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The logistic regression model is frequently used in epidemiologic studies, yielding odds ratio or relative risk interpretations. Inspired by the theory of linear normal models, the logistic regression model has been extended to allow for correlated responses by introducing random effects. However, the model does not inherit the interpretational features of the normal model. In this paper, the authors argue that the existing measures are unsatisfactory (and some of them are even improper) when quantifying results from multilevel logistic regression analyses. The authors suggest a measure of heterogeneity, the median odds ratio, that quantifies cluster heterogeneity and facilitates a direct comparison between covariate effects and the magnitude of heterogeneity in terms of well-known odds ratios. Quantifying cluster-level covariates in a meaningful way is a challenge in multilevel logistic regression. For this purpose, the authors propose an odds ratio measure, the interval odds ratio, that takes these difficulties into account. The authors demonstrate the two measures by investigating heterogeneity between neighborhoods and effects of neighborhood-level covariates in two examples--public physician visits and ischemic heart disease hospitalizations--using 1999 data on 11,312 men aged 45-85 years in Malmo, Sweden.

Appropriate Assessment of Neighborhood Effects on Individual Health: Integrating Random and Fixed Effects in Multilevel Logistic Regression