Simple step-stress models with a cure fraction

作     者：Kannan, Nandini Kundu, Debasis 

作者机构：Natl Sci Fdn Div Math Sci Arlington VA 22230 USA Indian Inst Technol Kanpur Dept Math & Stat Kanpur 208016 Uttar Pradesh India 

出 版 物：《BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS》 (Braz. J. Prob. Stat.)

年 卷 期：2020年第34卷第1期

页      面：2-17页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：NSF IR/D program 

主　　题：Cumulative exposure model step-stress tests cured fraction maximum likelihood estimation EM algorithm 

摘      要：In this article, we consider models for time-to-event data obtained from experiments in which stress levels are altered at intermediate stages during the observation period. These experiments, known as step-stress tests, belong to the larger class of accelerated tests used extensively in the reliability literature. The analysis of data from step-stress tests largely relies on the popular cumulative exposure model. However, despite its simple form, the utility of the model is limited, as it is assumed that the hazard function of the underlying distribution is discontinuous at the points at which the stress levels are changed, which may not be very reasonable. Due to this deficiency, Kannan et al. (Journal of Applied Statistics 37 (2010b) 1625-1636) introduced the cumulative risk model, where the hazard function is continuous. In this paper, we propose a class of parametric models based on the cumulative risk model assuming the underlying population contains long-term survivors or cured fraction. An EM algorithm to compute the maximum likelihood estimators of the unknown parameters is proposed. This research is motivated by a study on altitude decompression sickness. The performance of different parametric models will be evaluated using data from this study.