Some Comments on Rosner's Multiple Logistic Model for Clustered Data

John M. Neuhaus, Dept. of Epidemiology & Biostatistics, University of California, San Francisco
Nicholas P. Jewell, Division of Biostatistics, School of Public Health, University of California, Berkeley

Abstract

Rosner (1984, Biometrics 41, 1025-1035) proposed a binary regression model for analyzing binary response data gathered in clusters or groups. This model is useful for understanding the degree of intracluster correlation among responses, adjusted for the potential confounding effects of other covariates. However, estimates of the effects of covariates on the binary outcome obtained using Rosner's model can be misleading. For example, we show that the covariate effects given by Rosner's model do not correspond to those measured by either of the two standard approaches for correlated binary data. We present an example which compares the regression coefficients arising from fits of Rosner's model to other logistic models for clustered observations, using data from a study of breast disease.