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On the proportional hazards model with last observation carried forward covariates

Author

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  • Hongyuan Cao

    (Jilin University
    Florida State University)

  • Jason P. Fine

    (University of North Carolina at Chapel Hill)

Abstract

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.

Suggested Citation

  • Hongyuan Cao & Jason P. Fine, 2021. "On the proportional hazards model with last observation carried forward covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 115-134, February.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:1:d:10.1007_s10463-019-00739-x
    DOI: 10.1007/s10463-019-00739-x
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    References listed on IDEAS

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    1. Hongyuan Cao & Mathew M. Churpek & Donglin Zeng & Jason P. Fine, 2015. "Analysis of the Proportional Hazards Model With Sparse Longitudinal Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1187-1196, September.
    2. Jane Xu & Scott L. Zeger, 2001. "Joint analysis of longitudinal data comprising repeated measures and times to events," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(3), pages 375-387.
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