
Hierarchical hazard rates for partially exchangeable survival times
Federico Camerlenghi, Bocconi University
Survival analysis represents one among the first areas of applications of Bayesian nonparametric techniques. A large amount of literature has been developed to model prior distributions of hazard rates for exchangeable, and possibly censored, survival times. Exchangeability corresponds to assuming homogeneity among the data, which is quite restrictive in a large variety of applied problems where data are generated by different experiments. Even if these experiments may be related, they represent a source of heterogeneity that cannot be accommodated for by the exchangeability assumption. Hence, one needs to resort to more general dependence structures. In such situations partial exchangeability is a more suitable assumption. Here we define a novel class of dependent random hazard rates, which work as prior distributions in presence of partially exchangeable survival times. They are expressed as mixtures of kernels with respect to a vector of hierarchical completely random measures, which has the advantage to enable dependence across the diverse groups of observations. We characterize the posterior distribution of the hierarchical completely random measures, which is the key tool to estimate the survival functions through a Markov chain Monte Carlo algorithm. Besides we are able to obtain reliable credible intervals for the estimated quantities developing a novel and efficient Ferguson & Klass–type algorithm, that avoids to marginalize out the infinite–dimensional random elements of the model. Finally we concentrate on some illustrative examples, both real and simulated, to show the benefits of the whole construction (joint work with Antonio Lijoi and Igor Prünster).

