A potential outcomes approach to selection bias

We propose a novel definition of selection bias in analytical epidemiology using potential outcomes. This definition captures selection bias under both the structural approach (where conditioning on selection into the study opens a noncausal path from exposure to disease in a directed acyclic graph) and the traditional definition (where a given measure of association differs between the study population and the population eligible for inclusion). It is nonparametric, so selection bias under this approach can be analyzed using single-world intervention graphs both under and away from the null hypothesis. It allows the simultaneous analysis of confounding and selection bias, and it can be adapted to handle selection bias in descriptive epidemiology. The potential outcomes approach explicitly links the selection of study participants to the measures of association that can be estimated using study data, and we prove that analytical selection bias must be handled more carefully than descriptive selection bias for all measures of association. Through examples, we show that this approach provides a novel perspective on the variety of mechanisms that can generate selection bias and that it simplifies the analysis of selection bias in matched studies and case-cohort studies.