On two-step residual inclusion estimator for instrument variable additive hazards model

ABSTRACT

Instrumental variable (IV) methods are popular in non-experimental settings to estimate the causal effects of scientific interventions. These approaches allow for the consistent estimation of treatment effects even if major confounders are unavailable. There have been some extensions of IV methods to survival analysis recently. We specifically consider the two-step residual inclusion (2SRI) estimator proposed recently in the literature for the additive hazards regression model in this paper. Assuming linear structural equation models for the hazard function, we may attain a closed-form, two-stage estimator for the causal effect in the additive hazards model. The main contribution of this paper is to provide theoretical works for the 2SRI approach. The asymptotic properties of the estimators are rigorously established and the resulting inferences are shown to perform well in numerical studies.

KEYWORDS:

• Additive hazards model
• independent censoring
• instrumental variable
• two-stage least squares estimation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was partially supported by AcRF [grant number R-155-000-152-112];, National Medical Research Council in Singapore; the Early Career Scheme from Hong Kong Research Grants Council [grant number PolyU 253023/16P].

Notes on contributors

Binyan Jiang

Dr Binyan Jiang is an assistant professor in the Department of Applied Mathematics, The Hong Kong Polytechnic University. His research interests include high-dimensional data analysis, and survival analysis.

Jialiang Li

Jialiang Li is an associate professor in the Department of Statistics & Applied Probability, National University of Singapore, the Duke-NUS Graduate Medical School and the Singapore Eye Research Institute. His current research interests are semi-parametric analysis, longitudinal data, high-dimensional data, diagnostic medicine, and survival analysis.

Jason Fine

Jason Fine is a full professor with tenure jointly appointed in the Department of Biostatistics and the Department of Statistics and Operations Research at the University of North Carolina, Chapel Hill. He has extensive experience in statistical methodology development and collaborative research related to observation studies and clinical trials, survival data, genetics and imaging data, and statistical methods in diagnostic medicine.