# How many subjects are necessary for population pharmacokinetic experiments? Confidence interval approach.

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## Abstract

OBJECTIVE: To describe an approach using simulations for determining sample size for population pharmacokinetic experiments METHODS: We address this problem by proposing method based on the estimation of the model parameters. The power to estimate the confidence interval of a parameter of choice to a particular precision is determined for different sample sizes by making stepwise increases in the sample size until the power is achieved. The method is based on simulation using previous information about the model and parameter estimates. Two examples are presented based on one-compartment and two-compartment first-order absorption models. RESULTS: Sample size depends on the parameter of choice, the sampling designs and the method for the analysis of the collected data among other things. For the one-compartment first-order absorption model, assuming the parameter of choice is rate of absorption, the sample sizes required to estimate the 95% confidence interval within a 20% precision level with a power of 0.9 using the FO, FOCE and FOCE/INTERACTION methods in NONMEM and WINBUGS for a design that involved sampling at 0.01, 7.75 and 12 h (the population optimal design) are 20, 30, 30 and 30 respectively. For an extensive design (sampling at 0.5, 2, 4, 8, 12 and 24 h), the sample sizes are 20, 20, 20 and 30, respectively. For the two-compartment first-order absorption model, assuming the parameter of choice is initial volume of distribution, the sample sizes required to estimate the 95% confidence interval within a 50% precision level with a power of 0.8 for FO, FOCE/INTERACTION and WINBUGS were 50, 50 and 20, respectively. CONCLUSION: The determination of sample size using the confidence interval approach appears to be a pragmatic approach to determine the minimum number of subjects for a population pharmacokinetic experiment.

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