Data Integration for Estimating Subgroup-Specific Conditional Average Treatment Effects (CATEs) Using Coarsened External Information in Randomized Trials

TL;DR

This paper introduces a novel James-Stein-type estimator that leverages coarsened external data to improve subgroup-specific treatment effect estimates in RCTs, especially when internal data are sparse.

Contribution

It develops a new shrinkage estimator that combines internal and external data for finer subgroup CATE estimation, accommodating population differences.

Findings

The estimator outperforms traditional methods in simulations.

It detects subgroup effects not visible with internal data alone.

Application to weight-loss trials reveals significant subgroup differences.

Abstract

Randomized controlled trials (RCTs) are often underpowered to detect treatment heterogeneity in subgroups defined by cross-classifications of multiple covariates, due to sparse sample sizes in some strata. External RCT data can help, but typically provide treatment effect estimates at a coarser level (e.g., by sex or race) rather than for the finer subgroups of interest (e.g., race-by-sex). We propose a novel James-Stein (JS)-type estimator that borrows strength from such coarsened external estimates to improve estimation of finer subgroup-specific conditional average treatment effects (CATEs) in an internal study, while accommodating potential incompatibility in marginal CATEs across populations. Based on asymptotic theory, we derive a practical analytic variance estimator for the JS estimator that exhibits acceptable empirical performance. Under mild conditions, we show that the proposed estimator uniformly dominates the ordinary least squares (OLS) estimator based on internal data regarding a weighted quadratic loss. Simulation studies demonstrate favorable performance compared with existing shrinkage methods, including empirical Bayes and generalized ridge estimators. We illustrate our method by estimating race-by-sex subgroup CATEs in a tirzepatide weight-loss trial (SURMOUNT-1), borrowing sex-specific and race-specific estimates from two previous semaglutide trials (STEP 1 and STEP 2). The proposed method detects a significantly larger treatment effect on percentage weight loss in the female-White subgroup than in the female-Asian subgroup, a difference not detected using internal data alone.