Generalized definition of the geometric mean of a non negative random variable

Equivalence tests for ratio of means in bioequivalence studies under crossover design

There are several problems concerning the statistical definition of average bioequivalence provided by the U.S. Food and Drug Administration. We proposed a ratio of means based on the original bioavailability measure as the definition for average bioequivalence. Under the log-normal distribution assumption, we proposed a hypothesis testing-based method and a confidence interval-based method to answer the question of whether the ratio of means falls into a predetermined interval. For the hypothesis testing-based method, we decomposed the null two-sided hypothesis of the ratio of means into two one-sided hypotheses. With the intersection-union theorem for asymptotic tests, we constructed two asymptotic size-α tests for the original null hypothesis. The method of variance estimation recovery was adopted to develop the confidence interval-based method. Simulation studies showed that the proposed methods can maintain the empirical type I error rate closely at the nominal level and is as powerful as the two one-sided t-test for testing the ratio of means under different settings. The application of the proposed methods was illustrated through six datasets in real-world examples.

Methods to control the empirical type I error rate in average bioequivalence tests for highly variable drugs

Average bioequivalence tests are used in clinical trials to determine whether a generic drug has the same effect as an original drug in the population. For highly variable drugs whose intra-subject variances of direct drug effects are high, extra criteria are needed in bioequivalence studies. Currently used average bioequivalence tests for highly variable drugs recommended by the European Medicines Agency and the US Food and Drug Administration use sample estimators in the null hypotheses of interest. They cannot control the empirical type I error rate, so the consumer's risk is higher than the predetermined level. In this paper, we propose two new statistically sound methods that can control the empirical type I error rate without involving any sample estimators in the null hypotheses. In the proposed methods, we consider the average level of direct drug effects and the intra-subject variance of the direct drug effects. The first proposed method tests the latter parameter first to determine whether a product should be regarded as a highly variable drug, and then tests the former using corresponding bioequivalence limits. The second proposed method tests these two parameters simultaneously to capture the bioequivalence region. Extensive simulations are done to compare these methods. The simulation results show that the proposed methods have good performance on controlling the empirical type I error rate. The proposed methods are useful for pharmaceutical manufacturers and regulators.