A computationally tractable multivariate random effects model for clustered binary data

We consider a multivariate random effects model for clustered binary data that is useful when interest focuses on the association structure among clustered observations. Based on a vector of gamma random effects and a complementary log-log link function, the model yields a likelihood that has closed form, making a frequentist approach to model-fitting straightforward. This closed form yields several advantages over existing methods, including easy inspection of model identifiability and straightforward adjustment for nonrandom ascertainment of subjects, such as that which occurs in family studies of disease aggregation. We use the proposed model to analyse two different binary datasets concerning disease outcome data from a familial aggregation study of breast and ovarian cancer in women and loss of heterozygosity outcomes from a brain tumour study.