An improved quadratic inference function for parameter estimation in the analysis of correlated data

Generalized estimating equations (GEE) are commonly employed for the analysis of correlated data. However, the quadratic inference function (QIF) method is increasing in popularity because of its multiple theoretical advantages over GEE. We base our focus on the fact that the QIF method is more efficient than GEE when the working covariance structure for the data is misspecified. It has been shown that because of the use of an empirical weighting covariance matrix inside its estimating equations, the QIF method's realized estimation performance can potentially be inferior to GEE's when the number of independent clusters is not large. We therefore propose an alternative weighting matrix for the QIF, which asymptotically is an optimally weighted combination of the empirical covariance matrix and its model-based version, which is derived by minimizing its expected quadratic loss. Use of the proposed weighting matrix maintains the large-sample advantages the QIF approach has over GEE and, as shown via simulation, improves small-sample parameter estimation. We also illustrated the proposed method in the analysis of a longitudinal study.