Two-Stage Residual Inclusion under the Additive Hazards Model - An Instrumental Variable Approach with Application to SEER-Medicare Linked Data

TL;DR

This paper extends the two-stage residual inclusion (2SRI) method under the additive hazards model to accommodate binary treatments and generalized linear relationships, providing theoretical properties and practical application to prostate cancer data.

Contribution

It introduces a generalized 2SRI estimator for survival data with competing risks, allowing nonlinear treatment-instrument relationships and deriving its asymptotic properties.

Findings

The 2SRI estimator has desirable asymptotic properties.

Simulation studies demonstrate accurate finite-sample performance.

Application to SEER-Medicare data illustrates practical utility.

Abstract

Instrumental variable is an essential tool for addressing unmeasured confounding in observational studies. Two stage predictor substitution (2SPS) estimator and two stage residual inclusion(2SRI) are two commonly used approaches in applying instrumental variables. Recently 2SPS was studied under the additive hazards model in the presence of competing risks of time-to-events data, where linearity was assumed for the relationship between the treatment and the instrument variable. This assumption may not be the most appropriate when we have binary treatments. In this paper, we consider the 2SRI estimator under the additive hazards model for general survival data and in the presence of competing risks, which allows generalized linear models for the relation between the treatment and the instrumental variable. We derive the asymptotic properties including a closed-form asymptotic variance estimate for the 2SRI estimator. We carry out numerical studies in finite samples, and apply our methodology to the linked Surveillance, Epidemiology and End Results (SEER) - Medicare database comparing radical prostatectomy versus conservative treatment in early-stage prostate cancer patients.