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Nonparametric Estimation of Proportional Hazards with Monotone Baseline Hazard and Covariate Effect

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  • Yunro Chung

    (Arizona State University
    Arizona State University)

Abstract

Order-restricted inference has been applied to survival analysis when its hazard function is known to have a specific shape prior to data analysis. Under the proportional hazards assumption, the partial likelihood approach is commonly used to estimate a covariate effect on the distribution of survival time without specifying its baseline hazard function, but at the same time, the shape information of the baseline hazard function cannot be used in the partial liklelihood estimation procedure. In this paper, we propose a nonparametric full likelihood method for estimating the covariate effect and baseline hazard functions simultaneously under monotone shape restriction. We develop an efficient algorithm using generalized isotonic regression techniques. We extend the algorithm to model with time-dependent covariates. Simulation studies demonstrate that the proposed full likelihood method shows smaller variance than the partial likelihood approach with reduction of bias. Analysis of data from a bone marrow transplantation study illustrates the practical utility of the isotonic methodology in estimating a nonlinear and monotone hazard function.

Suggested Citation

  • Yunro Chung, 2024. "Nonparametric Estimation of Proportional Hazards with Monotone Baseline Hazard and Covariate Effect," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 16(3), pages 787-800, December.
    • Handle: RePEc:spr:stabio:v:16:y:2024:i:3:d:10.1007_s12561-024-09420-1
    DOI: 10.1007/s12561-024-09420-1
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    References listed on IDEAS

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    1. Hendrik P. Lopuhaä & Gabriela F. Nane, 2013. "Shape Constrained Non-parametric Estimators of the Baseline Distribution in Cox Proportional Hazards Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 619-646, September.
    2. Yunro Chung & Anastasia Ivanova & Michael G Hudgens & Jason P Fine, 2018. "Partial likelihood estimation of isotonic proportional hazards models," Biometrika, Biometrika Trust, vol. 105(1), pages 133-148.
    3. Jian-Jian Ren & Mai Zhou, 2011. "Full likelihood inferences in the Cox model: an empirical likelihood approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(5), pages 1005-1018, October.
    4. Jianhua Z. Huang & Linxu Liu, 2006. "Polynomial Spline Estimation and Inference of Proportional Hazards Regression Models with Flexible Relative Risk Form," Biometrics, The International Biometric Society, vol. 62(3), pages 793-802, September.
    5. Chung, Daehyun & Chang, Myron N., 1994. "An isotonic estimator of the baseline hazard function in Cox's regression model under order restriction," Statistics & Probability Letters, Elsevier, vol. 21(3), pages 223-228, October.
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