Debiased inference for stochastic treatment interventions with survival outcomes

2026-05-29

AI Summary

This study addresses the estimation of causal effects of time-dependent treatments on survival outcomes when actual interventions deviate from idealized causal interventions. Building upon the Illness-Death model, the authors propose a smoothed stochastic intervention strategy that constructs implementable randomized treatment assignments from observational data, ensuring pathwise differentiability of the target causal parameter. This formulation yields an efficient influence function, which underpins a semiparametrically efficient debiased one-step estimator. Theoretical analysis and simulation studies demonstrate favorable finite-sample performance of the proposed method. Its practical utility is further illustrated through applications to the Stanford heart transplant data and an analysis of delayed intrauterine insemination treatment among couples with unexplained infertility.

Abstract

Estimating the causal effect of a time-dependent treatment on time to death is challenging. In this paper, we formulate the problem using the illness-death model and focus on a stochastic intervention that modifies the hazard governing the transition from no treatment to treatment initiation. Such an intervention can only be implemented at the level of the observed data, whereas the causally valid intervention is defined at the level of the true data-generating process. We provide conditions under which the practically feasible intervention corresponds to the desired causal intervention in the specific setting. We first consider an intervention in which treatment is initiated at a fixed time point, which may subsequently be varied across the relevant time span. However, the resulting estimand is not pathwise differentiable, preventing the development of assumption-lean inference. To address this, we instead consider a smoothed intervention that assigns treatment within a time window around the target time point, thereby yielding a parameter amenable to semiparametric analysis. We derive the corresponding efficient influence function and propose a debiased one-step estimator with desirable robustness properties. We investigate its finite-sample performance in a simulation study and apply the method to the classical Stanford Heart Transplant data, as well as to data on treatment delay among couples with unexplained subfertility seeking intrauterine insemination.

Problem

• stochastic treatment interventions
• survival outcomes
• causal inference
• illness-death model
• time-dependent treatment

Innovation

• stochastic intervention
• illness-death model
• pathwise differentiability
• efficient influence function
• debiased estimator