Re-examining and calibrating weighted survival analysis for causal inference

TL;DR

This paper re-examines weighted survival analysis methods for causal inference, linking them to augmented inverse probability weighting, and develops calibrated methods that improve confidence interval coverage and precision.

Contribution

It introduces new calibrated survival analysis methods with theoretical backing, addressing limitations of existing weighted approaches in both low- and high-dimensional settings.

Findings

Calibrated methods achieve better coverage proportions.

Calibrated methods produce shorter confidence intervals.

Empirical application demonstrates improved inference for treatment effects.

Abstract

Causal inference with time-to-event outcomes is fundamental in various scientific studies. In a static setup with fitted propensity scores, weighted Kaplan-Meier estimation for survival probabilities and weighted Breslow-Peto estimation for hazard ratios have been widely used, but their statistical properties have been overlooked or studied only to a limited extent. We re-examine the weighted Kaplan-Meier method by formally linking it with the general framework of augmented inverse probability weighted estimation including both point and variance estimation. Furthermore, to address limitations of existing weighted methods for survival analysis, we develop new methods and associated theory through calibrated estimation in both low-dimensional and high-dimensional settings. We present a simulation study and an empirical application on the effectiveness of adjunctive psychotropic treatments for patients with schizophrenia. The calibrated methods yield coverage proportions closer to target ones in the simulation study, and produce shorter confidence intervals in both simulation and empirical studies.