A generalized model of logistic regression for clustered data

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Abstract
This paper proposes a generalized logistic regression model that can account for the correlation among responses on subunits. The subunits may arise as data on multiple observations within an individual. This method generalizes earlier work by Rosner (1984 a,b) and others. Methodological generalizations include: (1) the use of the more general Polya-Eggenberger distribution instead of the beta-binomial distribution to model the correlation structure, so that cases with negative, positive, or zero intraclass correlation can be handled; (2) a stepwise approach; (3) linear and non-linear regression; and, (4) the inclusion of the case of a truncated distribution. The model can accommodate missing data and covariates on the unit and subunit level. The derivative-free simplex algorithm is used to estimate the parameters. The model is applied to data describing the progression of obstruction in coronary disease where multiple arterial segments are studied for each patient. The correlation in response that may exist for these multiple segments is accounted for in the analyses while attempting to examine associations with individual-specific (e.g., history of diabetes) and segment-specific (e.g., initial percent stenosis) covariates. Analyses were performed on a data set describing 382 patients with unoperated coronary artery disease and two coronary angiograms separated by at least one month and on a data set describing 284 patients undergoing percutaneous transluminal coronary angioplasty and studied by coronary angiograms.

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