Multiply robust estimation of causal effects using linked data

TL;DR

This paper develops multiply robust estimators for causal effects in linked observational data, addressing unmeasured confounding and selection bias through multiple identification strategies and combining estimators for improved robustness.

Contribution

It introduces triply robust estimators that remain consistent if any one of three data components is correctly modeled, advancing causal inference with linked data.

Findings

Estimators are consistent under at least one correct model component.

Simulation studies demonstrate estimator robustness and efficiency.

Application to real data confirms practical utility.

Abstract

Unmeasured confounding presents a common challenge in observational studies, potentially making standard causal parameters unidentifiable without additional assumptions. Given the increasing availability of diverse data sources, exploiting data linkage offers a potential solution to mitigate unmeasured confounding within a primary study of interest. However, this approach often introduces selection bias, as data linkage is feasible only for a subset of the study population. To address this concern, we explore three nonparametric identification strategies under the assumption that a unit' s inclusion in the linked cohort is determined solely by the observed confounders, while acknowledging that the ignorability assumption may depend on some partially unobserved covariates. The existence of multiple identification strategies motivates the development of estimators that effectively capture distinct components of the observed data distribution. Appropriately combining these estimators yields triply robust estimators for the average treatment effect. These estimators remain consistent if at least one of the three distinct parts of the observed data law is correct. Moreover, they are locally efficient if all the models are correctly specified. We evaluate the proposed estimators using simulation studies and real data analysis.