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Traditional methods for the analysis of longitudinal data make unrealistic assumptions regarding the underlying nature of the response process (e.g., measurements are equally correlated over time with constant variance) and typically break down in the presence of missing data. Alternative procedures, such as end-point analysis lead to biased estimates of treatment related effects by treating all individuals as if they had been measured equally. During our first two years of funding, we have developed a class of random regression models (RRM) that accommodate missing data, irregularly spaced measurement occasions, unequal variances and covariances of measurements over time, and residual autocorrelation of a variety of forms. We have clearly illustrated that these conditions are not merely statistical "luxuries," but that they epitomize real psychiatric data and Mental Health Services data in particular. The products of this work are two prototype computer programs capable of running on typical DOS based 386 and 486 microcomputers that provide RRM for continuous, ordinal, and binary data. The focus of this competitive renewal application is to further generalize these models to the case in which subjects are nested within clusters (e.g., catchment area, multimodality facility, inpatient services, specific ward or research unit, individual practitioner) and followed longitudinally. We show here that ignoring the structure within which subjects are imbedded leads to invalid inferences and tests of hypotheses. We propose to develop a "three-level" model for continuous, ordinal, and binary response data, that incorporates the advancers that we have made during our initial funding period for the two-level RRM. Our computer programs and manuals will be updated to incorporate three level problems (e.g., center, subject, and measurement occasion) and the statistical properties of the estimation procedures (e.g., power, robustness, bias) will be studied.
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