When multiple time-to-event measures are made for an individual, within-subject correlation can create substantial bias in the estimation of the effect of duration under a working 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 in practice parameter estimates were unstable. A subject-specific log-normal accelerated failure time (AFT) is proposed to model the expected time-to-event. A Bayesian approach is utilized, imputing the unobserved failure times and slope-intercept random effects to account for right censoring and between-subject variability. This model is used to determine the separate effects of duration of licensure and delay of licensure on risk of crash for a sample of 13,794 Michigan public school students who were followed for up to 13 years from their initial licensure. A combination of Gibbs and Metropolis algorithms are used to construct the inference for the target quantities of interest. Model fit is assessed via posterior predictive distributions.
R code used to obtain draws from a repeated time-to-event model with non-informative censoring and a random slope-intercept structure (USE AT YOUR OWN RISK!!!)