  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.
