Confounding, homogeneity and collapsibility for causal effects in epidemiologic studies

Detection of confounding and confounders is important for observational stu dies, and especially so for epidemiologic studies. Miettinen and Cook (1981 ) derived two criteria for detecting confounders. Using a model, Wickramara tne and Holford (1987) proved that the two criteria are necessary but not s ufficient conditions for confounders. We take uniform nonconfounding to mea n there is no confounding at a coarse-subpopulation-level obtained by pooli ng any number of subpopulations. We discuss the necessity and sufficiency o f the two criteria for uniform nonconfounding. The concepts of homogeneity and collapsibility for causal effects are also defined, and the relation am ong confounding, homogeneity and collapsibility is discussed. We show that the common causal effect over all fine subpopulations is just the causal ef fect of the whole population.