Abstract: In this study, we examine event durations when study units may be spatially correlated and the time origins of the events are missing. We develop regression models based on the partly observed durations with the aid of available longitudinal information. We use the first-hitting-time model to link the data of event durations and the associated longitudinal measures with shared random effects. We present procedures for estimating the model parameters and an induced estimator of the conditional distribution of the event duration. We apply the EM algorithm and Monte Carlo methods to compute the proposed estimators. We establish the consistency and asymptotic normality of the estimators, and present their variance estimation. We demonstrate the proposed approach using a collection of wildfire records from Alberta, Canada. We also examine its performance numerically, and compare it with that of two competitors using simulation.

Key words and phrases: Asymptomatic event, EM algorithm and Monte Carlo method, first hitting time, joint modelling, mixed effects model.