Stratified Regression Analysis of Zero-Truncated Recurrent Event Data

This paper is motivated by an ongoing pediatric mental health care (PMHC) program in which records of mental health-related emergency department (MHED) visits are extracted from population-based administrative databases. A particular interest of this paper is to understand how the visit occurrence depends on the occurrences in the past in a general population. Only information on subjects experiencing MHED visits is available within a subject-specific time window. Thus, the MHED visits may be viewed as zero-truncated recurrent events. Some population census information can be utilized as supplementary information on the covariates of subjects without MHED visits during the study period. We consider an innovative stratified Cox regression model, which is an intensity-based model but requiring only a summary of the event history. We propose an estimation procedure with zero-truncated data integrated with some supplementary information. We establish the consistency and asymptotic normality of the proposed estimator. The finite-sample properties of the estimator are evaluated by simulation, which demonstrates improved performance of the proposed estimator over the maximum likelihood estimator based on zero-truncated data only. We use the PMHC program to illustrate the proposed approach throughout the paper.