Group Sequential Monitoring of Clinical Trials with Multivariate Outcomes

Abstract

In clinical trials with staggered patient entry, the results become available sequentially. For scientific and ethical reasons, such clinical trials are often monitored for potential early stopping. This paper addresses the issues of monitoring clinical trials using multivariate outcomes. Monitoring procedures which account for the multiplicity from repeatedly applying the significance testing as well as from correlation of multivariate outcomes are proposed to preserve the overall significance level. The repeated measures of the same outcome variable over time as one form of multivariate outcome are first considered. A semiparametric approach to conduct interim analyses in longitudinal clinical trials using the generalized estimating equations of Liang and Zeger (1) is taken. By incorporating the consistently estimated variance structure of the repeated measures into the generalized estimating equations, it is shown that the monitoring procedure is more sensitive in detecting treatment differences. It is also demonstrated that with consistent estimate of the variance structure, sequentially computed test statistics have an asymptotic independent increment structure. This theoretical result has important implications in the conduct of longitudinal clinical trials in that well-established standard group sequential methods become directly applicable in design and analysis. In order to account for dependent censoring in longitudinal clinical trials, a similar approach is also proposed using the weighted estimating equations of Robins, Rotnitzky, and Zhao (2). As another form of multivariate outcomes, bivariate time-to-event endpoints are considered. A group sequential method based on the exact sequential χ² test of Jennison and Turnbull (3) is derived. For parametric or semiparametric survival models, this method can produce repeated confidence ellipsoids which provide the most efficient confidence region for bivariate parameters. The proposed group sequential methods are illustrated by using the dataseis from clinical trials reported in the literature.