Propensity score weighted Cox regression for survival outcomes in observational studies with multiple or factorial treatments

2026-01-30

AI Summary

This study addresses the challenge of estimating causal marginal hazard ratios for survival outcomes under multiple or factorial treatments in observational studies—a setting where existing methods are largely restricted to binary comparisons. The authors propose a novel approach that integrates multi-treatment propensity score weighting with a marginal Cox model, using treatment indicator variables to estimate causal marginal hazard ratios relative to a common reference. For the first time, propensity score weighting—including inverse probability and overlap weighting—is extended to marginal Cox regression under both multi-treatment and factorial designs. The paper establishes the consistency of the proposed estimator and derives a robust sandwich variance estimator. The method is successfully applied to a real-world comparative analysis of three anti-obesity medications on heart failure risk, and an accompanying R package, ‘PSsurvival’, is released to facilitate broader implementation.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Multiagent Systems: Mechanism Design

Application Category

• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In observational studies with survival or time-to-event outcomes, a propensity score weighted marginal Cox proportional hazard model with the treatment variable as the only predictor is commonly used to estimate the causal marginal hazard ratio between two treatments. Observational studies often have more than two treatments, but corresponding analysis methods are limited. In this paper, we combine the propensity score weighting method for multiple treatments and a marginal Cox model with indicators for each treatment to estimate the causal hazard ratios between multiple treatments and a common reference treatment. We illustrate two weighting schemes: inverse probability of treatment weighting and overlap weighting. We prove the consistency of the maximum weighted partial likelihood estimator of the causal marginal hazard ratio and derive a robust sandwich variance estimator. As an important special case of multiple treatments, we elaborate the Cox model for two-way factorial treatments. We apply the method to evaluate the real-world comparative effectiveness of three types of anti-obesity medications on heart failure. We develop an associated R package'PSsurvival'.

Problem

• propensity score weighting
• Cox regression
• multiple treatments
• factorial treatments
• causal hazard ratio

Innovation

• propensity score weighting
• marginal Cox model
• multiple treatments
• factorial treatments
• causal hazard ratio