Identification and multiply robust estimation of causal effects via instrumental variables from an auxiliary population

TL;DR

This paper proposes new methods for estimating causal effects in a target population using instrumental variables from auxiliary populations, addressing unmeasured confounding and heterogeneity.

Contribution

It introduces the equi-confounding assumption and develops multiply robust estimators for causal inference across populations with unmeasured confounders.

Findings

The proposed estimators perform well in simulations.

They effectively recover causal effects in real data.

The methods are robust to certain model misspecifications.

Abstract

Estimating causal effects in a target population with unmeasured confounders is challenging, especially when instrumental variables (IVs) are unavailable. However, IVs from auxiliary populations with similar problems can help infer causal effects in the target population. While the homogeneous conditional average treatment effect assumption has been widely used for effect transportability, it has not been explored in IV-based data fusion. We include it as a basic approach, though it may be biased when treatment effect heterogeneity exists. As an alternative approach, we introduce the equi-confounding assumption that the unmeasured confounding bias remains the same after adjusting for observed covariates, while allowing conditional average treatment effects to differ across populations. This allows us to identify the confounding bias in the auxiliary population and remove it from the treatment-outcome association in the target population to recover the causal effect. We develop multiply robust estimators under both approaches and demonstrate them through simulation studies and a real data application.