Toward a Clearer Definition of Selection Bias When Estimating Causal Effects

Abstract

Selection bias remains a subject of controversy. Existing definitions of selection bias are ambiguous. To improve communication and the conduct of epidemiologic research focused on estimating causal effects, we propose to unify the various existing definitions of selection bias in the literature by considering any bias away from the true causal effect in the referent population (the population before the selection process), due to selecting the sample from the referent population, as selection bias. Given this unified definition, selection bias can be further categorized into two broad types: type 1 selection bias owing to restricting to one or more level(s) of a collider (or a descendant of a collider) and type 2 selection bias owing to restricting to one or more level(s) of an effect measure modifier. To aid in explaining these two types-which can co-occur-we start by reviewing the concepts of the target population, the study sample, and the analytic sample. Then, we illustrate both types of selection bias using causal diagrams. In addition, we explore the differences between these two types of selection bias, and describe methods to minimize selection bias. Finally, we use an example of "M-bias" to demonstrate the advantage of classifying selection bias into these two types.

Figure 1:

Relationships between target population, study sample, and analytic sample. Note that, in addition to selection bias, threats to internal validity also includes confounding and measurement bias.

Figure 2:

examples of type 1 selection bias. E is exposure, D is outcome, S is selection, L (i.e., L1, L2) are covariates. The dashed line indicates the potential hidden cause.

Figure 2:

examples of type 1 selection bias. E is exposure, D is outcome, S is selection, L (i.e., L1, L2) are covariates. The dashed line indicates the potential hidden cause.

Figure 3:

two basic causal diagrams for type 2 selection bias. E is exposure, D is outcome, S is selection, L (i.e., L1, L2) is covariates.

Figure 4:

A typical example of “M-bias”. E is exposure, D is outcome, S is selection, L (i.e., L1, L2) is covariates.