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

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  • Ding, Jieli
  • Tian, Guo-Liang
  • Yuen, Kam Chuen

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.

Suggested Citation

  • Ding, Jieli & Tian, Guo-Liang & Yuen, Kam Chuen, 2015. "A new MM algorithm for constrained estimation in the proportional hazards model," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 135-151.
    • Handle: RePEc:eee:csdana:v:84:y:2015:i:c:p:135-151
    DOI: 10.1016/j.csda.2014.11.005
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    References listed on IDEAS

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    Cited by:

    1. Deng, Lifeng & Ding, Jieli & Liu, Yanyan & Wei, Chengdong, 2018. "Regression analysis for the proportional hazards model with parameter constraints under case-cohort design," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 194-206.
    2. Xifen Huang & Jinfeng Xu & Yunpeng Zhou, 2023. "Exploring Complex Survival Data through Frailty Modeling and Regularization," Mathematics, MDPI, vol. 11(21), pages 1-14, October.

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