Bayesian nonparametric bivariate survival regression for current status data

We consider nonparametric inference for event time distributions based on current status data. We show that in this scenario conventional mixture priors, including the popular Dirichlet process mixture prior, lead to uninterpretable results as they unnaturally skew the probability mass for the event times toward the extremes of the observed data. Simple assumptions on dependent censoring can fix the problem. We extend the model to bivariate current status data with partial ordering of the two outcomes. In addition to dependent censoring, we exploit some minimal known structure relating the two event times to represent dependence across the two outcomes. We design a Markov chain Monte Carlo algorithm for posterior simulation. Applied to a recurrent infection study, the method provides novel insights into how symptoms-related hospital visits are affected by covariates. This is joint work with Giorgio Paulon (UT Austin, US) and Giancarlo Sal y Rosas (PUCP, Peru).