Optimal sample allocation in clinical trials designed to investigate relative risks.

Clinical trials with more than two groups are becoming increasingly common, especially trials with both active and placebo control groups. Equal allocation of subjects to each of the groups is the most common sample allocation, but in clinical trials where the purpose is to test hypotheses of relative risk, such as vaccine trials, equal allocation can be substantially sub-optimal. Optimal allocation for clinical trials has been considered previously, but not for trials with more than two groups. In this paper optimal sample allocation for relative risk trials is investigated in a variety of situations. The main results are as follows: (i) there are many situations where reductions of more than 20 per cent in sample size can be obtained by using optimal allocation instead of equal allocation; (ii) the optimal allocation for two group studies is not optimal in general; (iii) in many situations optimal allocation increases a subject's chances of being enrolled to a test treatment, and (iv) in most cases a grid search using the likelihood score asymptotic power function is the easiest method of finding an approximately optimal allocation. Extensions to situations more general than those covered here are sketched.