Maximum Likelihood Estimation for Shape-restricted Single-index Hazard Models

Qin, Jing; Sun, Yifei; Yuan, Ao; Huang, Chiung-Yu

doi:10.6339/22-JDS1061

Journal of Data Science

Maximum Likelihood Estimation for Shape-restricted Single-index Hazard Models

Volume 21, Issue 4 (2023), pp. 681–695

Jing Qin Yifei Sun Ao Yuan All authors (4)

https://doi.org/10.6339/22-JDS1061

Pub. online: 4 November 2022 Type: Statistical Data Science

Open Access

Received
2 June 2022

Accepted
5 July 2022

Published
4 November 2022

Abstract

Single-index models are becoming increasingly popular in many scientific applications as they offer the advantages of flexibility in regression modeling as well as interpretable covariate effects. In the context of survival analysis, the single-index hazards models are natural extensions of the Cox proportional hazards models. In this paper, we propose a novel estimation procedure for single-index hazard models under a monotone constraint of the index. We apply the profile likelihood method to obtain the semiparametric maximum likelihood estimator, where the novelty of the estimation procedure lies in estimating the unknown monotone link function by embedding the problem in isotonic regression with exponentially distributed random variables. The consistency of the proposed semiparametric maximum likelihood estimator is established under suitable regularity conditions. Numerical simulations are conducted to examine the finite-sample performance of the proposed method. An analysis of breast cancer data is presented for illustration.

Supplementary material

Supplementary Material

The Supplementary Material includes the proof of Theorem 2, additonal simulation results, and the R code to implement the proposed method.

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2023 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.

Open access article under the CC BY license.

Keywords

isotonic regression pool-adjacent-violators algorithm profile likelihood semiparametric estimation

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