A new MM algorithm for constrained estimation in the proportional hazards model

Jieli Ding, Guo-Liang Tian and Kam Chuen Yuen

Computational Statistics & Data Analysis, 2015, vol. 84, issue C, 135-151

Abstract: The constrained estimation in Cox’s model for the right-censored survival data is studied and the asymptotic properties of the constrained estimators are derived by using the Lagrangian method based on Karush–Kuhn–Tucker conditions. A novel minorization–maximization (MM) algorithm is developed for calculating the maximum likelihood estimates of the regression coefficients subject to box or linear inequality restrictions in the proportional hazards model. The first M-step of the proposed MM algorithm is to construct a surrogate function with a diagonal Hessian matrix, which can be reached by utilizing the convexity of the exponential function and the negative logarithm function. The second M-step is to maximize the surrogate function with a diagonal Hessian matrix subject to box constraints, which is equivalent to separately maximizing several one-dimensional concave functions with a lower bound and an upper bound constraint, resulting in an explicit solution via a median function. The ascent property of the proposed MM algorithm under constraints is theoretically justified. Standard error estimation is also presented via a non-parametric bootstrap approach. Simulation studies are performed to compare the estimations with and without constraints. Two real data sets are used to illustrate the proposed methods.

Keywords: Asymptotic properties; Bootstrap approach; Constrained estimation; Karush–Kuhn–Tucker conditions; MM algorithm; Proportional hazards model (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:84:y:2015:i:c:p:135-151

DOI: 10.1016/j.csda.2014.11.005

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