Instrumental variable estimation of dynamic treatment effects on a duration outcome

TL;DR

This paper develops an instrumental variable approach to estimate the causal effect of treatment timing on survival outcomes, addressing endogeneity and censoring in a nonparametric framework with practical estimation procedures.

Contribution

It introduces a novel integral equation-based identification method for dynamic treatment effects with censored duration data, and proposes a parametric estimation approach with asymptotic properties.

Findings

Estimator shows good finite sample performance in simulations

Method provides evidence supporting therapy efficacy for burn-out

Identification relies on solving an integral equation for the regression function

Abstract

This paper considers identification and estimation of the causal effect of the time Z until a subject is treated on a survival outcome T. The treatment is not randomly assigned, T is randomly right censored by a random variable C and the time to treatment Z is right censored by min(T,C). The endogeneity issue is treated using an instrumental variable explaining Z and independent of the error term of the model. We study identification in a fully nonparametric framework. We show that our specification generates an integral equation, of which the regression function of interest is a solution. We provide identification conditions that rely on this identification equation. For estimation purposes, we assume that the regression function follows a parametric model. We propose an estimation procedure and give conditions under which the estimator is asymptotically normal. The estimators exhibit good finite sample properties in simulations. Our methodology is applied to find evidence supporting the efficacy of a therapy for burn-out.