Marginal logistic regression for spatially clustered binary data

Clustered data are often analysed under the assumption that observations from distinct clusters are independent. The assumption may not be correct when the clusters are associated with different locations within a study region, as, for example, in epidemiological studies involving subjects nested within larger units such as hospitals, districts or villages. In such cases, correct inferential conclusions critically depend on the amount of spatial dependence between locations. We develop a modification of the method of generalized estimating equations to detect and account for spatial dependence between clusters in logistic regression for binary data. The approach proposed is based on parametric modelling of the lorelogram as a function of the distance between clusters. Model parameters are estimated by the hybrid pairwise likelihood method that combines optimal estimating equations for the regression parameters and pairwise likelihood for the lorelogram parameters. The methodology is illustrated with an analysis of prevalence disease survey data.