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Partial likelihood estimation of isotonic proportional hazards models.
Biometrika 2018; 105(1):133-148B

Abstract

We consider the estimation of the semiparametric proportional hazards model with an unspecified baseline hazard function where the effect of a continuous covariate is assumed to be monotone. Previous work on nonparametric maximum likelihood estimation for isotonic proportional hazard regression with right-censored data is computationally intensive, lacks theoretical justification, and may be prohibitive in large samples. In this paper, partial likelihood estimation is studied. An iterative quadratic programming method is considered, which has performed well with likelihoods for isotonic parametric regression models. However, the iterative quadratic programming method for the partial likelihood cannot be implemented using standard pool-adjacent-violators techniques, increasing the computational burden and numerical instability. The iterative convex minorant algorithm which uses pool-adjacent-violators techniques has also been shown to perform well in related parametric likelihood set-ups, but evidences computational difficulties under the proportional hazards model. An alternative pseudo-iterative convex minorant algorithm is proposed which exploits the pool-adjacent-violators techniques, is theoretically justified, and exhibits computational stability. A separate estimator of the baseline hazard function is provided. The algorithms are extended to models with time-dependent covariates. Simulation studies demonstrate that the pseudo-iterative convex minorant algorithm may yield orders-of-magnitude reduction in computing time relative to the iterative quadratic programming method and the iterative convex minorant algorithm, with moderate reductions in the bias and variance of the estimators. Analysis of data from a recent HIV prevention study illustrates the practical utility of the isotonic methodology in estimating nonlinear, monotonic covariate effects.

Authors+Show Affiliations

Public Health Sciences Division, Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue North, Seattle, Washington 98109, U.S.A.Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A.Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A.Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A.

Pub Type(s)

Journal Article

Language

eng

PubMed ID

29808076

Citation

Chung, Yunro, et al. "Partial Likelihood Estimation of Isotonic Proportional Hazards Models." Biometrika, vol. 105, no. 1, 2018, pp. 133-148.
Chung Y, Ivanova A, Hudgens MG, et al. Partial likelihood estimation of isotonic proportional hazards models. Biometrika. 2018;105(1):133-148.
Chung, Y., Ivanova, A., Hudgens, M. G., & Fine, J. P. (2018). Partial likelihood estimation of isotonic proportional hazards models. Biometrika, 105(1), pp. 133-148. doi:10.1093/biomet/asx064.
Chung Y, et al. Partial Likelihood Estimation of Isotonic Proportional Hazards Models. Biometrika. 2018 Mar 1;105(1):133-148. PubMed PMID: 29808076.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Partial likelihood estimation of isotonic proportional hazards models. AU - Chung,Yunro, AU - Ivanova,Anastasia, AU - Hudgens,Michael G, AU - Fine,Jason P, Y1 - 2017/12/05/ PY - 2018/5/30/entrez PY - 2018/5/29/pubmed PY - 2018/5/29/medline KW - Algorithmic convergence KW - Concavity KW - Constrained partial likelihood KW - Isotonic regression KW - Shape-restricted inference SP - 133 EP - 148 JF - Biometrika JO - Biometrika VL - 105 IS - 1 N2 - We consider the estimation of the semiparametric proportional hazards model with an unspecified baseline hazard function where the effect of a continuous covariate is assumed to be monotone. Previous work on nonparametric maximum likelihood estimation for isotonic proportional hazard regression with right-censored data is computationally intensive, lacks theoretical justification, and may be prohibitive in large samples. In this paper, partial likelihood estimation is studied. An iterative quadratic programming method is considered, which has performed well with likelihoods for isotonic parametric regression models. However, the iterative quadratic programming method for the partial likelihood cannot be implemented using standard pool-adjacent-violators techniques, increasing the computational burden and numerical instability. The iterative convex minorant algorithm which uses pool-adjacent-violators techniques has also been shown to perform well in related parametric likelihood set-ups, but evidences computational difficulties under the proportional hazards model. An alternative pseudo-iterative convex minorant algorithm is proposed which exploits the pool-adjacent-violators techniques, is theoretically justified, and exhibits computational stability. A separate estimator of the baseline hazard function is provided. The algorithms are extended to models with time-dependent covariates. Simulation studies demonstrate that the pseudo-iterative convex minorant algorithm may yield orders-of-magnitude reduction in computing time relative to the iterative quadratic programming method and the iterative convex minorant algorithm, with moderate reductions in the bias and variance of the estimators. Analysis of data from a recent HIV prevention study illustrates the practical utility of the isotonic methodology in estimating nonlinear, monotonic covariate effects. SN - 0006-3444 UR - https://www.unboundmedicine.com/medline/citation/29808076/Partial_likelihood_estimation_of_isotonic_proportional_hazards_models_ L2 - https://academic.oup.com/biomet/article-lookup/doi/10.1093/biomet/asx064 DB - PRIME DP - Unbound Medicine ER -