Graphical tools for detection and control of selection bias with multiple exposures and samples

TL;DR

This paper introduces graphical tools based on potential outcomes and conditional separable effects to detect and control selection bias across multiple exposures and samples, simplifying identification in complex study designs.

Contribution

It presents an alternative formulation of the potential outcomes framework that handles multiple, nested, or overlapping samples and time-dependent exposures, extending existing methods.

Findings

Simplifies identification conditions for selection bias.

Provides examples for case-cohort and time-dependent exposures.

Extends graphical tools to complex sampling scenarios.

Abstract

Among recent developments in definitions and analysis of selection bias is the potential outcomes approach of Kenah (Epidemiology, 2023), which allows non-parametric analysis using single-world intervention graphs, linking selection of study participants to identification of causal effects. Mohan & Pearl (JASA, 2021) provide a framework for missing data via directed acyclic graphs augmented with nodes indicating missingness for each sometimes-missing variable, which allows for analysis of more general missing data problems but cannot easily encode scenarios in which different groups of variables are observed in specific subsamples. We give an alternative formulation of the potential outcomes framework based on conditional separable effects and indicators for selection into subsamples. This is practical for problems between the single-sample scenarios considered by Kenah and the variable-wise missingness considered by Mohan & Pearl. This simplifies identification conditions and admits generalizations to scenarios with multiple, potentially nested or overlapping study samples, as well as multiple or time-dependent exposures. We give examples of identifiability arguments for case-cohort studies, multiple or time-dependent exposures, and direct effects of selection.