the legend or the grid. There is only one legend for all plots.
  • Information: display/hide the correlation coefficient associated with each scatter plot.
• Display
  • Selection. The user can select some of the parameters to display only the corresponding scatter plots. A simple click selects one parameter, whereas multiple clicks while holding the Ctrl key selects a set of parameters.
  • Visual cues. Add/remove the regression line or the spline interpolation.

Purpose

The sequence-by-period plot allows to visualize, for each parameter, the mean and standard deviation for each period, sequence and formulation.

Description

For each formulation, period and sequence (as defined in the Bioequivalence settings), the mean and standard deviation is displayed. The dots are colored according to the formulation, and dots belonging to the same sequence connected by lines. Dots are placed on the x-axis according to the occasion value.

If the parameter has a log-transform (see Bioequivalence settings), the dots represents the geometric mean and the error bars */ the geometric standard deviation. If the parameter is not log-transformed, the dots represent the arithmetic mean and the error bars +/- the standard deviation. NCA parameter values being NaN are excluded and a warning message is displayed.

The example below shows a repeated crossover with sequences RTRT and TRTR. Three NCA parameters are displayed.

Troubleshooting

• The connecting lines to do appear:
  If the plot setting “Lines” in selected and the connecting lines do not appear, it is because no categorical covariate column as been defined as “Sequence” in the Bioequivalence settings.
  
• There are vertical connecting lines:
  This means that the column defined as “Sequence” in the Bioequivalence settings is not consistent with the sequence of formulation according to the Occasion column. In the tab “Data”, you can define an “additional covariate” and select the “covariate sequence (XXX)” with XXX being the column representing the formulation. Then use this column as “Sequence” when defining the factors in the model.
  
• There are several periods on the x-axis although no column was indicated as “period” in the Bioequivalence settings:
  When no column is indicated as “period”, we use the column tagged as “occasion” in the data set. If no column has been tagged as “occasion” (parallel design), the occasion is considered to be 1 for all individuals.

Settings

• General
  • Legend: hide/show the legend. The legends adapts automatically to the elements displayed on the plot. The same legend box applies to all subplots and it is possible to drag and drop the legend at the desired place.
  • Grid : hide/show the grid in the background of the plots.
  • Units: hide/show the units of the NCA parameters. Note that the color and surrounding character can be chosen in the plot “Preferences”.
• Display
  • Dots: hide/show the dots representing the means
  • Lines: hide/show the lines connecting the dots belonging to the same sequence
  • Error bars: hide/show the error bars representing the standard deviation
  • Individual parameters: select which individual parameters to show on the plot

Stratify

This plot can be split and filtered by the covariates but not colored. The categorical covariate indicated of Formulation in the Bioequivalence settings is automatically used to color the dots. The colors can be changed in the plot “Preferences > Formulations”:

 

Purpose

This plot allows to visualize, for each parameter, the subject-by-formulation interaction and the inter-subject variability.

Description

Each subplot corresponds to one NCA parameter and one non-reference (test) formulation. The individual parameter values for the test and reference formulations are displayed side by side. Values corresponding to the same individual are connected by a line. When an individual has received several times the same formulation (repeated crossover), the average for each formulation is calculated and plotted.

Settings

• General
  • Legend: hide/show the legend. The legends adapts automatically to the elements displayed on the plot. The same legend box applies to all subplots and it is possible to drag and drop the legend at the desired place.
  • Grid : hide/show the grid in the background of the plots.
  • Units: hide/show the units of the NCA parameters. Note that the color and surrounding character can be chosen in the plot “Preferences”.
• Display
  • Dots: hide/show the dots representing the individual parameter values
  • Lines: hide/show the lines connecting the dots belonging to the same individual
  • Individual parameters: select which individual parameters to show on the plot

Stratify

The plot can split and filtered but not (yet) colored.

 

Purpose

This plot allows to visualize the confidence interval for the ratio for each parameter, as well as the BE limits. Confidence intervals within the BE limits are shown in green while the others are shown in red.

Settings

• General
  • Legend: hide/show the legend. The legends adapts automatically to the elements displayed on the plot. The same legend box applies to all subplots and it is possible to drag and drop the legend at the desired place.
  • Grid : hide/show the grid in the background of the plots.
  • Units: hide/show the units of the NCA parameters. Note that the color and surrounding character can be chosen in the plot “Preferences”.
• Display
  • Median: hide/show the line at ratio=100%.
  • Bioequivalence limits: hide/show the horizontal lines at the BE limits, which can be set in the BE settings
  • Individual parameters: select which individual parameters to show on the plot

Stratify

This plot cannot be stratified by covariates.

 

Note: the features described on this page are not available in MonolixSuite versions prior to 2024R1.

MonolixSuite offers the ability to transfer plot formatting from one plot to another within the same project or across projects. This can save you time and effort when you want to apply the same formatting options, such as stratification, preferences, or settings, to multiple plots, or when you want to use the same plot formatting for different analyses or datasets.

• Transferring plot formatting within one project
  • Selecting the source and target plots
  • Choosing the sections to transfer
• Transferring plot formatting across projects with plot presets
  • Defining a plot preset
  • Applying a plot preset
  • Managing plot presets
• Applying pre-defined plot formatting
• Restoring default plot formatting
  • Using the Reset button
  • Defining a custom default

 

Transferring plot formatting within one project

 

To transfer plot formatting within one project, you need to use the “Apply…” button on the bottom left of the Plots tab and select “From plot” in the window that opens:

Selecting the source and target plots

The window allows you to select the source plot, which is the plot that has the formatting you want to transfer, and the target plots, which are the plots that you want to apply the formatting to. You can select all plots by clicking on the Select all button, or select all plots specific to some observation id with the “Fast selection”.

Choosing the sections to transfer

You can also choose which sections of the configuration you want to transfer: Stratify, Settings, or Preferences.

By default, Stratify and Preferences are selected.

• The Stratify section includes the options to stratify the plots by covariates or occasions.
• The Settings section includes the options to customize the content of the plots: elements displayed or not on the plots, such as the legend, the grid, the observed data points, etc, and calculation settings such as the axes, bins etc.
• The Preferences section includes the options to change the colors, fonts, sizes, etc.

Once you have selected the source plot, the target plots, and the sections to transfer, you can click on the Apply button to transfer the plot configurations.

 

Transferring plot formatting across projects with plot presets

 

To transfer plot formatting across different projects, you need to use the plot presets feature, which allows you to define and apply presets for plot configurations.

Defining a plot preset

To define a plot preset, you need to first set up your plot configuration as you would like by choosing the stratification, preferences, and settings options for each plot (you can use the transfer or plot formatting between plots within the same project, described in the first section, to help you). Then, you can save this configuration as a preset by clicking on the Save icon in the Apply from the Plot Formatting  panel:

You will be asked to give a name and a description to your preset, and to select which sections of the formatting you want to include in the preset among Stratify, Settings and Preferences. If the project has several types of observations, only the plots corresponding to one of them can be used to define the preset so it is necessary to select the observation id. You can also choose to set this preset as your default, which means that when you click on Reset, the plot formatting from this preset will be applied instead of the system default.

Applying a plot preset

 

After saving your preset, it will be available in the list of presets that you can choose from when you click on “From preset” in the window that opens with “Apply…” in the Plot Formatting panel.

You can apply your preset to a list of plots in another project, by opening this project, clicking on “Apply…” and “From preset” and by selecting the preset and the target plots, and finally clicking on Apply. This will transfer the plot configurations from the preset to the target plots.

The target plots must be the same type of plots that were used to define the preset: for example if no CA plot had been generated in the project used to define the preset, then the plot preset cannot be applied to a CA plot in a new project, as there is no CA formatting option to apply.

Note that axis limits values and bins settings are not saved as part of the preset because they are considered too project-specific.

Note this major difference between “Apply formatting from plot” and “Apply formatting from preset”:

• “Apply formatting from plot” applies all selected options from the source plot to all selected target plots. Thus, if you select the NCA data plot stratified by STUDY as source plot and the Observed data plot as target plot, and “Stratify” section in plot formatting to be transfer, you will obtain the Observed data plot stratified by STUDY.
• “Apply formatting from preset” applies the selected options from each plot saved in the preset to the corresponding plot in your project. Thus, if you saved a preset including the “Stratify” section based on a project where the NCA data plot is stratified by STUDY but not the Observed data plot, applying that preset to another project will stratify the NCA data plot by STUDY but not the Observed data plot.

 

Managing plot presets

You can also manage your presets by going to Settings > Manage presets > Plot formatting.

This will open a window where you can see all presets, modify, update or remove your custom presets, and export or import them as separate files with a lixpst extension. That way you can easily share your presets with your colleagues or collaborators to standardize your plot formatting.

 

Applying pre-defined plot formatting

 

In addition to your custom presets, MonolixSuite also provides two pre-defined presets that you can use to apply plot formatting. These presets are:

• Greyscale_Preferences: This preset affects only the Preferences section of the plot configurations, and produces publication-ready greyscale plots with optimized size and spacing of the texts to improve readability of the plots (example shown below for the NCA Individual fits).

• Typical_Reporting_Settings: This preset affects only the Settings section of the plot configuration, and corresponds to plot settings typically chosen to report the analysis results. It has additional settings for Monolix plots, but in PKanalix it only removes the grid in the background for all plots:

You can apply these presets to any plot in your project by selecting them from the list of presets and clicking on Apply. You can also combine these presets with your own presets or with the Apply from plot feature, to create the plot configuration that suits your needs.

 

Restoring default plot configuration

 

Using the Reset button

If you want to restore the default plot configuration, you can click on the Reset icon in the Apply from plot panel. This will reset all plots to the system default, or to your custom default if you have defined one.

Note that resetting the plot configuration will not affect the plot presets that you have defined or imported. You can still apply them to any plot after resetting.

 

Defining a custom default

To define a custom default, you need to create a preset and select the option “Use this preset as default” when saving it. This will make this preset the default configuration for all plots. You can also unset a preset as default by going to Settings > Manage presets > Plot formatting, and unchecking the option “Use this preset as default” for the preset.