Modeling Longitudinal Data with Nonignorable Dropouts Using a Latent Dropout Class Model

• Published in: Biometrics Vol. 59; no. 4; pp. 829 - 836
• Main Author: Roy, Jason
• Format: Journal Article
• Language: English
• Published: 350 Main Street , Malden , MA 02148 , U.S.A , and P.O. Box 1354, 9600 Garsington Road , Oxford OX4 2DQ , U.K Blackwell Publishing 01.12.2003; International Biometric Society
• Subjects: Analysis of Variance; Analytical estimating; Biometrics; Biometry - methods; Data models; Depression - etiology; Female; HIV; HIV Infections - psychology; Humans; Incomplete data; Inference; Latent variable; Longitudinal data; Longitudinal Studies; Maximum likelihood estimation; Missing data; Modeling; Models, Statistical; Parametric models; Patient Dropouts; Pattern-mixture model; Repeated measures; Reproducibility of Results; School dropouts; Shared-parameter model
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/j.0006-341X.2003.00097.x

In longitudinal studies with dropout, pattern-mixture models form an attractive modeling framework to account for nonignorable missing data. However, pattern-mixture models assume that the components of the mixture distribution are entirely determined by the dropout times. That is, two subjects with the same dropout time have the same distribution for their response with probability one. As that is unlikely to be the case, this assumption made lead to classification error. In addition, if there are certain dropout patterns with very few subjects, which often occurs when the number of observation times is relatively large, pattern-specific parameters may be weakly identified or require identifying restrictions. We propose an alternative approach, which is a latent-class model. The dropout time is assumed to be related to the unobserved (latent) class membership, where the number of classes is less than the number of observed patterns; a regression model for the response is specified conditional on the latent variable. This is a type of shared-parameter model, where the shared "parameter" is discrete. Parameter estimates are obtained using the method of maximum likelihood. Averaging the estimates of the conditional parameters over the distribution of the latent variable yields estimates of the marginal regression parameters. The methodology is illustrated using longitudinal data on depression from a study of HIV in women.