A Bayesian Time-Varying Coefficient Model for Multi-Type Recurrent Events

This paper proposes a Bayesian time-varying coefficient model to evaluate the temporal profile of intensity for multi-type recurrent events. The model obtains smooth estimates for both time-varying coefficients and the baseline intensity using Bayesian penalized splines. One major challenge in Bayesian penalized splines is that the smoothness of a spline fit is sensitive to the subjective choice of hyperparameters. We establish a procedure to objectively determine the hyperparameters through robust prior specification. To effectively update the high-dimensional spline parameters, we develop a Markov chain Monte Carlo procedure based on the Metropolis-adjusted Langevin algorithms. A joint sampling scheme is used to achieve better convergence and mixing properties. A simulation study confirms satisfactory model performance in estimating time-varying coefficients under different curvature and event rate scenarios. Application to a commercial truck driver naturalistic driving data reveals that drivers with 7-hours-or-less sleep time have a significantly higher safety-critical event intensity after 8 hours of driving and the intensity remains high after taking a break. The findings provide crucial information for the truck driver hours-of-service regulation and fatigue management. The proposed model provides a flexible and robust tool to evaluate the temporal profile of intensity for multi-type recurrent events.