A potential outcomes approach to selection bias
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Selection bias occurs when the association between exposure and disease in the study population differs from that in the population eligible for inclusion. Along with confounding, it is one of the fundamental threats to the validity of epidemiologic research. In this paper, we propose a definition of selection bias in terms of potential outcomes. This approach generalizes the structural approach of Hernan et al. (2004), which defines selection bias as a distortion of the exposure-disease association that is caused by conditioning on a collider. Both approaches agree in all situations where the structural approach identifies selection bias, but the potential outcomes approach identifies selection bias in situations where the earlier approach does not. Selection bias defined by potential outcomes can involve a collider at exposure, a collider at disease, or no collider at all. This broader definition of selection bias does not depend on the parameterization of the association between exposure and disease, so it can be analyzed using nonparametric single-world intervention graphs (SWIGs) both under the null hypothesis and away from it. It provides a more nuanced interpretation of the role of randomization in clinical trials, simplifies the analysis of matched studies and case cohort studies, and distinguishes more clearly between the estimation of causal effects within the study population and generalization to the eligible population. This analysis of selection bias is an important theoretical and practical application of SWIGs in epidemiology.
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