Semiparametric spatial model for interval-censored data with time-varying covariate effects

Cox regression is one of the most commonly used methods in the analysis of interval-censored failure time data. In many practical studies, the covariate effects on the failure time may not be constant over time. Time-varying coefficients are therefore of great interest due to their flexibility in capturing the temporal covariate effects. To analyze spatially correlated interval-censored time-to-event data with time-varying covariate effects, a Bayesian approach with dynamic Cox regression model is proposed. The coefficient is estimated as a piecewise constant function and the number of jump points estimated from the data. A conditional autoregressive distribution is employed to model the spatial dependency. The posterior summaries are obtained via an efficient reversible jump Markov chain Monte Carlo algorithm. The properties of our method are illustrated by simulation studies as well as an application to smoking cessation data in southeast Minnesota.