A generalized estimating equation approach for modeling random length binary vector data

A common measure in clinical trials and epidemiologic studies is the number of events such as seizures, hospitalizations, or bouts of disease. Frequently, a binary measure of severity for each event is available but is not incorporated in the analysis. This paper proposes methodology for jointly modeling the number of events and the vector of correlated binary severity measures. Our formulation exploits the notion that a given covariate may affect both outcomes in a similar way. We functionally link the regression parameters for the counts and binary means and discuss a generalized estimating equation (GEE) approach for parameter estimation. We discuss conditions under which the proposed joint modeling approach provides marked gains in efficiency relative to the common procedure of simply modeling the counts, and we illustrate the methodology with epilepsy clinical trial data.