Ensuring Valid Inference for Cox Hazard Ratios After Variable Selection

Author:

Van Lancker Kelly12ORCID,Dukes Oliver1ORCID,Vansteelandt Stijn1ORCID

Affiliation:

1. Department of Applied Mathematics, Computer Science and Statistics, Ghent University , Ghent , Belgium

2. Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health , Baltimore, Maryland , USA

Abstract

Abstract The problem of how to best select variables for confounding adjustment forms one of the key challenges in the evaluation of exposure effects in observational studies, and has been the subject of vigorous recent activity in causal inference. A major drawback of routine procedures is that there is no finite sample size at which they are guaranteed to deliver exposure effect estimators and associated confidence intervals with adequate performance. In this work, we will consider this problem when inferring conditional causal hazard ratios from observational studies under the assumption of no unmeasured confounding. The major complication that we face with survival data is that the key confounding variables may not be those that explain the censoring mechanism. In this paper, we overcome this problem using a novel and simple procedure that can be implemented using off-the-shelf software for penalized Cox regression. In particular, we will propose tests of the null hypothesis that the exposure has no effect on the considered survival endpoint, which are uniformly valid under standard sparsity conditions. Simulation results show that the proposed methods yield valid inferences even when covariates are high-dimensional.

Funder

Fulbright Association

Belgian American Educational Foundation

Fonds Wetenschappelijk Onderzoek

Agentschap Innoveren en Ondernemen

Bijzonder Onderzoeksfonds UGent

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,General Agricultural and Biological Sciences,General Immunology and Microbiology,General Biochemistry, Genetics and Molecular Biology,General Medicine,Statistics and Probability

Reference23 articles.

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4. Regularization for Cox's proportional hazards model with np-dimensionality;Bradic;The Annals of Statistics,2011

5. Regression models and life-tables;Cox;Journal of the Royal Statistical Society: Series B (Methodological),1972

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