Marginal Methods for the Design and Analysis of Cluster Randomized Trials and Related Studies

Abstract

Cluster randomized trials (CRTs) are used to study the effectiveness of complex or community-level interventions across a diverse range of contexts. These contexts present a range of logistical and statistical challenges to the design and analysis of CRTs and related studies, such as individually randomized group treatment (IRGT) trials, for which clustering of outcomes arises. This dissertation, consisting of four distinct topics, uses real-world CRTs and IRGT trials to identify unanswered statistical challenges in the design and analysis of those trials and then tackles those questions and provide solutions. All four topics focus on the marginal modeling framework to accommodate the correlated outcome data that arises in CRTs and IRGT trials, with two topics focused on design and two on analysis.The two design-focused topics assume a marginal modeling framework with data analyzed using generalized estimating equations paired with matrix-adjusted estimating equations with a bias-corrected sandwich variance estimator for the correlation parameters. In the first topic, we develop methods for sample size and power calculations in four-level intervention studies when intervention assignment is carried out at any level, with a particular focus on CRTs, assuming arbitrary link and variance functions. We demonstrate that, under both balanced and unbalanced designs, empirical power corresponds well with that predicted by the proposed method for as few as 8 clusters. In the second topic, we develop sample size formulas for longitudinal IRGT trials, under four models with different assumptions regarding the time effect. We show that empirical power corresponds well with that predicted by the proposed method for as few as 6 groups in the intervention arm. The two analysis-focused topics relate to current challenges in the analysis of CRTs. In the first, we propose 9 bias-corrected sandwich variance estimators for CRTs with time-to-event data analyzed through the marginal Cox model, evaluate the performance of the proposed variance estimators, and develop an R package CoxBcv to facilitate their implementation. Our results indicate that the optimal choice of bias-corrected sandwich variance estimator for CRTs with survival outcomes can depend on the variability of cluster sizes, and can also differ whether it is evaluated according to relative bias or type I error rate. In the second, we compare four methods of generalized estimating equations analyses for CRTs, when cluster sizes vary and the goal is to generalize to a hypothetical population of clusters. We conclude that an analysis using both an exchangeable working correlation matrix and weighting by inverse cluster size, which may be considered the natural analytic approach, can lead to incorrect results. Furthermore, an analysis with both an independence working correlation matrix and weighting by inverse cluster size is the only approach that always provides valid results.