All ETDs from UAB

Advisory Committee Chair

David T Redden

Advisory Committee Members

Charles R Katholi

Leslie A McClure

Paul M Muntner

Joshua S Richman

Document Type

Dissertation

Date of Award

2014

Degree Name by School

Doctor of Philosophy (PhD) School of Public Health

Abstract

Generalized estimating equation (GEE) and generalized linear mixed model (GLMM) are two statistical modeling methods commonly used in the analyses of correlated outcomes from cluster-randomized trials (CRTs). The fact that most CRTs involve only a small number of clusters makes the small sample adjustment critical to preserve the type I error rates in testing the null hypothesis of intervention effects. To improve the small sample performance of GEE, some bias-corrected sandwich estimators have been proposed. To improve the small sample performance of GLMM, the approximated Wald F test is used to replace the asymptotic ÷^2 test and the denominator degrees of freedom are carefully estimated. However, these approaches are proposed and evaluated under different study designs and their validity and performance under the CRT frameworks are either not satisfying or not well explored. In this thesis, we present three perspectives that, taken together, strengthen existing solutions and provide new solutions to improve the small sample inference of CRTs. i) We propose a cluster randomization test in the GEE approach that can help preserve the type I error rate in the analyses of CRTs with a small number of clusters. ii) We systematically compare and contrast the performance of five bias-corrected sandwich estimators and conclude that with t-distribution approximation, the Kauermann and Carroll proposed bias-corrected sandwich estimator can both keep the test size to nominal levels even when the number of clusters is as low as 10 and is robust to the moderate variation of the cluster sizes. However, in cases with large variations in cluster sizes, the Fay and Graubard proposed bias-corrected sandwich estimator should be used instead. Based on the GEE Wald t test with the Kauermann and Carroll proposed bias-corrected sandwich estimator, we derive a formula for the power and sample size calculation for CRTs with small numbers of clusters. The power levels as predicted by the proposed formula agree well with the empirically derived powers from the simulations. iii) We compare and contrast the small sample performances of five approximation methods of denominator degrees of freedom (DDF) for the GLMM Wald F test under the framework of CRTs and conclude that the Between-Within method of the denominator degrees of freedom for F test should be recommended when the GLMM is used for the analyses of CRTs with a small number of clusters and considerable variation of cluster sizes.

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