In etiologic research, the goal is to estimate the causal effect of an exposure on a disease outcome, which means the result that would be obtained in a large randomized trial with perfect adherence if exposure could be assigned without regard to the baseline characteristics of the study participants. But there is no reason to think that effects must be homogeneous across units in a randomized trial or in an observational study. Exposure may cause more or less disease in subgroups defined by age, sex, or any other background characteristic, whether measured or unmeasured. Indeed, the summary estimate over the population may reflect a mix of different effect magnitudes, or even a mix of subjects who are benefitted and harmed by the same treatment.Suppose that we obtain a summary estimate of causal effect from a perfectly conducted randomized controlled trial, for example a relative risk (RR) = 1.74. Across strata of baseline variables, however, the effect estimate will generally differ. Suppose that for men we observe RR= 1.87 and for an equal number of women, RR= 1.65. Now it is necessary to make a binary decision between 2 opposing views of reality. The first possibility (Fig. 1A) is that the 2 stratum-specific estimates (1.87 and 1.65) are 2 independent draws from a single underlying sampling distribution of the homogeneous effect. The difference between these 2 values is therefore due to sampling variability alone.
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