PubMed · 10935748
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M Bobbio. 2000. [The SET-UP study].. https://pubmed.ncbi.nlm.nih.gov/10935748/
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Allocating a proportion k'=1/(1+ radicalr(0)) of subjects to an intervention is a practical approach to approximately maximize power for testing whether an intervention reduces relative risk of disease below a null ratio r(0)<1. Furthermore, allocating k'(s), a convenient fraction close to k', to intervention performs nearly as well; for example, allocating k'(s)=3/5 for 0.5> or =r(0)>0.33,2/3 for 0.33> or =r(0)>0.17 and 3/4 for 0.17> or =r(0)> or =0.10. Both k' and k'(s) are easily calculated and invariant to alterations in disease rate estimates under null and alternative hypotheses, when r(0) remains constant. In examples that we studied, allocating k' (or k'(s)) subjects to intervention achieved close to the minimum possible sample size, given test size and power (equivalently, maximum power, given test size and sample size), for likelihood score tests. Compared to equal allocation, k' and k'(s) reduced sample sizes by amounts ranging from approximately 5.5 per cent for r(0)=0.50 to approximately 24 per cent for r(0)=0.10. These sample size savings may be particularly important for large studies of prophylactic interventions such as vaccines. While k' was derived from variance minimization for an arcsine transformation, we do not recommend the arcsine test, since its true size exceeded the nominal value. In contrast, the true size for the uncorrected score test was less than the nominal size. A skewness correction made the size of the score test very close to the nominal level and slightly increased power. We recommend using the score test, or the skewness-corrected score test, for planing studies designed to show a ratio of proportions is less than a prespecified null ratio r(0)<1.
Many clinical trials of uncommon diseases are underpowered because of the difficulty of recruiting adequate numbers of subjects. We propose a clinical trial design with improved statistical power compared to the traditional randomized trial for use in clinical trials of rare diseases. The three-stage clinical trial design consists of an initial randomized placebo-controlled stage, a randomized withdrawal stage for subjects who responded, and a third randomized stage for placebo non-responders who subsequently respond to treatment. Test level and power were assessed by computer-intensive exact calculations. The three-stage clinical trial design was found to be consistently superior to the traditional randomized trial design in all cases examined, with sample sizes typically reduced by 20 per cent to 30 per cent while maintaining comparable power. When a treatment clearly superior to placebo was considered, our design reached a power of 75 per cent with a sample of 21 patients compared with the 52 needed to attain this power when only a randomized controlled trial was used. In situations where patient numbers are limited, a three-stage clinical trial design may be a more powerful design than the traditional randomized trial for detecting clinical benefits.
In a number of clinical trials there is interest in testing more than one hypothesis concerning the treatment effect on a single primary endpoint. For instance, a sponsor of a trial to demonstrate that a test treatment (T) is non-inferior to an active control (R) may also be interested in showing that T is superior to R, if this is the case. Using the closed testing method for constructing tests of multiple hypotheses which control the multiple level of significance, we provide a framework for testing these hypotheses sequentially during a trial at pre-planned interim analyses.