  Generalized estimating equation (GEE) is widely adopted for regression
modeling for longitudinal data, taking account of potential correlations within
the same subjects. Although the standard GEE assumes common regression
coefficients among all the subjects, such an assumption may not be realistic
when there is potential heterogeneity in regression coefficients among
subjects. In this paper, we develop a flexible and interpretable approach,
called grouped GEE analysis, to modeling longitudinal data with allowing
heterogeneity in regression coefficients. The proposed method assumes that the
subjects are divided into a finite number of groups and subjects within the
same group share the same regression coefficient. We provide a simple algorithm
for grouping subjects and estimating the regression coefficients
simultaneously, and show the asymptotic properties of the proposed estimator.
The number of groups can be determined by the cross-validation with averaging
method. We demonstrate the proposed method through simulation studies and an
application to a real dataset.
