Comparison of population-averaged and cluster-specific models for the analysis of cluster randomized trials with missing binary outcomes: a simulation study

Jinhui Ma,Joseph Beyene,Lehana Thabane,Parminder Raina

doi:10.1186/1471-2288-13-9

Abstract

sBackgroundThe objective of this simulation study is to compare the accuracy and efficiency of population-averaged (i.e. generalized estimating equations (GEE)) and cluster-specific (i.e. random-effects logistic regression (RELR)) models for analyzing data from cluster randomized trials (CRTs) with missing binary responses.MethodsIn this simulation study, clustered responses were generated from a beta-binomial distribution. The number of clusters per trial arm, the number of subjects per cluster, intra-cluster correlation coefficient, and the percentage of missing data were allowed to vary. Under the assumption of covariate dependent missingness, missing outcomes were handled by complete case analysis, standard multiple imputation (MI) and within-cluster MI strategies. Data were analyzed using GEE and RELR. Performance of the methods was assessed using standardized bias, empirical standard error, root mean squared error (RMSE), and coverage probability.ResultsGEE performs well on all four measures — provided the downward bias of the standard error (when the number of clusters per arm is small) is adjusted appropriately — under the following scenarios: complete case analysis for CRTs with a small amount of missing data; standard MI for CRTs with variance inflation factor (VIF) <3; within-cluster MI for CRTs with VIF≥3 and cluster size>50. RELR performs well only when a small amount of data was missing, and complete case analysis was applied.ConclusionGEE performs well as long as appropriate missing data strategies are adopted based on the design of CRTs and the percentage of missing data. In contrast, RELR does not perform well when either standard or within-cluster MI strategy is applied prior to the analysis.

Highlights

The objective of this simulation study is to compare the accuracy and efficiency of population-averaged (i.e. generalized estimating equations (GEE)) and cluster-specific (i.e. random-effects logistic regression (RELR)) models for analyzing data from cluster randomized trials (CRTs) with missing binary responses
Statistical analysis methods Generalized estimating equations The GEE approach for fitting the logistic regression developed by Liang and Zeger [12] can be formulated as logit Pr yijl 1⁄4 1 1⁄4 Xijlβmarginal; ð1Þ
When complete case analysis was used to handle missing data, empirical standard errors from GEE and RELR for all designs of CRTs increased with the increasing percentage of missing data

Summary

Introduction

The objective of this simulation study is to compare the accuracy and efficiency of population-averaged (i.e. generalized estimating equations (GEE)) and cluster-specific (i.e. random-effects logistic regression (RELR)) models for analyzing data from cluster randomized trials (CRTs) with missing binary responses. Cluster randomized trials (CRTs) are randomized controlled trials in which clusters of subjects rather than independent subjects are randomly allocated to trial arms and outcomes are measured for individual subjects or clusters. The correlation within clusters, which is quantified by the intracluster correlation coefficient (ICC) ρ, may result in substantially reduced statistical efficiency relative to trials that randomize the same number of individuals. The reduction in efficiency is a function of the variance inflation due to clustering, known as the design effect or variance inflation factor (VIF), given by VIF 1⁄4 1 þ ðm À 1Þρ , where m denotes the average cluster size

Methods

Results

Discussion

Conclusion