A new, powerful approach to the study of effect modification in observational studies
Kwonsang Lee, Dylan S. Small, Paul R. Rosenbaum
Effect modification occurs when the magnitude or stability of a treatment effect varies as a function of an observed covariate. Generally, larger and more stable treatment effects are insensitive to larger biases from unmeasured covariates, so a causal conclusion may be considerably firmer if effect modification is noted when it occurs. We propose a new strategy, called the submax-method, that combines exploratory and confirmatory efforts to discover effect modification. It uses the joint distribution of test statistics that split the data in various ways based on observed covariates. The method splits the population L times into two subpopulations, computing a test statistic from each subpopulation, and appends the test statistic for the whole population, making 2L+1 test statistics in total. The submax-method achieves the highest design sensitivity and the highest Bahadur efficiency of its component tests. Moreover, the form of the test is sufficiently tractable that its large sample power may be studied analytically. A simulation confirms and elaborates large sample results. An observational study of the effects of physical activity on survival is used to illustrate the method.