A potential outcomes approach to selection bias

Along with confounding, selection bias is one of the fundamental threats to the validity of epidemiologic research. Unlike confounding, it has yet to be given a standard definition in terms of potential outcomes. Traditionally, selection bias has been defined as a systematic difference in a measure of the exposure-disease association in the study population and the population eligible for inclusion. This definition depends on the parameterization of the association between exposure and disease. The structural approach to selection bias defines selection bias as a spurious exposure-disease association within the study population that occurs when selection is a collider or a descendant of a collider on a causal path from exposure to disease in the eligible population. This definition covers only selection bias that can occur under the null hypothesis. Here, we propose a definition of selection bias in terms of potential outcomes that identifies selection bias whenever disease risks and exposure prevalences are distorted by the selection of study participants, not just a given measure of association (as in the traditional approach) or all measures of association (as in the structural approach). This definition is nonparametric, so it can be analyzed using causal graphs both under and away from the null. It unifies the theoretical frameworks used to understand selection bias and confounding, explicitly links selection to the estimation of causal effects, distinguishes clearly between internal and external validity, and simplifies the analysis of complex study designs.