  In this article we suggest a new statistical approach considering survival
heterogeneity as a breakpoint model in an ordered sequence of time to event
variables. The survival responses need to be ordered according to a numerical
covariate. Our esti- mation method will aim at detecting heterogeneity that
could arise through the or- dering covariate. We formally introduce our model
as a constrained Hidden Markov Model (HMM) where the hidden states are the
unknown segmentation (breakpoint locations) and the observed states are the
survival responses. We derive an efficient Expectation-Maximization (EM)
framework for maximizing the likelihood of this model for a wide range of
baseline hazard forms (parametrics or nonparametric). The posterior
distribution of the breakpoints is also derived and the selection of the number
of segments using penalized likelihood criterion is discussed. The performance
of our survival breakpoint model is finally illustrated on a diabetes dataset
where the observed survival times are ordered according to the calendar time of
disease onset.
