Goodness-of-fit for GEE: An example with mental health service utilization

Suppose we use generalized estimating equations to estimate a marginal regr ession model for repeated binary observations. There are no established sum mary statistics available for assessing the adequacy of the fitted model. I n this paper we propose a goodness-of-fit test statistic which has an appro ximate chi-squared distribution when we have specified the model correctly. The proposed statistic can be viewed as an extension of the Hosmer and Lem eshow goodness-of-fit statistic for ordinary logistic regression to margina l regression models for repeated binary responses. We illustrate the method s using data from a study of mental health service utilization by children. The repeated responses are a set of binary measures of service use. We fit a marginal logistic regression model to the data using generalized estimat ing equations, and we apply the proposed goodness-of-fit statistic to asses s the adequacy of the fitted model. Copyright (C) 1999 John Wiley & Sons, L td.