Group Sequential Design With Change of Endpoint

Abstract

ABSTRACTIn Rheumatoid Arthritis studies, scientists usually need to focus on multiple endpoints simultaneously. Regulatory agencies require ACR20 as the primary endpoint for approval and making decisions. However, the proportional measurement for a binary variable is less reliable with a small sample size. DAS28 is an increasingly popular co-primary or key secondary endpoint for decision making in interim analyses because it is a continuous variable as well as a linear combination of multiple measurements that are also contained in ACR20. In a group sequential (GS) design, one of the most important parts is to compute the correlation among test statistics in interim and final analyses. We perform a logistic regression to link DAS28 and ACR20 and compute the correlation numerically. We also prove that the covariance matrix between binary and continuous variables with underlying logistic regression is a consistent estimator. Three methods including “GS design with univariate variable (ACR20),” “GS design with change of endpoints (DAS28 and ACR20),” and “Bonferroni tests with change of endpoints” are compared in three cases—“early stopping for efficacy,” “early stopping for futility,” and “early stopping for both” through simulation. The results show that in the first and third cases, the power of tests with a change of endpoint is much higher than tests that only use ACR20. In the case of “early stopping for futility,” the methods with a change of endpoint also provide a higher probability of correctly stopping early for futility.