Analysis of Multivariate Longitudinal Outcomes With Nonignorable Dropouts and Missing Covariates

Abstract

This article analyzes changes in treatment practices in outpatient methadone treatment units from a national panel study. The analysis of this dataset is challenging due to several difficulties, including multiple longitudinal outcomes, nonignorable nonresponses, and missing covariates. Specifically, the data included several variables that measure the effectiveness of methadone treatment practices for each unit. A substantial percentage of units (33%%) did not respond during the follow-up. These dropout units tended to be units with less effective treatment practices; the dropout mechanism thus may be nonignorable. Finally, the time-varying covariates for the units that dropped out were missing at the time of dropout. A valid analysis hence needs to address these three issues simultaneously. Our approach assumes that the observed outcomes measure a latent variable (e.g., treatment practice effectiveness) with error. We model the relationship between this latent variable and covariates using a linear mixed model. To account for nonignorable dropouts, we apply a selection model in which the dropout probability depends on the latent variable. Finally, we accommodate missing time-varying covariates by modeling them using a transition model. In view of multidimensional integration in full-likelihood estimation, we develop the EM algorithm to estimate the model parameters. We apply the proposed approach to the methadone treatment practices data. Our results show that methadone treatment practices have improved in the last decade. Our results are also useful for identifying the types of methadone treatment units that need improvement.

KEY WORDS:

• Em algorithm
• Latent variable model
• Missing covariate
• Multiple outcomes
• Nonignorable dropout
• Panel data
• Random-effects model