Understanding potential collider bias in external validity analysis depending on types of effect measure modifiers

Covariate selection is a challenging part of estimating effects, whether accounting for confounding or improving external validity by addressing different distributions of effect measure modifiers between a study and target population. However, current recommendations on covariate selection for external validity analyses might be misleading. We investigate how directions of causal relationships between sample membership, types of effect measure modification, and collider bias impact sufficient adjustment sets for external validity analysis. We provide a simulated example to underpin the theoretical results and examine how impacts of collider bias depend on the colliders' associations, strength of interactions and sample size. When sample membership is caused by effect measure modifiers (e.g., when sociodemographics have an effect on the probability of trial participation), conditioning on effect measure modifiers (regardless of type) does not bias target population estimates. However, in the converse scenario where effect measure modifiers are caused by sample membership (e.g., under trial engagement effects), conditioning on some types of effect measure modifiers can be problematic. This is because sample membership can become an effect measure modifier by collider conditioning. We term adjustment sets that differ in their sufficiency according to the specific causal relationships between effect measure modifiers and sample membership "selection dependent" (s-dependent) sets. It is important to note, however, that weak interactions and collider-parent associations may not be sufficient to generate substantial collider bias. Nevertheless, we argue that researchers should consider the direction of the relationships between sample membership and effect measure modifiers to avoid inducing collider bias in external validity analyses.