Efficiency of generalized estimating equations for binary responses

Using standard correlation bounds, we show that in generalized estimation equations (GEEs) the so-called 'working correlation matrix'<b>R</b>("&agr;") for analysing binary data cannot in general be the true correlation matrix of the data. Methods for estimating the correlation param-eter in current GEE software for binary responses disregard these bounds. To show that the GEE applied on binary data has high efficiency, we use a multivariate binary model so that the covariance matrix from estimating equation theory can be compared with the inverse Fisher information matrix. But <b>R</b>("&agr;") should be viewed as the weight matrix, and it should not be confused with the correlation matrix of the binary responses. We also do a comparison with more general weighted estimating equations by using a matrix Cauchy-Schwarz inequality. Our analysis leads to simple rules for the choice of "&agr;" in an exchangeable or autoregressive AR(1) weight matrix <b>R</b>("&agr;"), based on the strength of dependence between the binary variables. An example is given to illustrate the assessment of dependence and choice of "&agr;". Copyright 2004 Royal Statistical Society.