A likelihood-based method for analysing longitudinal binary responses

In this paper, we discuss a likelihood-based method for analysing correlated binary responses based on a multivariate model. It is related to the pseudo-maximum likelihood approach suggested recently by Zhao & Prentice (1990). Their parameterization results in a simple pairwise model, in which the association between responses is modelled in terms of correlations, while the present paper uses conditional log odds-ratios. With this approach, higher-order associations can be incorporated in a natural way. One important advantage of this parameterization is that the maximum likelihood estimates of the marginal mean parameters are robust to misspecification of the time dependence. We describe an iterative two-stage procedure for obtaining the maximum likelihood estimates. Two examples are presented to illustrate this methodology.