Western University Scholarship@Western Electronic Thesis and Dissertation Repository 4-1-2011 12:00 AM Confidence Interval Estimation for Continuous Outcomes in Cluster Randomization Trials Julia Taleban The University of Western Ontario Supervisor Dr. Guang Yong Zou The University of Western Ontario Graduate Program in Biostatistics A thesis submitted in partial fulfillment of the equirr ements for the degree in Doctor of Philosophy © Julia Taleban 2011 Follow this and additional works at: https://ir.lib.uwo.ca/etd Part of the Biostatistics Commons Recommended Citation Taleban, Julia, "Confidence Interval Estimation for Continuous Outcomes in Cluster Randomization Trials" (2011). Electronic Thesis and Dissertation Repository. 121. https://ir.lib.uwo.ca/etd/121 This Dissertation/Thesis is brought to you for free and open access by Scholarship@Western. 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CONFIDENCE INTERVAL ESTIMATION FOR CONTINUOUS OUTCOMES IN CLUSTER RANDOMIZATION TRIALS (Spine title: Confidence Intervals in Cluster Randomization Trials) (Thesis format: Monograph) by Julia Taleban Graduate Program in Epidemiology & Biostatistics A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy School of Graduate and Postdoctoral Studies University of Western Ontario London, Ontario April 27, 2011 c Julia Taleban, 2011 THE UNIVERSITY OF WESTERN ONTARIO SCHOOL OF GRADUATE AND POSTDOCTORAL STUDIES CERTIFICATE OF EXAMINATION Supervisor Examining Board aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaa Dr. Guangyong Zou Dr. Neil Klar Co-Supervisor aaaaaaaaaaaaaaaaaaaaaa Dr. Duncan Murdoch aaaaaaaaaaaaaaaaaaaaaa Dr. John Koval aaaaaaaaaaaaaaaaaaaaaa Dr. Serge Provost Committee member aaaaaaaaaaaaaaaaaaaaaa Dr. Wendy Lou aaaaaaaaaaaaaaaaaaaaaa Dr. Allan Donner The thesis by Julia Taleban Entitled Confidence Interval Estimation for Continuous Outcomes in Cluster Randomization Trials is accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Date: aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa Chair of the Thesis Examination Board ii ABSTRACT Cluster randomization trials are experiments where intact social units (e.g. hos- pitals, schools, communities, and families) are randomized to the arms of the trial rather than individuals. The popularity of this design among health researchers is partially due to reduced contamination of treatment effects and convenience. How- ever, the advantages of cluster randomization trials come with a price. Due to the dependence of individuals within a cluster, cluster randomization trials suffer reduced statistical efficiency and often require a complex analysis of study outcomes. The primary purpose of this thesis is to propose new confidence intervals for effect measures commonly of interest for continuous outcomes arising from cluster random- ization trials. Specifically, we construct new confidence intervals for the difference between two normal means, the difference between two lognormal means, and the exceedance probability. The proposed confidence intervals, which use the method of variance estimates recovery (MOVER), do not make certain assumptions that existing procedures make on the data. For instance, symmetry is not forced when the sampling distribution of the parameter estimate is skewed and the assumption of homoscedasticity is not made. Furthermore, the MOVER results in simple confidence interval procedures rather than complex simulation-based methods which currently exist. Simulation studies are used to investigate the small sample properties of the MOVER as compared with existing procedures. Unbalanced cluster sizes are sim- ulated, with an average range of 50 to 200 individuals per cluster and 6 to 24 clusters per arm. The effects of various degrees of dependence between individuals within the same cluster are also investigated. When comparing the empirical coverage, tail errors, and median widths of confi- dence interval procedures, the MOVER has coverage close to the nominal, relatively balanced tail errors, and narrow widths as compared to existing procedure for the iii majority of the parameter combinations investigated. Existing data from cluster ran- domization trials are then used to illustrate each of the methods. Keywords: cluster randomization trials, confidence intervals, normal mean, lognor- mal mean, exceedance probability, method of variance estimates recovery, generalized confidence interval procedure, Wald method. iv ACKNOWLEDGMENTS The completion of this thesis would not have been possible without the help and support of many people. First, I would like to thank my Ph.D. supervisor, Dr. Guang Yong Zou, who provided me with invaluable guidance and insight. I would also like to thank my co-supervisor, Dr. John Koval, whose encouragement and suggestions have been a great help, and Dr. Allan Donner for the time he took to discuss the drafts of the thesis and his helpful suggestions. I am grateful to Dr. Thomas Marrie and Dr. Alan Montgomery for the use of their datasets while illustrating various confidence interval methods in Chapter 5. I am indebted to my parents and friends for their moral support and encourage- ment. My fiance Luc has shown constant support and endless patience, and for that I am thankful. This work has been financially supported in part by the Ontario Graduate Schol- arship in Science and Technology and by the Ontario Graduate Scholarship from the Ontario Ministry of Training, Colleges, and Universities. v TABLE OF CONTENTS Certificate of Examination ii Abstract iii Acknowledgments v List of Tables x List of Figures xiii Chapter 1 Introduction 1 1.1 Randomizedcontrolledtrials. 1 1.2 Clusterrandomizationtrials . 1 1.3 Notation.................................. 5 1.4 Brief summary of methods for cluster randomization trials with con- tinuousdata................................ 8 Cluster-levelanalyses... .. .. .. .. ... .. .. .. .. ... .. 8 Individuallevelanalyses . 9 Current methods for a difference between two normal means . 12 1.5 Alternative effect measures in cluster randomization trials ...... 15 Thestandardizedmeandifference . 15 Thedifferencebetweentwolognormalmeans . 21 1.6 Scopeofthethesis ............................ 24 1.7 Objectives................................. 26 1.8 Organizationofthethesis .. .. .. .. ... .. .. .. .. ... .. 27 Chapter 2 Fundamentals of confidence interval estimation 28 2.1 Introduction................................ 28 2.2 Definitionofaconfidenceinterval . 31 2.3 Confidence interval estimation for a single parameter . ....... 32 Theinversionprinciple . 32 Thetransformationprinciple. 33 2.4 Wald-type confidence intervals and the delta method . ..... 33 Asingleparameter ............................ 34 Afunctionofmultipleparameters . 34 Properties of Wald-type confidence intervals . 35 vi 2.5 Confidence intervals for a function of multiple parameters....... 37 The MOVER for a linear combination of parameters . 38 The MOVER for the ratio of two independent parameters . 45 PropertiesoftheMOVER .. .. .. .. ... .. .. .. .. ... .. 47 Previousapplications . 49 Chapter 3 Confidence interval estimation for effect measures in clus- ter randomization trials 53 3.1 Adifferencebetweentwonormalmeans. 54 TheMOVER ............................... 54 Alternativeconfidenceintervals . 55 Waldconfidenceinterval . 55 Cluster-adjusted confidence interval . 56 Generalizedconfidenceinterval . 57 3.2 Adifferencebetweentwolognormalmeans . 59 TheMOVERforasinglemean . 59 The MOVER for a difference between two lognormal means . 62 Alternativeconfidenceintervals . 62 Wald confidence interval and the delta method . 62 Generalizedconfidenceintervals . 64 3.3 Theexceedanceprobability . 65 TheMOVER ............................... 65 Alternativeconfidenceintervals . 66 Wald confidence interval and the delta method . 66 Generalizedconfidenceinterval . 68 Chapter 4 Simulation study of confidence interval procedures 70 4.1 Introduction................................ 70 4.2 Objectives................................. 71 4.3 Methods.................................. 72 Parametercombinations . 72 Datageneration.............................. 75 Clustersizes............................ 75 Correlatednormaldata. 77 Correlatedlognormaldata . 78 Computer software for data generation . 79 Methodsofcomparison.. .. .. .. .. ... .. .. .. .. ... .. 79 4.4 Results................................... 80 Thedifferencebetweentwonormalmeans . 80 Confidenceintervalcoverage . 81 Tailerrors............................. 87 Medianwidth........................... 87 vii Thedifferencebetweentwolognormalmeans . 88 Confidenceintervalcoverage . 88 Tailerrors............................. 89 Medianwidth........................... 95 Theexceedanceprobability . 95 Confidenceintervalcoverage . 95 Tailerrors............................. 97 Medianwidth ........................... 108 4.5 Discussion................................. 108 Thedifferencebetweentwonormalmeans . 108 Confidence interval coverage . 109 Confidenceintervaltailerrors . 110 Confidenceintervalwidths . 111 Thedifferencebetweentwolognormalmeans . 111 Confidence interval coverage . 112 Confidenceintervaltailerrors . 113 Confidenceintervalwidths . 114 Theexceedanceprobability . 114 Confidence interval coverage . 115 Confidenceintervaltailerrors . 115 Confidenceintervalwidths . 116 4.6 Overallconclusions . ... .. .. .. .. ... .. .. .. .. ... .. 116 Chapter 5