Effect modification occurs when the magnitude of a treatment effect varies in a predictable way as a function of measured covariates -- e.g., the treatment has a larger effect on children than on adults. Effect modification is important in observational studies for at least two reasons. First, if there truly is effect modification, then it is important to understand it in order to use the treatment in the most effective way. Second, other things being equal, a larger treatment effect is insensitive to larger biases from unmeasured confounding; so, the strongest evidence that a treatment has any causal effect may come from a subpopulation that experiences large effects. Having established that the treatment has a causal effect in such a subpopulation, it becomes more plausible that it has causal effects also in other subpopulations where the magnitude of the effect is smaller.
Because effect modification refers to an effect that varies predictably as a function of measured covariates, we could see it in a randomized experiment of sufficient size. Effect modification is often confused with other useful topics. In a randomized experiment, an effect may not be constant -- it may vary from person to person -- in a manner that is unpredictable, yet this may be evident and visible in the marginal distributions of responses in the treated and control groups, because the marginal distributions are not shifted but rather transformed in shape or dispersion. In observational studies, such transformations of marginal distribution affect the design sensitivity; see Chapters 16 and 17 in my book, Design of Observational Studies (Springer, 2020).
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Zubizarreta JR, Paredes RD, Rosenbaum PR. Matching for Balance, Pairing for Heterogeneity in an Observational Study of the Effectiveness of For-Profit and Not-For-Profit High Schools in Chile. Annals of Applied Statistics. 2014 Jan 1;8(361):204-31. Open access at ProjectEuclid: https://doi.org/10.1214/13-AOAS713