The Analysis of Methadone Clinic Data Using Marginal and Conditional Logistic Models with Mixture or Random Effects

The paper develops methods for the statistical analysis of outcomes of methadone maintenance treatment (MMT). Subjects for this study were a cohort of patients entering MMT in Sydney in 1986. Urine drug tests on these subjects were performed weekly during MMT, and were reported as either positive or negative for morphine, the marker of recent heroin use. To allow correlation between the repeated binary measurements, a marginal logistic model was fitted using the generalized estimating equation (GEE) approach and the alternating logistic regression approach. Conditional logistic models are also considered. Results of separate fitting to each patient and score tests suggest that there is substantial between-patient variation in response to MMT. To account for the population heterogeneity and to facilitate subject-specific inference, the conditional logistic model is extended by introducing random intercepts. The two, three and four group mixture models are also investigated. The model of best fit is a three group mixture model, in which about a quarter of the subjects have a poor response to MMT, with continued heroin use independent of daily dose of methadone; about a quarter of the subjects have a very good response, with little or no heroin use, again independent of dose; and about half the subjects responded in a dose-dependent fashion, with reduced heroin use while receiving higher doses of methadone. These findings are consistent with clinical experience. There is also an association between reduced drug use and increased duration in treatment. The mixture model is recommended since it is quite tractable in terms of estimation and model selection as well as being supported by clinical experience.