This paper addresses sequential testing in randomized clinical trials with multiple endpoints. Patients enter treatments serially and are subject to random loss to followup. The endpoints of interest may be time-to-event variables or other quantitative measurements. The proposed test statistic at a given look is a weighted sum of the linear rank statistics with respect to the marginal distributions of the multiple endpoints. The weights can be chosen to maximize asymptotic power against certain local alternatives. Stopping boundaries are obtained from the asymptotic joint distribution of the proposed test statistics calculated at different looks. This new approach preserves a single preset overall significance level and can lead to quicker termination of the trial than sequential procedures based on single endpoints. An example taken from an aids clinical trial is presented.
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D. Y. Lin (1991) studied this question.