Network generalized estimating equations for complexly correlated data with applications to cluster randomized trials

Estimating parameters corresponding to mean outcomes and their intricate association structures in cluster randomized trials (CRTs) can pose significant methodological challenges. This paper introduces a novel framework that leverages network concepts to represent complex dependency structures and estimate these parameters using generalized estimating equations (GEE). We focus on modeling complex correlation structures by partitioning observations into potentially overlapping groups of interrelated data, where observations are assumed locally exchangeable within each group. This network GEE framework is inherently flexible, and we demonstrate its application to multiple exchangeable structures (simple, nested, block), moving average structures, and exponential decay structures. Furthermore, to address computational challenges arising in GEEs with large cluster sizes, we present the networkGEE R package, enabling the fitting of models beyond the capabilities of existing statistical software. The proposed methods are evaluated through extensive simulation studies. To illustrate their practical application, we analyze data from the Washington State Expedited Partners Therapy trial, a stepped-wedge CRT designed to assess the impact of a public health intervention aimed at reducing sexually transmitted infections through free patient-delivered partner therapy.