Group-Sequential Response-Adaptive Designs for Comparing Several Treatments
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Previous work on two-treatment comparisons has shown that the use of optimal response-adaptive randomisation with group sequential analysis can allocate more patients to the better-performing treatment while preserving the overall type I error rate. The sequence of test statistics for this adaptive design asymptotically satisfi es the canonical joint distribution. The overall type I error rate can be controlled by utilising the error-spending approach. However, previous work focused on immediate responses. The application of the adaptive design to censored survival responses is investigated and different optimal response-adaptive randomised procedures compared. For a maximum duration trial, the information level at the fi nal look is usually unpredictable. An approximate information time is defi ned. Several treatments are often compared in a clinical trial nowadays. The adaptive design generalised to multi-arm clinical trials is studied. First, a global test is considered. The joint distribution of the sequence of test statistics no longer has the canonical distribution. However, the joint distribution can be derived, since the test statistic is a quadratic form of independent normal variables. Existing critical boundaries are based on normal responses and known variances with equal allocation and equal increments in information. Our results show that these boundaries can be used approximately for designs with other types of responses, unequal variances or unbalanced allocation. If the global null hypothesis is rejected, then pairwise comparisons are conducted at the current and subsequent looks to investigate which treatment effects differ. This is an analogue of Fisher's least signi cant difference method that can control the family-wise error rate. The adaptive design can target any optimal allocation to achieve some optimality criterion, and allows dropping of inferior treatments at interim looks, which can be unequally spaced in information time. Optimal allocation proportions after dropping arms are described. The power is not adversely affected by unbalanced allocation.
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