Modelling and analysis of time in-homogeneous recurrent event processes in a heterogeneous population: A case study of HRTs

In this work we present a method for the statistical analysis of continually monitored data arising in a recurrent diseases problem. The model enables individual level inference in the presence of time transience and population heterogeneity. This is achieved by applying Bayesian hierarchical modelling, where marked point processes are used as descriptions of the individual data, with latent variables providing a means of modelling long range dependence and transience over time. In addition to providing a sound probabilistic formulation of a rather complex data set, the proposed method is also successful in prediction of future outcomes. Computational difficulties arising from the analytic intractability of this Bayesian model were solved by implementing the method into the BUGS software and using standard computational facilities. We illustrate this approach by an analysis of a data set on hormone replacement therapies (HRTs). The data contain, in the form of diaries on bleeding patterns maintained by individual patients, detailed information on how they responded to different HRTs. The proposed model is able to capture the essential features of these treatments as well as provide realistic individual level predictions on the future bleeding patterns.