Statistical considerations regarding correlated lots in analytical biosimilar equivalence test

In the evaluation of the analytical similarity data, an equivalence testing approach for most critical and quantitative quality attributes, which are assigned to Tier 1 in their proposed three-tier approach, was proposed. The Food and Drug Administration (FDA) has recommended the proposed equivalence testing approach to sponsors through meeting comments for Pre-Investigational New Drug Applications (PINDs) and Investigational New Drug Applications (INDs) since 2014. The FDA has received some feedback on the statistical issues of potentially correlated reference lot values subjected to equivalence testing since independent and identical observations (lot values) from the proposed biosimilar product and the reference product are assumed. In this article, we describe one method for correcting the estimation bias of the reference variability so as to increase the equivalence margin and its modified versions for increasing the equivalence margin and correcting the standard errors in the confidence intervals, assuming that the lot values are correlated under a few known correlation matrices. Our comparisons between these correcting methods and no correction for bias in the reference variability under several assumed correlation structures indicate that all correcting methods would increase the type I error rate dramatically but only improve the power slightly for most of the simulated scenarios. For some particular simulated cases, the type I error rate can be extremely large (e.g., 59%) if the guessed correlation is larger than the assumed correlation. Since the source of a reference drug product lot is unknown in nature, correlation between lots is a design issue. Hence, to obtain independent reference lot values by purchasing the reference lots at a wide time window often is a design remedy for correlated reference lot values.