Bayesian criterion‐based assessments of recurrent event models with applications to commercial truck driver behavior studies

Multitype recurrent events are commonly observed in transportation studies, since commercial truck drivers may encounter different types of safety critical events (SCEs) and take different lengths of on‐duty breaks in a driving shift. Bayesian nonhomogeneous Poisson process models are a flexible approach to jointly model the intensity functions of the multitype recurrent events. For evaluating and comparing these models, the deviance information criterion (DIC) and the logarithm of the pseudo‐marginal likelihood (LPML) are studied and Monte Carlo methods are developed for computing these model assessment measures. We also propose a set of new concordance indices (C‐indices) to evaluate various discrimination abilities of a Bayesian multitype recurrent event model. Specifically, the within‐event C‐index quantifies adequacy of a given model in fitting the recurrent event data for each type, the between‐event C‐index provides an assessment of the model fit between two types of recurrent events, and the overall C‐index measures the model's discrimination ability among multiple types of recurrent events simultaneously. Moreover, we jointly model the incidence of SCEs and on‐duty breaks with driving behaviors using a Bayesian Poisson process model with time‐varying coefficients and time‐dependent covariates. An in‐depth analysis of a real dataset from the commercial truck driver naturalistic driving study is carried out to demonstrate the usefulness and applicability of the proposed methodology.