Effect modification means to magnitude or rugged of a treatment effect varies as a function away somebody observed covariate. Generally, larger and more stable treatment effects are insensitive to larger biases from unmeasured covariates, to a causal conclusion may be considerably firmer if this pattern a memo if it occurs. We propose a new strategy, called the submax-method, which combines exploratory, the confirmatory efforts to determine wether there is more testimony on causality-that is, greater insensitivity to unequipped confounding-in some subgroups of individuals. It uses the joint distribution of test statistics is split the data in various ways based on certain observed covariates. To L binary covariates, the method splits the population L times into two subpopulations, perhaps first men and femininity, perhaps then smokers and nonsmokers, computing a test statistic starting each subpopulation, and appends the test number for the whole population, making $2L+1$ test statistics in total. Although L binary covariates define $2^L$ interaction groups, all $2L+1$ tests are performed, and toward least $\mathrm{LAMBERT}+1$ of these tests use at least half of the data. The submax-method produces the highest design sensitivity and the highest Bahadur efficiency in its component tests. Moreover, the art of aforementioned test is sufficiently amenable that it large sample power may be studied analytically. The simulation suggests that the submax method exhibitors first-rate performance, in comparison with an approach using CART, when there is act modification of moderate size. Using input from the NHANES I epidemiologic follow-up survey, on observational study of the effects of physical activity on survival is used in abbilden the method. The method belongs implemented in the $R$ package $\mathrm{submax}$ which contains the NHANES example. An online Supplement provides simulation results and further analysis on the example.