Classification non supervis{é}e des processus d'{é}v{é}nements r{é}currents

Abstract: Event of the same type occurring several times for one individual (recurrent events) are present in various domains (industrial systems reliability, episodes of unemployment, political conflicts, chronic diseases episodes). Analysis of such kind of data should account for the whole recurrence process dynamics rather than only focusing on the number of observed events. Statistical models for recurrent events analysis are developed in the counting process probabilistic framework. One of the often-used models is the Andersen-Gill model, a generalization of the well-known Cox model for durations, which assumes that the baseline intensity of the recurrence process is time-dependent and is adjusted for covariates. For an individual i with covariates Xi, the intensity is as follows: $\lambda${ik}(t;$\theta$) = $\lambda$_0(t) exp (X_i $\beta$). The baseline intensity can be specified parametrically, in a form of Weibull: $\lambda$_0 (t) = $\gamma${1} $\gamma${2} t^{$\gamma$_2-1}, with $\gamma$1 scale parameter et $\gamma$2 shape parameter. However, the observed covariates are often insufficient to explain the observed heterogeneity in data. This is often the case of clinical trials data containing information on patients. In this article a mixture model for recurrent events analysis is proposed. This model allows to account for unobserved heterogeneity and to cluster individuals according to their recurrence process. The intensity of the process is parametrically specified within each class and depend on observed covariates. Thus, the intensity becomes specific to class k: $\lambda${ik} (t; $\theta$k) = $\gamma${1k} $\gamma${2k} t^{$\gamma${2k}-1} exp (X_i $\beta$_k). The model parameters are estimated by the Maximum Likelihood method, using the EM algorithm. The BIC criterion is employed to choose the optimal number of classes. Model feasibility is verified by Monte Carlo simulations. An application to real data concerning hospital readmissions of elderly patients is proposed. The proposed model feasibility is empirically verified (the optimization algorithm converges, providing non-biased estimates). The real data application allows to identify two clinically relevant classes of patients.