Bayesian estimation of a proportional hazards model for double-censored durations

Double-censored data consist of uncensored, left- and right-censored observations and occur in survival time analysis. In this paper, parametric Bayes estimation is investigated for a proportional hazards model with durations subject to double-censoring. We prove consistency and asymptotic normality of the posterior mean with the Bernstein–von Mises theorem. In addition, we estimate asymptotic standard errors. A simulation study shows that the finite-sample performance is similar to that of the maximum likelihood estimator. Finally, the proposed model is applied to rating transition data. The analysis suggests that an upgrade of a rating increases the duration in that class by about 10 days on average.