A likelihood approach to analysing longitudinal bivariate binary data

Abstract

To study the effect of methadone treatment in reducing multiple drug use, say heroin and benzodiazepines while controlling for their possible interaction, we analyse the results of urine drug screens from patients in treatment at a Sydney clinic in 1986. Weekly tests are either positive or negative for each type of drug and a bivariate binary model was developed to analyse such repeated bivariate binary outcomes. It models simultaneously the logit of each type of drug use and their log odds ratio linearly in some covariates. The serial correlation within subject is accounted for by including the previous outcome of both drugs and their interaction as covariates. Our main conclusion is that drug use is reduced over time and the interaction between dose and time effects is not significant. It also suggests that while methadone maintenance is effective in reducing heroin use (CHAN et al., 1995), it does not suppress non-opioid drug use. Concerning the association between the two drugs, it is found that the present strength of their association depends on the previous outcomes only through a measure of concordance. The proposed model has a tractable likelihood function and so a full likelihood analysis is possible. It can be easily extended to incorporate mixture effects. The EM algorithm is used for the estimation of parameters in the mixture model and model selection can be based on the Akaike Information Criterion.