Joint modeling of two count variables using a shared random effect model in the presence of clusters for complex data

In epidemiology, it is often the case that two or more correlated count response variables are encountered. Under this scenario, it is more efficient to model the data using a joint model. Besides, if one of these count variables has an excess of zeros (spike at zero) the log link cannot be used in general. The situation is more complicated when the data is grouped into clusters. A Generalized Linear Mixed Model (GLMM) is used to accommodate this cluster covariance. The objective of this research is to develop a new modeling approach that can handle this situation. The method is illustrated on a global data set of Covid 19 patients. The important conclusions are that the new model was successfully implemented both in theory and practice. A plot of the residuals indicated a well-fitting model to the data.