An evaluation of quadratic inference functions for estimating intervention effects in cluster randomized trials

Cluster randomized trials (CRTs) usually randomize groups of individuals to interventions, and outcomes are typically measured at the individual level. Marginal intervention effects are frequently of interest in CRTs due to their population-averaged interpretations. Such effects are estimated using generalized estimating equations (GEE), or a recent alternative called the quadratic inference function (QIF). However, the performance of QIF relative to GEE have not been extensively evaluated in the CRT context, especially when the marginal mean model includes additional covariates. Motivated by the HALI trial, we conduct simulation studies to compare the finite-sample operating characteristics of QIF and GEE. We demonstrate that QIF and GEE are equivalent under some conditions. When the marginal mean model includes individual-level covariates, QIF shows an efficiency improvement over GEE with overall larger power, but its test size may be more liberal than GEE and GEE achieves better coverage than QIF. The test size inflation may not by fully addressed from using finite-sample bias corrections. The estimates of QIF tend to be closer to GEE in the HALI data, although the former presents a small standard error. Overall, we confirm that the QIF approach generally has potentially better efficiency than GEE in our simulation studies but might be more cautiously used as a viable approach for the analysis of CRTs. More research is needed, however, to address the finite-sample bias in the variance estimation of the QIF to better control its test size.