Estimation of separable direct and indirect effects in continuous time

TL;DR

This paper develops new methods for estimating causal direct and indirect effects in continuous-time survival analysis, addressing challenges in causal interpretation of traditional estimands and providing robust estimators with practical applications.

Contribution

It introduces nonparametric influence function-based and semiparametric estimators for separable effects in continuous time, with proven asymptotic properties and simulation validation.

Findings

Estimators perform well in finite samples

Proposed methods are robust to model misspecification

Application to prostate cancer trial demonstrates practical utility

Abstract

Many research questions involve time-to-event outcomes that can be prevented from occurring due to competing events. In these settings, we must be careful about the causal interpretation of classical statistical estimands. In particular, estimands on the hazard scale, such as ratios of cause specific or subdistribution hazards, are fundamentally hard to be interpret causally. Estimands on the risk scale, such as contrasts of cumulative incidence functions, do have a causal interpretation, but they only capture the total effect of the treatment on the event of interest; that is, effects both through and outside of the competing event. To disentangle causal treatment effects on the event of interest and competing events, the separable direct and indirect effects were recently introduced. Here we provide new results on the estimation of direct and indirect separable effects in continuous time. In particular, we derive the nonparametric influence function in continuous time and use it to construct an estimator that has certain robustness properties. We also propose a simple estimator based on semiparametric models for the two cause specific hazard functions. We describe the asymptotic properties of these estimators, and present results from simulation studies, suggesting that the estimators behave satisfactorily in finite samples. Finally, we re-analyze the prostate cancer trial from Stensrud et al (2020).