Procedures for testing the homogeneity of relative difference in sparse data

Estimation of the relative difference (or relative risk reduction) under the sequential parallel comparison design

To increase power or reduce the number of patients needed in trials studying treatments for psychiatric or mental disorders with a high placebo response rate, we may consider use of the sequential parallel comparison design proposed elsewhere. Because statistical significance does not necessarily imply that the difference between treatment and placebo is of clinical importance, it is always of importance to quantify the treatment effect in clinical trials. When the patient responses are dichotomous, the treatment and other covariates effects are not likely additive. Thus, using a weighted average of the risk differences over two phases may not be a meaningful summary index to measure the treatment effect. To alleviate this concern, we consider use of the relative difference or relative risk reduction to measure the treatment effect. We derive both point and interval estimators for the relative difference by use of the weighted-least-squares estimator and Mantel-Haenszel type estimator. We employ Monte Carlo simulation to evaluate the finite-sample performance of these estimators in a variety of situations. We also include a procedure for testing the homogeneity of the relative difference between phases under the sequential parallel comparison design. We use the placebo-controlled study to assess the efficacy of a low dose of aripiprazole adjunctive to antidepressant therapy in the treatment of patients with major depressive disorder to illustrate the use of estimators developed here.

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.