Partial likelihood estimation of isotonic proportional hazards models.

TitlePartial likelihood estimation of isotonic proportional hazards models.
Publication TypeJournal Article
Year of Publication2018
AuthorsChung, Yunro, Anastasia Ivanova, Michael G. Hudgens, and Jason P. Fine
Date Published2018 Mar 01

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.

Alternate JournalBiometrika
Original PublicationPartial likelihood estimation of isotonic proportional hazards models.
PubMed ID29808076
PubMed Central IDPMC5969539
Grant ListP01 CA142538 / CA / NCI NIH HHS / United States
P30 AI050410 / AI / NIAID NIH HHS / United States
R01 AI029168 / AI / NIAID NIH HHS / United States
R37 AI029168 / AI / NIAID NIH HHS / United States