Testing and Estimating Causal Treatment Effect Heterogeneity in Observational Studies via Revised Deep Semiparametric Regression: A Lung Transplant Case Study

Lung transplantation programs must decide when bilateral lung transplantation (BLT) offers meaningful functional benefit over single lung transplantation (SLT). Because donor and recipient characteristics jointly shape outcomes, the BLT-SLT contrast may differ across patients. However, analyzing observational registries poses a statistical challenge: apparent subgroup differences can be artifacts of complex confounding, while true heterogeneity can be missed or poorly quantified. Using a large national registry, we investigate whether the BLT effect varies across recipients and identify clinically relevant profiles of benefit using post-transplant lung function measured by forced expiratory volume in 1 second (FEV1). We develop deepHTL, a framework that tests for treatment effect heterogeneity and estimates how the BLT-SLT effect varies with patient features. In extensive simulations designed to resemble registry-like confounding, deepHTL controls false positives for detecting heterogeneity and yields more accurate individualized effect estimates than common machine learning methods. In the lung transplant cohort, we find strong evidence of heterogeneity in the BLT-SLT effect on FEV1: younger, lower risk recipients with better baseline status show the largest FEV1 gains from BLT, whereas older, higher risk candidates exhibit diminished marginal benefit. These findings provide statistically grounded guidance for patient selection and allocation of scarce donor organs.