Power calculations for large multi-arm placebo-controlled studies of dichotomous outcomes

Power considerations for trials of two experimental arms versus a standard active control or placebo

The power of the two-experimental arm trial depends on three choices: (1) when one arm is dropped (if at all); (2) the final testing procedure, assuming no dropping; and (3) the sampling ratio for the three arms. Multiple-arm designs require critical values which were calculated using Mathematica. Power calculations were exact based on probabilities from binomial distributions. The "drop the loser" strategy is optimal for the primary endpoint. The equal sized two treated arm trial gives reasonable power for the primary as well as good power to select the best treated arm. The best power was provided by the 3:3:4 sampling, but it was only marginally better.

How to deal with multiple treatment or dose groups in randomized clinical trials?

Multiplicity adjustment in general is currently a controversial topic. This review focuses on the proof of efficacy in randomized clinical trials. The ICH guidelines mandate control of the familywise error rate. Confidence intervals are clinically more appropriate than P-values or yes/no decisions. Therefore, simultaneous confidence intervals are proposed for several designs and aims in clinical trials. The computation of simultaneous confidence intervals for the difference or the ratio is demonstrated by means of real data examples using the R-packages multcomp and mratios. A special problem is the evaluation of dose-finding trials with and without the assumption that the effects increase with increasing doses. Simultaneous intervals are presented not only for one-way layouts and normal distributed endpoints, but also for higher way layouts, generalized linear models, and mixed models. Under importance ordering, the conditional testing of all hypotheses at level alpha will be shown using the intersection-union test principle. Other multiplicity issues (i.e. multiple endpoints, multiple analyses, and subgroup analyses) are discussed.

Optimal design of clinical trials comparing several treatments with a control

Clinical trials are often designed to compare several treatments with a common control arm in pairwise fashion. In this paper we study optimal designs for such studies, based on minimizing the total number of patients required to achieve a given level of power. A common approach when designing studies to compare several treatments with a control is to achieve the desired power for each individual pairwise treatment comparison. However, it is often more appropriate to characterize power in terms of the family of null hypotheses being tested, and to control the probability of rejecting all, or alternatively any, of these individual hypotheses. While all approaches lead to unbalanced designs with more patients allocated to the control arm, it is found that the optimal design and required number of patients can vary substantially depending on the chosen characterization of power. The methods make allowance for both continuous and binary outcomes and are illustrated with reference to two clinical trials, one involving multiple doses compared to placebo and the other involving combination therapy compared to mono-therapies. In one example a 55% reduction in sample size is achieved through an optimal design combined with the appropriate characterization of power.

Sample size calculation for simulation-based multiple-testing procedures

In this article, we present a simple method to calculate sample size and power for a simulation-based multiple testing procedure which gives a sharper critical value than the standard Bonferroni method. The method is especially useful when several highly correlated test statistics are involved in a multiple-testing procedure. The formula for sample size calculation will be useful in designing clinical trials with multiple endpoints or correlated outcomes. We illustrate our method with a quality-of-life study for patients with early stage prostate cancer. Our method can also be used for comparing multiple independent groups.