Jason Roy, University of Michigan

Analysis of Multivariate Longitudinal Outcomes With Non-Ignorable Dropouts and Missing Covariates: Changes in Methadone Treatment Practices

We consider the analysis of data from a national panel study on changes in the treatment practices of outpatient methadone treatment units. The analysis of this data set is challenging due to several difficulties: multiple longitudinal outcomes; non-ignorable non-responses; and missing covariates. Specifically, several variables were used to measure the effectiveness of methadone treatment practices for each unit. A substantial number of units did not respond (33%) during the follow-up. These dropout units tended to be units with less effective treatment practices and were hence non-ignorable. Finally, for the units that dropped out, their time-varying covariates were missing at the time of dropout. We propose a latent variable model for multivariate longitudinal outcomes, where the observed outcomes are related to a latent variable (e.g., treatment practices effectiveness), and the latent variable is associated with covariates through a linear mixed model. A selection model is then developed to model non-ignorable dropouts, where the dropout probability depends on the latent variable. To accommodate missing time-varying covariates at the time of dropout, a transition model for these covariates is proposed. Maximum likelihood estimates are obtained using the EM algorithm. We also investigate the asymptotic bias of parameter estimates when missing time-varying covariates are filled in using a naive approach such as last observation carried forward.