Estimating Group Average Treatment Effects in High-Risk Populations with Unobserved Target Membership

Abstract

Estimating treatment effects within a prespecified high-risk population is challenging. When risk status is unobserved or the target population is small, analyses restricted to high-risk individuals can be unstable or inefficient. We propose a risk-score-weighted soft-targeting (RSW) estimator for group average treatment effects in high-risk populations. It accommodates two settings: when high-risk status is observed, the membership probability can be estimated within the analysis sample; when unobserved, it can be obtained from a reference model using covariates in the analysis sample. RSW uses these probabilities to represent the target population, learns a doubly robust treatment effect in the full sample, and aggregates a low-dimensional treatment-effect surface over the risk-weighted target distribution. We establish pointwise asymptotic normality and an influence-function-based variance estimator. In simulations with continuous and binary outcomes, RSW had similar bias and lower variance than two hard-targeting alternatives. Sensitivity analyses showed that the gain persisted when treatment-effect sufficiency was violated, although RSW bias increased under strong violations. We applied the method to the All of Us study to estimate effects of non-GLP antidiabetic and antihypertensive medication use on mild cognitive impairment (MCI)-free time restricted at 48 months within comorbidity-defined high-risk subgroups. We estimated the risk score in a nonoverlapping internal reference sample and applied it to the outcome-analysis sample. This illustrates how soft targeting can improve precision while retaining an interpretable high-risk target population.