Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Epidemiology and Biostatistics


Drs Allan Donner

2nd Supervisor

Neil Klar

Joint Supervisor


An increasing number of systematic reviews summarize results from cluster randomization trials. Applying existing meta-analysis methods to such trials is problematic because responses of subjects within clusters are likely correlated. The aim of this thesis is to evaluate heterogeneity in the context of fixed effects models providing guidance for conducting a meta-analysis of such trials. The approaches include the adjusted Q statistic, adjusted heterogeneity variance estimators and their corresponding confidence intervals and adjusted measures of heterogeneity and their corresponding confidence intervals. Attention is limited to meta-analyses of completely randomized trials having a binary outcome. An analytic expression for power of Q test is derived, which may be useful in planning a meta-analysis. The Type I error and power for the Q statistic, bias and mean square errors for the estimators and the coverage, tail errors and interval width for the confidence interval methods are investigated using Monte Carlo simulation.

Simulation results show that the adjusted Q statistic has a Type I error close to the nominal level of 0.05 as compared to the unadjusted Q statistic which has a highly inflated Type I error. Power estimated using the algebraic formula had similar results to empirical power. For the heterogeneity variance estimators, the iterative REML estimator consistently had little bias. However, the noniterative MVVC and DLVC estimators with relatively low bias may also be recommended for small and large heterogeneity, respectively. The Q profile confidence interval approach for heterogeneity variance had generally nominal coverage for large heterogeneity. The measures of heterogeneity had generally low bias for large number of trials. For confidence interval approaches, the MOVER consistently maintained nominal coverage for 'low' to 'moderate' heterogeneity. For the absence of heterogeneity, the approach based on the Q statistic is preferred. Data from four cluster randomization trials are used to illustrate methods of analysis.