[Paper Review] Addressing Extreme Propensity Scores in Estimating Counterfactual Survival Functions via the Overlap Weights

Chao Cheng, Fan Li+2 more|arXiv (Cornell University)|Aug 10, 2021

Advanced Causal Inference Techniques4 citations

TL;DR

This paper proposes overlap weighting estimators that combine propensity score weighting and inverse probability of censoring weighting to improve estimation of counterfactual survival functions in observational studies with time-to-event outcomes. The method reduces bias and variance compared to standard inverse probability weighting, especially when covariate overlap between treatment groups is low.

ABSTRACT

The inverse probability weighting approach is popular for evaluating treatment effects in observational studies, but extreme propensity scores could bias the estimator and induce excessive variance. Recently, the overlap weighting approach has been proposed to alleviate this problem, which smoothly down-weighs the subjects with extreme propensity scores. Although advantages of overlap weighting have been extensively demonstrated in literature with continuous and binary outcomes, research on its performance with time-to-event or survival outcomes is limited. In this article, we propose two weighting estimators that combine propensity score weighting and inverse probability of censoring weighting to estimate the counterfactual survival functions. These estimators are applicable to the general class of balancing weights, which includes inverse probability weighting, trimming, and overlap weighting as special cases. We conduct simulations to examine the empirical performance of these estimators with different weighting schemes in terms of bias, variance, and 95% confidence interval coverage, under various degree of covariate overlap between treatment groups and censoring rate. We demonstrate that overlap weighting consistently outperforms inverse probability weighting and associated trimming methods in bias, variance, and coverage for time-to-event outcomes, and the advantages increase as the degree of covariate overlap between the treatment groups decreases.

Motivation & Objective

• To address the issue of extreme propensity scores in estimating counterfactual survival functions using observational data.
• To improve estimation accuracy and precision in survival analysis when treatment and control groups have limited covariate overlap.
• To extend the overlap weighting approach—previously used for continuous and binary outcomes—to time-to-event outcomes with censoring.
• To evaluate the performance of overlap weighting relative to inverse probability weighting and trimming under varying degrees of covariate overlap and censoring rates.

Proposed method

• Proposes two weighting estimators that integrate propensity score weighting with inverse probability of censoring weighting to adjust for both treatment assignment and censoring.
• Applies the general class of balancing weights, including inverse probability weighting, trimming, and overlap weighting, as special cases.
• Uses overlap weights that smoothly down-weight units with extreme propensity scores to stabilize estimation.
• Employs weighted estimating equations to produce consistent estimators of the counterfactual survival function.
• Applies variance estimation techniques that account for the weighting structure to construct valid confidence intervals.
• Employs simulation studies to compare performance across different weighting schemes under controlled scenarios.

Experimental results

Research questions

• RQ1 How does overlap weighting compare to inverse probability weighting and trimming in estimating counterfactual survival functions under varying degrees of covariate overlap?
• RQ2 What is the impact of censoring rate on the performance of different weighting schemes in survival outcome estimation?
• RQ3 Does overlap weighting reduce bias and variance in survival function estimation when propensity scores are extreme?
• RQ4 How does the degree of covariate overlap between treatment groups affect the relative performance of weighting methods?
• RQ5 Do overlap weighting estimators maintain adequate 95% confidence interval coverage under realistic simulation conditions?

Key findings

• Overlap weighting consistently outperforms inverse probability weighting and trimming in terms of bias, variance, and 95% confidence interval coverage for time-to-event outcomes.
• The performance advantage of overlap weighting increases as the degree of covariate overlap between treatment groups decreases.
• Overlap weighting maintains good coverage properties even under high censoring rates, where traditional methods show increased coverage error.
• Bias and mean squared error are significantly reduced under overlap weighting compared to inverse probability weighting when extreme propensity scores are present.
• The proposed estimators achieve better balance in covariate distributions across treatment groups, leading to more reliable counterfactual survival estimates.
• Simulation results show that overlap weighting provides more stable estimates with lower variance, especially in scenarios with limited overlap.