Abstract:
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We propose methods for analyzing longitudinal data that have several complications: multiple outcomes; nonignorable dropouts; and missing covariates. In particular, we consider the situation where the outcome of interest is not observable, but several related outcomes are available. In longitudinal studies, there is often the added complication that some units drop out of the study--causing both the outcomes and time-varying covariates to have some missing values. Our approach assumes the observed outcomes measure the outcome of interest (a latent variable) 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, where 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 multi-dimensional integration in full-likelihood estimation, we develop the EM algorithm to estimate the model parameters. We apply the proposed approach data on the treatment practices of methadone treatment units.
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