Proximal Methods for Causally Interpretable Meta-analysis

Abstract

Causally interpretable meta-analysis (CIMA) extends conventional meta-analysis by transporting treatment effects from multiple randomized controlled trials to a prespecified target population. Existing CIMA methods assume that all shifted effect modifiers required for transportability are adequately captured by observed covariates. In practice, however, important effect modifiers may be partially observed or completely unobserved, limiting the applicability of these methods. In this thesis, we develop a proximal extension of CIMA for settings with unmeasured shifted effect modifiers. Building on proximal causal inference and proximal indirect comparison, we show that proximal indirect comparison cannot be directly adapted to CIMA because pooling multiple randomized trials induces an unmeasured treatment assignment mechanism in the source population. To address this challenge, we introduce proximal bridge functions and derive identification formulas for treatment-specific mean potential outcomes under a set of proximal assumptions. Based on these identification results, we propose outcome regression, inverse probability weighting, and doubly robust estimators for the target potential outcome means. Simulation studies demonstrate clear improvements over the original CIMA estimators in the presence of unmeasured shifted effect modifiers, while maintaining good finite-sample performance under a range of simulation settings.