A method for analyzing longitudinal outcomes with many zeros

Health care utilization and cost data have challenged analysts because they are often correlated over time, highly skewed, and clumped at 0. Traditional approaches do not address all these problems, and evaluators of mental health and substance abuse interventions often grapple with the problem of how to analyze these data in a way that accurately represents program impact. Recently, the traditional 2-part model has been extended to mixed-effects mixed-distribution model with correlated random effects to deal simultaneously with excess zeros, skewness, and correlated observations. We introduce and demonstrate this new method to mental health services researchers and evaluators by analyzing the data from a study of assertive community treatment (ACT). The response variable is the number of days of hospitalization, collected every 6 months over 3 years. The explanatory variable is group: ACT vs. standard case management. Diagnosis (schizophrenia vs. bipolar disorder), time, and the baseline values of hospital days are covariates. Results indicate that clients in the ACT group have a higher probability of hospital admission, but tend to have shorter lengths of stay. The mixed-distribution model provides greater specification of a model to fit these data and leads to more refined interpretation of the results.