A State-Space Model for Bivariate Time-Series Counts with Excessive Zeros: An Application to Workplace Injury Data

Bivariate time-series counts with excessive zeros frequently occur in medical, biological, social, and environmental sciences. An appropriate analysis of such data must account for serial correlation over time, cross correlation between bivariate responses, and excessive zeros. We first introduce a serially correlated random effect series shared by both responses to account for a common temporal trend. The shared temporal random effects can also characterize the correlation between two responses. Given the common temporal random effects, we incorporate a compound Poisson random effect series into a Poisson model for each response to capture excessive zeros and additional variation. Our approach models zero and positive parts of the responses in an integral way. Our approach also unifies marginal modeling and conditional modeling analyses. We develop a quasi-likelihood approach for the estimation of the model parameters. Our method is illustrated with the analysis of musculoskeletal and non-musculoskeletal workplace injuries recorded every four weeks on a group of hospital cleaners over a seven-year period. Performance of the proposed model is evaluated through simulation studies.