The Effect of Duration and Delay of Licensure on Risk of Crash: a Bayesian Analysis of Repeated Time-to-Event Measures

The driving history records of a sample of 13,794 Michigan public school students were followed for up to 13 years from their initial time-of-license to determine the separate effects of duration of licensure and delay of licensure on risk of crash. We propose a subject-specific lognormal accelerated failure time to model the expected time-to-crash as a function of age at time of licensure, duration of licensure, and a set of control covariates. When multiple time-to-crash measures are observed for an individual, within-subject correlation can create substantial bias in the estimation of the effect of duration of licensure under an independence model, Generalized estimating equations provide consistent estimators of the variance when independence is misspecified but do not correct for this bias, Full maximum Likelihood models generally require numerical integration and differentiation, and in practice, parameter estimates were unattainable for the dataset of interest. We instead adopt a Bayesian approach, imputing the unobserved failure times and slope-intercept random effects to account for right censoring and between-subject variability. We implement this approach using a Gibbs algorithm, We assess model fit via posterior predictive distributions, Our approach also allows for subject-specific risk estimates based on subject-level history. We compare the repeated sampling properties of this approach with those obtained using some frequentist approaches, and find that duration of licensure is a stronger predictor of risk of crash than age of licensure.