Nonparametric survival regression using the beta-Stacy process

A novel class of hierarchical nonparametric Bayesian survival regression models for time-to-event data with uninformative right censoring is introduced. The survival curve is modeled as a random function whose prior distribution is defined using the beta-Stacy (BS) process. The prior mean of each survival probability and its prior variance are linked to a standard parametric survival regression model. This nonparametric survival regression can thus be anchored to any reference parametric form, such as a proportional hazards or an accelerated failure time model, allowing substantial departures of the predictive survival probabilities when the reference model is not supported by the data. Also, under this formulation the predictive survival probabilities will be close to the empirical survival distribution near the mode of the reference model and they will be shrunken towards its probability density in the tails of the empirical distribution.Examples of our approach are presented using a Weibull-centered BS process whose variance decreases proportionally to the centering Weibull probability density function. By the conjugacy of the BS process to random right censoring, marginal posterior inferences for the survival probabilities and for the regression coefficients are approximated using the standard Gibbs sampler. Three applications of the BS Weibull survival regression model are illustrated, focussing on toxicological and clinical data and comparing the BS model estimates with those of standard parametric and semi-parametric survival regressions.