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February 2020 Simple step-stress models with a cure fraction
Nandini Kannan, Debasis Kundu
Braz. J. Probab. Stat. 34(1): 2-17 (February 2020). DOI: 10.1214/18-BJPS409

Abstract

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.

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Nandini Kannan. Debasis Kundu. "Simple step-stress models with a cure fraction." Braz. J. Probab. Stat. 34 (1) 2 - 17, February 2020. https://doi.org/10.1214/18-BJPS409

Information

Received: 1 September 2017; Accepted: 1 July 2018; Published: February 2020
First available in Project Euclid: 3 February 2020

zbMATH: 07200388
MathSciNet: MR4058967
Digital Object Identifier: 10.1214/18-BJPS409

Rights: Copyright © 2020 Brazilian Statistical Association

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Vol.34 • No. 1 • February 2020
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