Generalized Estimating Equations using the new R package glmtoolbox

Abstract

This paper introduces a very comprehensive implementation, available in the new `R` package `glmtoolbox`, of a very flexible statistical tool known as Generalized Estimating Equations (GEE), which analyzes cluster correlated data utilizing marginal models. As well as providing more built-in structures for the working correlation matrix than other GEE implementations in `R`, this GEE implementation also allows the user to: $(1)$ compute several estimates of the variance-covariance matrix of the estimators of the parameters of interest; $(2)$ compute several criteria to assist the selection of the structure for the working-correlation matrix; $(3)$ compare nested models using the Wald test as well as the generalized score test; $(4)$ assess the goodness-of-fit of the model using Pearson-, deviance- and Mahalanobis-type residuals; $(5)$ perform sensibility analysis using the global influence approach (that is, dfbeta statistic and Cook's distance) as well as the local influence approach; $(6)$ use several criteria to perform variable selection using a hybrid stepwise procedure; $(7)$ fit models with nonlinear predictors; $(8)$ handle dropout-type missing data under MAR rather than MCAR assumption by using observation-specific or cluster-specific weighted methods. The capabilities of this GEE implementation are illustrated by analyzing four real datasets obtained from longitudinal studies.