Confounding, Homogeneity and Collapsibility for Causal Effects in Epidemiologic Studies

Detection of confounding and confounders is important for observational studies, and especially so for epidemiologic studies. Miettinen and Cook (1981) derived two criteria for detecting confounders. Using a model, Wickramaratne and Holford (1987) proved that the two criteria are necessary but not sufficient conditions for confounders. We take uniform nonconfounding to mean there is no confounding at a coarse-subpopulation-level obtained by pooling any number of subpopulations. We discuss the necessity and sufficiency of the two criteria for uniform nonconfounding. The concepts of homogeneity and collapsibility for causal effects are also defined, and the relation among confounding, homogeneity and collapsibility is discussed. We show that the common causal effect over all fine subpopulations is just the causal effect of the whole population.