Generalized estimating equations for correlated binary data: Using the odds ratio as a measure of association

Moment methods for analyzing repeated binary responses have been proposed by Liang & Zeger (1986), and extended by Prentice (1988). In their generalized estimating equations, both Liang & Zeger (1986) and Prentice (1988) estimate the parameters associated with the expected value of an individual's vector of binary responses as well as the correlations between pairs of binary responses. Because the odds ratio has many desirable properties, and some investigators may find the odds ratio is easier to interpret, we discuss modelling the association between binary responses at pairs of times with the odds ratio. We then modify the estimating equations of Prentice to estimate the odds ratios. In simulations, the parameter estimates for the logistic regression model for the marginal probabilities appear slightly more efficient when using the odds ratio parameterization.