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In this article we suggest a new statistical approach considering survivalheterogeneity as a breakpoint model in an ordered sequence of time to eventvariables. The survival responses need to be ordered according to a numericalcovariate. Our esti- mation method will aim at detecting heterogeneity thatcould arise through the or- dering covariate. We formally introduce our modelas a constrained Hidden Markov Model (HMM) where the hidden states are theunknown segmentation (breakpoint locations) and the observed states are thesurvival responses. We derive an efficient Expectation-Maximization (EM)framework for maximizing the likelihood of this model for a wide range ofbaseline hazard forms (parametrics or nonparametric). The posteriordistribution of the breakpoints is also derived and the selection of the numberof segments using penalized likelihood criterion is discussed. The performanceof our survival breakpoint model is finally illustrated on a diabetes datasetwhere the observed survival times are ordered according to the calendar time ofdisease onset.

A Change-Point Model for Detecting Heterogeneity in Ordered Survival Responses