Nonparametric estimation of survival functions by means of partial exchangeability structures

In the causal analysis of survival data a time-based response is related to a set of explanatory variables. However, selection and proper design of the latter may become a difficult task, particularly in the preliminary stage, when the information is limited. We propose an alternative nonparametric approach to estimate the survival function which allows one to evaluate the relative importance of each potential explanatory variable, in a simple and exploratory fashion. To achieve this aim, each of the explanatory variables is used to partition the observed survival times. The observations are assumed to be partially exchangeable according to such partition. We then consider, conditionally on each partition, a hierarchical nonparametric Bayesian model on the hazard functions. In order to measure the importance of each explanatory variable, we derive the posterior probability of the corresponding partition. Such probabilities are then employed to estimate the hazard functions by averaging the estimated conditional hazard over the set of all entertained partitions.