Simple Step-Stress Models with a Cure Fraction

TL;DR

This paper introduces a new class of parametric step-stress models incorporating a cure fraction, utilizing an EM algorithm for estimation, and evaluates their performance with altitude decompression sickness data.

Contribution

It extends the cumulative risk model to include a cure fraction and develops an EM algorithm for parameter estimation in this context.

Findings

The proposed models effectively fit altitude decompression sickness data.

The EM algorithm provides reliable maximum likelihood estimates.

Models with cure fraction outperform traditional models in certain scenarios.

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. \cite{KKNT:2010} 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.