Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series B, Pt. 1, 70--103

APPLICATIONS OF MIXED-EFFECTS MODELS IN BIOSTATISTICS

By

ROBERT D. GIBBONS,

and

DONALD HEDEKER, University of Illinois at Chicago

SUMMARY. We present recent developments in mixed-effects models relevant to application in biostatistics. The major focus is on application of mixed-effects models to analysis of longitudinal data in general and longitudinal controlled clinical trials in detail. We present application of mixed-effects models to the case of unbalanced longitudinal data with complex residual error structures for continuous, binary and ordinal outcome measures for data with two and three levels of nesting (eg a multi-center longitudinal clinical trial). We also examine other applications of mixed-effects models in the biological and behavioral sciences, such as analysis of clustered data, and simultaneous assessment of multiple biologic endpoints (eg multivariate probit analysis). We describe the general statistical theory and then present relevant examples of these models to problems in the biological sciences.

AMS (1991) subject classification. 92B15.

Key words and phrases. mixed models, longitudinal data, binary data, ordinal data, empirical Bayes, missing data.

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