Testing homogeneity of the risk ratio in stratified noncompliance randomized trials

The risk ratio (RR), defined as the ratio of probabilities of having an adverse event between an experimental treatment and a control treatment, is one of the most commonly used indices to measure the efficacy of an experimental treatment in a randomized clinical trial (RCT). When we want to obtain a summary estimator of the RR in stratified analysis, it is important that we can examine the assumption whether the underlying RR varies between strata. Although we can find a few publications on testing the homogeneity of RR, all these papers focus the ideal situation in which every patient complies with his/her assigned treatment. The research on testing the homogeneity of RR for a noncompliance RCT is limited. In this paper, we develop three simple test statistics for testing homogeneity of the RR under a noncompliance stratified RCT with large strata. To evaluate the performance of these statistics, we apply Monte Carlo simulation to calculate Type I error and power in a variety of situations. Based on the findings, we provide a general guideline of selecting a preferable test statistic under various situations. Finally, we include a large field trial studying the effect of a multifactor intervention program on the mortality of coronary heart disease (CHD) in middle-aged men to illustrate the practical use of these test statistics.