Abstract
Multistage designs allow considerable reductions in the expected sample size of a trial. When stopping for futility or efficacy is allowed at each stage, the expected sample size under different possible true treatment effects (δ) is of interest. The δ-minimax design is the one for which the maximum expected sample size is minimised amongst all designs that meet the types I and II error constraints. Previous work has compared a two-stage δ-minimax design with other optimal two-stage designs. Applying the δ-minimax design to designs with more than two stages was not previously considered because of computational issues. In this paper, we identify the δ-minimax designs with more than two stages through use of a novel application of simulated annealing. We compare them with other optimal multistage designs and the triangular design. We show that, as for two-stage designs, the δ-minimax design has good expected sample size properties across a broad range of treatment effects but generally has a higher maximum sample size. To overcome this drawback, we use the concept of admissible designs to find trials which balance the maximum expected sample size and maximum sample size. We show that such designs have good expected sample size properties and a reasonable maximum sample size and, thus, are very appealing for use in clinical trials. Copyright © 2011 John Wiley & Sons, Ltd.
Highlights
When investigating a novel treatment in a randomised clinical trial, there are substantial advantages to be gained from using a multistage design
One may allow the option to stop the trial for futility, when the results so far show that the treatment is unlikely to be judged to be effective, or for efficacy, when the results so far provide sufficient evidence to reject the null hypothesis of no treatment advantage
If interim analyses are used within a frequentist paradigm, the significance level at each interim analysis must be smaller than the overall significance level required
Summary
When investigating a novel treatment in a randomised clinical trial, there are substantial advantages to be gained from using a multistage design. One may allow the option to stop the trial for futility, when the results so far show that the treatment is unlikely to be judged to be effective, or for efficacy, when the results so far provide sufficient evidence to reject the null hypothesis of no treatment advantage. Group-sequential designs are multistage designs in which equal numbers of patients are recruited at each stage. The purpose of a multistage design is to reduce the expected sample size, but this depends on the true treatment effect. An optimal design is one which has the minimum expected sample size conditional on a specific value for the true treatment effect
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