Bioequivalence evaluation of sparse sampling pharmacokinetics data using bootstrap resampling method

ABSTRACT

Bioequivalence studies are an essential part of the evaluation of generic drugs. The most common in vivo bioequivalence study design is the two-period two-treatment crossover design. The observed drug concentration–time profile for each subject from each treatment under each sequence can be obtained. AUC (the area under the concentration–time curve) and C_max (the maximum concentration) are obtained from the observed drug concentration–time profiles for each subject from each treatment under each sequence. However, such a drug concentration–time profile for each subject from each treatment under each sequence cannot possibly be available during the development of generic ophthalmic products since there is only one-time point measured drug concentration of aqueous humor for each eye. Instead, many subjects will be assigned to each of several prespecified sampling times. Then, the mean concentration at each sampling time can be obtained by the simple average of these subjects’ observed concentration. One profile of the mean concentration vs. time can be obtained for one product (either the test or the reference product). One AUC value for one product can be calculated from the mean concentration–time profile using trapezoidal rules. This article develops a novel nonparametric method for obtaining the 90% confidence interval for the ratio of AUC_T and AUC_R (or C_T,max/C_R,max) in crossover studies by bootstrapping subjects at each time point with replacement or bootstrapping subjects at all sampling time points with replacement. Here T represents the test product, and R represents the reference product. It also develops a novel nonparametric method for estimating the standard errors (SEs) of AUC_h and C_h,max in parallel studies by bootstrapping subjects treated by the hth product at each time point with replacement or bootstrapping subjects treated by the hth product at all sampling time points with replacement, h = T, R. Then, 90% confidence intervals for AUC_T/AUC_R and C_T,max/C_R,max are obtained from the nonparametric bootstrap resampling samples and are used for the evaluation of bioequivalence study for one-time sparse sampling data.

KEY WORDS:

• Bioequivalence
• bootstrap
• ophthalmic solution
• sparse data

Acknowledgments

The authors would like to thank the anonymous reviewers for their comments. The first author would like to thank her mentor and supervisor, Dr. Yi Tsong at the Food and Drug Administration, for his longtime support and encouragement.