Estimation of the complier causal hazard ratio under dependent censoring

TL;DR

The paper tackles estimating the causal effect of an endogenous binary treatment on a dependently censored duration outcome by targeting the complier causal hazard ratio (CCHR). It introduces a two-stage weighted likelihood method that uses the probability of being a complier as weights, combines a semiparametric proportional hazards model for the event time with a fully parametric model for censoring, and links them via a copula with an unspecified association parameter. The authors establish identifiability under new conditions, develop nonparametric and likelihood-based estimation steps, prove consistency and asymptotic normality, and validate the approach through extensive simulations and real-data applications (notably the JTPA study) showing meaningful and robust CCHR estimates even under dependent censoring. The method advances causal inference in survival analysis when censoring is informatively dependent on the outcome and provides practical tools and code for applied researchers.

Abstract

In this work, we are interested in studying the causal effect of an endogenous binary treatment on a dependently censored duration outcome. By dependent censoring, it is meant that the duration time ($T$) and right censoring time ($C$) are not statistically independent of each other, even after conditioning on the measured covariates. The endogeneity issue is handled by making use of a binary instrumental variable for the treatment. To deal with the dependent censoring problem, it is assumed that on the stratum of compliers: (i) $T$ follows a semiparametric proportional hazards model; (ii) $C$ follows a fully parametric model; and (iii) the relation between $T$ and $C$ is modeled by a parametric copula, such that the association parameter can be left unspecified. In this framework, the treatment effect of interest is the complier causal hazard ratio (CCHR). We devise an estimation procedure that is based on a weighted maximum likelihood approach, where the weights are the probabilities of an observation coming from a complier. The weights are estimated non-parametrically in a first stage, followed by the estimation of the CCHR. Novel conditions under which the model is identifiable are given, a two-step estimation procedure is proposed and some important asymptotic properties are established. Simulations are used to assess the validity and finite-sample performance of the estimation procedure. Finally, we apply the approach to estimate the CCHR of both job training programs on unemployment duration and periodic screening examinations on time until death from breast cancer. The data come from the National Job Training Partnership Act study and the Health Insurance Plan of Greater New York experiment respectively.

Figures (2)

• Figure 1: Effect of the complier ratio on the bias and RMSE of $\alpha$
• Figure 2: Effect of the sample size on the bias and RMSE of $\alpha$

Theorems & Definitions (4)

• Lemma 1
• Theorem 1
• Theorem 2
• Theorem 3