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Keywords: bioequivalence, permutation test, bootstrap, sparse sampling, pharmacokinetics, area under the curve, confidence interval
A bioequivalence (BE) pharmacokinetic study is used to determine whether the generic and the reference formulations of a pharmaceutical product are equivalent with respect to blood or tissue concentration-time profile, with the null hypothesis of inequivalence versus alternative of equivalence. The usual design includes collecting a full concentration-time profile from each subject, or dense sampling. In non-clinical studies, special problems arise if it is necessary to sacrifice the animals to obtain the measurement of internal tissue concentrations. Bailer (Bailer AJ. 1988. Testing for the equality of area under the curves when using destructive measurement techniques. J Pharmacokinet Biopharm, 16, 303-309) proposes a parametric method using trapezoidal linear combinations of mean concentrations at different time points to estimate the area under the concentration-time curve and its variance. However, it assumes a normal distribution of responses at each time point, or at least large enough samples to assure that the mean response is normally distributed. A modern alternative to the traditional parametric approach is the bootstrapping method. However, one essential requirement of the bootstrap method is a relatively large sample size. Many pharmacokinetic experiments involve a few observations per time point. In this presentation, we propose a permutation approach to evaluating the bioequivalence from animal pharmacokinetic data under sparse sampling and small sample size. The distribution-free permutation approach provides a practical alternative to asymptotic parametric approximation even with a small sample size. We also apply the permutation approach in a real case example of a sparse design. The proposed permutation approach may be used as part of the evidence to support BE evaluation with pharmacokinetic data under sparse sampling and small sample size.