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)]

- then:
**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)]

- then:

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.

### Read details on the calculations performed by these rules

- “Replace individual BLQ samples by [missing/zero/LOQ/(LOQ/2)]” = replace each individual censored sample by Missing (ie ignore the sample), LOQ (from the dataset for each sample) or LOQ/2.
- “If NBLQ > 33% of NTOT”: this condition is checked at each nominal time point and for each stratification group: NTOT is the total number of samples considered corresponding to that nominal time point and that stratification group, and NBLQ is the number of censored samples among them.
- “Replace mean sample by [missing/zero/LOQ/(LOQ/2)]” = replace the mean sample by Missing (ie ignore the mean sample in the mean profile), LOQ (largest LOQ found in the dataset among the censored samples involved in this mean sample), or LOQ/2.
- “Check that mean samples stay above the LOQ”: here the LOQ is the global LOQ value entered by the user in these settings.
- “If meanSample < LOQ then replace by LOQ”: here the LOQ in the condition and the replacement is the global LOQ value entered by the user in these settings.

# 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.