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Modeling Bivariate Zero- Inflated Longitudinal Ordinal Data: an Application to Marijuana and Cocaine Use

Keywords: ordinal, probit model, Zero-inflated, longitudinal, bivariate

Ordinal response data such as severity of pain, degree of disability, satisfaction with healthcare provider are prevalent in many areas of research including biomedical and social science research. Besides the ordinal nature of the data, there are often excess zeros occurring when measuring abnormal behavior such as illicit drug use, symptom and side effect of rare diseases. For example, in the Drug Abuse and Treatment Outcome Study (DATOS), where a cohort of adolescents were followed prospectively to study the effectiveness of adolescent drug treatment, the outcome data are ordinal data with excess zeros. Zero inflation in ordinal categorical data coupled with longitudinal structure makes it difficult to analyze and interpret. The traditional multinomial logit or probit model is not very appropriate to analyze such data. We propose a zero-inflated bivariate ordinal probit model to analyze longitudinal ordered categorical data with excess zeros. The methods proposed are illustrated with a real application of marijuana and Cocaine use data from DATOS, 1991-1994 and the results are compared with the existing methods.