Detecting multiple confounders

This paper proposes an approach for detecting multiple confounders which combines the advantages of two causal models, the potential outcome model and the causal diagram. The approach need not use a complete causal diagram as long as it is known that a known covariate set ZZ contains the parent set of the exposure E  . On the other hand, whether a covariate is or not a confounder may depend on its categorization. We introduce uniform non-confounding which implies non-confounding in any subpopulation defined by the interval of a covariate (or any pooled level for a discrete covariate). We show that the conditions in Miettinen and Cook's criteria for non-confounding also imply uniform non-confounding. Further we present an algorithm for deleting non-confounders from the potential confounder set ZZ, which extends Greenland et al.'s [1999a. Causal diagrams for epidemiologic research. Epidemiology 10, 37–48] approach by splitting ZZ into a series of potential confounder subsets. We also discuss conditions for non-confounding bias in the subpopulations in which we are interested, where the subpopulations may be defined by non-confounders.