Clustering of recurrent events data

Abstract

Nowadays data are often timestamped, thus, when analysing theevents which may occur several times (recurrent events), it is desir-able to model the whole dynamics of the counting process ratherthan to focus on a total number of events. Such kind of data canbe encountered in hospital readmissions, disease recurrences orrepeated failures of industrial systems. Recurrent events can be anal-ysed in the counting process framework, as in the Andersen–Gillmodel, assuming that the baseline intensity depends on time andon covariates, as in the Cox model. However, observed covariatesare often insufficient to explain the observed heterogeneity in thedata. We propose a mixture model for recurrent events, allowing toaccount for the unobserved heterogeneity and to perform clusteringof individuals (unsupervised classification allowing to partition of theheterogeneous data according to unobserved, or latent, variables).Within each cluster, the recurrent event process intensity is specifiedparametrically and is adjusted for covariates. Model parameters areestimated by maximum likelihood using the EM algorithm; the BICcriterion is adopted to choose an optimal number of clusters. Themodel feasibility is checked on simulated data. Real data on hospitalreadmissions of elderly people, which motivated the developmentof the proposed clustering model, are analysed. The obtained resultsallow a fine understanding of the recurrent event process in each cluster.