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Partial likelihood estimation of isotonic proportional hazards models
Biometrika ( IF 2.7 ) Pub Date : 2017-12-05 , DOI: 10.1093/biomet/asx064
Yunro Chung 1 , Anastasia Ivanova 2 , Michael G Hudgens 2 , Jason P Fine 2
Affiliation  

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.

中文翻译:

等渗比例风险模型的偏似然估计

我们考虑具有未指定基线风险函数的半参数比例风险模型的估计,其中假设连续协变量的影响是单调的。以前关于使用右删失数据的等张比例风险回归的非参数最大似然估计的工作计算量很大,缺乏理论依据,并且在大样本中可能会令人望而却步。本文研究了偏似然估计。考虑了迭代二次规划方法,该方法在等渗参数回归模型的似然性方面表现良好。然而,部分似然的迭代二次规划方法不能使用标准池相邻违反器技术实现,增加了计算负担和数值不稳定性。使用池相邻违反者技术的迭代凸次要算法也已被证明在相关的参数似然设置中表现良好,但证明了在比例风险模型下的计算困难。提出了一种替代的伪迭代凸次要算法,该算法利用池相邻违反者技术,理论上是合理的,并且表现出计算稳定性。提供了一个单独的基线危险函数估计器。这些算法扩展到具有时间相关协变量的模型。仿真研究表明,相对于迭代二次规划方法和迭代凸次要算法,伪迭代凸次要算法可以在计算时间上产生数量级的减少,适度减少估计量的偏差和方差。最近一项 HIV 预防研究的数据分析说明了等渗方法在估计非线性、单调协变量效应方面的实际效用。
更新日期:2017-12-05
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