  The stratified proportional hazards model represents a simple solution to
account for heterogeneity within the data while keeping the multiplicative
effect on the hazard function. Strata are typically defined a priori by
resorting to the values taken by a categorical covariate. A general framework
is proposed, which allows for the stratification of a generic accelerated life
time model, including as a special case the Weibull proportional hazard model.
The stratification is determined a posteriori by taking into account that
strata might be characterized by different baseline survivals as well as
different effects of the predictors. This is achieved by considering a Bayesian
nonparametric mixture model and the posterior distribution it induces on the
space of data partitions. The optimal stratification is then identified by
means of the variation of information criterion and, in turn, stratum-specific
inference is carried out. The performance of the proposed method and its
robustness to the presence of right-censored observations are investigated by
means of an extensive simulation study. A further illustration is provided by
the analysis of a data set extracted from the University of Massachusetts AIDS
Research Unit IMPACT Study.
