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.

N1 - Funding Information:
This project was supported by the Center for Drug Evaluation and Research administered by the Oak Ridge Institute for Science and Education through an agreement between the U.S. Department of Energy and the U.S. Food and Drug Administration, the University of North Carolina Center for AIDS Research and the U.S. Centers for Disease Control and Prevention and the U.S. National Institutes of Health. The content is solely the responsibility of the authors and does not represent the official views of any of the organizations above. The authors thank the Breastfeeding, Antiretroviral and Nutrition investigators for access to the data.
Publisher Copyright:
© 2017 Biometrika Trust.

PY - 2018/3/1

Y1 - 2018/3/1

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.

AB - 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.

KW - Algorithmic convergence

KW - Concavity

KW - Constrained partial ikelihood

KW - Isotonic regression

KW - Robustness

KW - Shape-restricted inference

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U2 - 10.1093/biomet/asx064

DO - 10.1093/biomet/asx064

M3 - Article

AN - SCOPUS:85043265327

VL - 105

SP - 133

EP - 148

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 1

ER -