On the proportional hazards model with last observation carried forward covariates

  • Hongyuan CaoEmail author
  • Jason P. Fine


Standard partial likelihood methodology for the proportional hazards model with time-dependent covariates requires knowledge of the covariates at the observed failure times, which is not realistic in practice. A simple and commonly used estimator imputes the most recently observed covariate prior to each failure time, which is known to be biased. In this paper, we show that a weighted last observation carried forward approach may yield valid estimation. We establish the consistency and asymptotic normality of the weighted partial likelihood estimators and provide a closed form variance estimator for inference. The estimator may be conveniently implemented using standard software. Interestingly, the convergence rate of the estimator is slower than the parametric rate achieved with fully observed covariates but the same as that obtained with all lagged covariate values. Simulation studies provide numerical support for the theoretical findings. Data from an Alzheimer’s study illustrate the practical utility of the methodology.


Convergence rates Kernel weighted estimation Last value imputation Partial likelihood Time-varying covariates 


Supplementary material

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10463_2019_739_MOESM6_ESM.r (7 kb)
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Supplementary material 7 (R 5 KB)


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2019

Authors and Affiliations

  1. 1.School of MathematicsJilin UniversityChangchunChina
  2. 2.Department of StatisticsFlorida State UniversityTallahasseeUSA
  3. 3.Department of BiostatisticsUniversity of North Carolina at Chapel HillChapel HillUSA

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