Regression Analysis of Spatially Correlated Event Durations With Missing Origins Annotated by Longitudinal Measures

This paper is concerned with event durations in situations where the 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. The first-hitting-time model (e.g. Lee and Whitmore, 2006) is employed 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 consistency and asymptotic normality of the estimators, and present their variance estimation. The proposed approach is illustrated with a collection of wildfire records from Alberta, Canada. Its performance is examined numerically and compared with two competitors via simulation.