Clustering of recurrent events data

Nowadays data are often timestamped, thus, when analysing the events which may occur several times (recurrent events), it is desirable to model the whole dynamics of the counting process rather than to focus on a total number of events. Such kind of data can be encountered in hospital readmissions, disease recurrences or repeated failures of industrial systems. Recurrent events can be analysed in the counting process framework, as in the Andersen–Gill model, assuming that the baseline intensity depends on time and on covariates, as in the Cox model. However, observed covariates are often insufficient to explain the observed heterogeneity in the data. We propose a mixture model for recurrent events, allowing to account for the unobserved heterogeneity and to perform clustering of individuals (unsupervised classification allowing to partition of the heterogeneous data according to unobserved, or latent, variables). Within each cluster, the recurrent event process intensity is specified parametrically and is adjusted for covariates. Model parameters are estimated by maximum likelihood using the EM algorithm; the BIC criterion is adopted to choose an optimal number of clusters. The model feasibility is checked on simulated data. Real data on hospital readmissions of elderly people, which motivated the development of the proposed clustering model, are analysed. The obtained results allow a fine understanding of the recurrent event process in each cluster.