  We propose autoregressive Bayesian semi-parametric models for waiting times
between recurrent events. The aim is two-fold: inference on the effect of
possibly time-varying covariates on the gap times and clustering of individuals
based on the time trajectory of the recurrent event. Time-dependency between
gap times is taken into account through the specification of an autoregressive
component for the random effects parameters influencing the response at
different times. The order of the autoregression may be assumed unknown and
object of inference and we consider two alternative approaches to perform model
selection under this scenario. Covariates may be easily included in the
regression framework and censoring and missing data are easily accounted for.
As the proposed methodologies lies within the class of Dirichlet process
mixtures, posterior inference can be performed through efficient MCMC
algorithms. We illustrate the approach through simulations and medical
applications involving recurrent hospitalizations of cancer patients and
successive urinary tract infections.
