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Lifetime Data Analysis

, Volume 22, Issue 4, pp 570–588 | Cite as

Cox regression with missing covariate data using a modified partial likelihood method

  • Torben Martinussen
  • Klaus K. Holst
  • Thomas H. Scheike
Article

Abstract

Missing covariate values is a common problem in survival analysis. In this paper we propose a novel method for the Cox regression model that is close to maximum likelihood but avoids the use of the EM-algorithm. It exploits that the observed hazard function is multiplicative in the baseline hazard function with the idea being to profile out this function before carrying out the estimation of the parameter of interest. In this step one uses a Breslow type estimator to estimate the cumulative baseline hazard function. We focus on the situation where the observed covariates are categorical which allows us to calculate estimators without having to assume anything about the distribution of the covariates. We show that the proposed estimator is consistent and asymptotically normal, and derive a consistent estimator of the variance–covariance matrix that does not involve any choice of a perturbation parameter. Moderate sample size performance of the estimators is investigated via simulation and by application to a real data example.

Keywords

Cox model Missing covariate data Recursive estimation  Survival data 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Torben Martinussen
    • 1
  • Klaus K. Holst
    • 1
  • Thomas H. Scheike
    • 1
  1. 1.Department of BiostatisticsUniversity of CopenhagenCopenhagen KDenmark

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