This article proposes an efficient Bayesian inference for piecewise exponential hazard (PEH) models, which allow the effect of a covariate to change over time. The proposed inference methodology is based on a particle smoothing (PS) algorithm that depends on three particle filters. Efficient proposal (importance) distributions for the particle filters tailored to the nature of survival data and PEH models are developedusing the Laplace approximation of the posterior distribution and linear Bayes theory. The algorithm is applied to both simulated and real data, and the results show that it generates an effective sample sizethat is more than two orders of magnitude larger than a state-of-the-art MCMC sampler for the samecomputing time, and scales well in high-dimensional and relatively large data.

We address a problem in inference from retrospective studies where the value of a variable is measured at the date of the survey but is used as covariate to events that have occurred long before the survey. This causes problem because the value of the current-date (anticipatory) covariate does not follow the temporal order of events. We propose a dynamic Bayesian approach for modelling jointly the anticipatory covariate and the event of interest, and allowing the effects of the anticipatory covariate to vary over time. The issues are illustrated with data on the effects of education attained by the survey-time on divorce risks among Swedish men. The overall results show that failure to adjust for the anticipatory nature of education leads to elevated relative risks of divorce across educational levels. The results are partially in accordance with previous findings based on analyses of the same data set. More importantly, our findings provide new insights in that the bias due to anticipatory covariates varies over marriage duration.