## Sparse sampling designs: a new method for estimating the complete AUC and its standard error

Fernández-Teruel C, Navarro-Fontestad MC, González-Álvarez I, Bermejo M, Casabo VG

Department of Pharmaceutics and Pharmaceutical Technology. College of Pharmacy. University of Valencia.

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Purpose: The area under the curve (AUC) is a pharmacokinetic parameter widely used in toxicokinetics and bioequivalence studies as a measure of drug exposure. In order to perform statistical comparisons, the parameter values and their variances in the different groups/treatments are necessaries, but depending on the experimental design the estimation may be unfeasible, principally the standard error of estimated parameter.

Method: The AUC value estimation is based on the trapezoidal rule, as was described by Yuan1. A new mathematical method for AUC standard error calculation in different sampling designs has been already developed. This method assumes a mixed effect model, where the experimental concentration is estimated by adding the subject effect and the residual effect to the mean concentration. In this model, the subject effect and the residual effect have been considered proportional deviations to the mean concentrations. Then, these values are used to construct the matrix variance-covariance of concentrations. Moreover, in the present work the aim was to expand this new mathematical method for estimating the complete area under the curve (AUC), from time zero to infinite, and its standard error. Furthermore this procedure includes the extrapolation for calculating the terminal slope, the extrapolation to the initial concentration in case of intravenous administrations and the transmission of this variability to standard error of AUC.

Data were simulated using NONMEM V as one hundred groups with twenty subjects each one. From the simulated data, different sampling scenarios were used corresponding to different experimental designs:

1. Complete design with 20 subjects and 12 samples per subject.
2. Complete design with 5 subjects and 12 samples per subject.
3. Batch design with 20 subjects where each subject is sampled at 3 time point. There are 4 batches covering a total of 12 time points.
4. Random design with 20 subjects where each subject is sampled at 3 time point. They are not allowed to coincide at more than one time point.

Results: The AUC and its standard error were estimated using the new method and the obtained values were compared between designs with true AUC value.

Conclusion: This procedure can be applied to any design for non-compartmental AUC estimation and also estimates accurately the standard error of the AUC under any circumstance. Moreover, the procedure shows the AUC estimation is more accurate in designs with more subjects for the same number of samples.

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