## 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.