Sample size calculation based on risk ratio under multiple matching

To increase the efficiency of comparisons between treatments in clinical trials, we may consider the use of a multiple matching design, in which, for each patient receiving the experimental treatment, we match with more than one patient receiving the standard treatment. To assess the efficacy of the experimental treatment, the risk ratio (RR) of patient responses between two treatments is certainly one of the most commonly used measures. Because the probability of patient responses in clinical trial is often not small, the odds ratio (OR), of which the practical interpretation is not easily understood, cannot approximate RR well. Thus, all sample size formulae in terms of OR for case-control studies with multiple matched controls per case can be of limited use here. In this paper, we develop three sample size formulae based on RR for randomized trials with multiple matching. We propose a test statistic for testing the equality of RR under multiple matching. On the basis of Monte Carlo simulation, we evaluate the performance of the proposed test statistic with respect to Type I error. To evaluate the accuracy and usefulness of the three sample size formulae developed in this paper, we further calculate their simulated powers and compare them with those of the sample size formula ignoring matching and the sample size formula based on OR for multiple matching published elsewhere. Finally, we include an example that employs the multiple matching study design about the use of the supplemental ascorbate in the supportive treatment of terminal cancer patients to illustrate the use of these formulae.