Design and Analysis Methods for Cluster Randomized Trials with Pair-Matching on Baseline Outcome: Reduction of Treatment Effect Variance
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1 Virginia Commonwealth University VCU Scholars Compass Theses and Dissertations Graduate School 2006 Design and Analysis Methods for Cluster Randomized Trials with Pair-Matching on Baseline Outcome: Reduction of Treatment Effect Variance Misook Park Virginia Commonwealth University Follow this and additional works at: Part of the Biostatistics Commons The Author Downloaded from This Dissertation is brought to you for free and open access by the Graduate School at VCU Scholars Compass. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of VCU Scholars Compass. For more information, please contact
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5 Table of Contents Page List of Tables... x List of Figures....xi.. Abstract... xi1 Chapter I Introduction... 1 Chapter I1 Background and Significance of Cluster Randomized Trials Introduction and Examples Background Significance Chapter I11 Review of Relevant Statistical Topics Introduction Variance-Covariance Structure of Linear Models Mean and Variance-Covariance of Random Vectors... 23
6 Conditional Mean and Variance of Multivariate Normal Vector Marginal and Conditional Moments of a Random Variable Marginal Variance Conditional Mean and Variance 25 Marginal Mean and Variance from Conditional Mean and... Variance -25 Quadratic Forms and Relevant Distributions Distributions of Quadratic Forms 26 Independence of Quadratic Forms Noncentral X Distribution Noncentral 3 Distribution Order Statistics 29 Distribution of Order Statistics Asynlptotic Distribution 30 Induced (Concomitant) Order Statistics Standard Normal Order Statistics 34 Mean and Covariance of Ordered and Induced Ordered... Normal Statistics -36 The Contrast of Treatment Effect Within a Block Methods for Simulation 38
7 3.7.1 Simulation of a Two-Stage Sample from a Multivariate Normal... Distribution Verification of Variance Calculations Power Calculations and Verification Computing the Power 41 Chapter IV Randomized Controlled Trials: 6-Case Scenarios Introduction 42 Methods Treatment Effect Variance of the Treatment Effect Methods for Significance Testing Approximations to the F Distribution Case Scenarios Case 1 : Posttest Data With No Matching Variance of Treatment Effect Inference on Treatment Effect Case 2: Posttest Data, Baseline as Covariable, No Matching Variance of Treatment Effect... 58
8 Inference on Treatment Effect Case 3: Pre-Post Difference. No Matching Variance of Treatment Effect Inference on Treatment Effect Case 4: Posttest Data With Matching Variance of Treatment Effect Inference on Treatment Effect Case 5: Posttest Data. Baseline as Covariable. With Matching Variance of Treatment Effect Inference on Treatment Effect Case 6: Pre-Post Differences With Matching Variance of Treatment Effect Inference on Treatment Effect Chapter V Cluster Randomized Trial: 6-Case Scenarios Introduction Cluster-Randomized Pre-Post Design Variance of Treatment Effect for the Six Cases Case 1 : Posttest Data With No Matching... 81
9 5.3.2 Case 2: Posttest Data. Baseline as Covariable. No Matching Case 3: Pre-Post Difference. No Matching Case 4: Posttest Data With Matching Case 5: Posttest Data. Baseline as Covariable. With Matching Case 6: Pre-Post Differences With Matching Chapter VI Results Introduction Comparison of Cases and Comparison of Variances between Cases 1. 2 and Case 1 versus Case Case 1 versus Case Case 2 versus Case Discussion Preferred Analysis from the Design Stage Case 1 versus Case Case 1 versus Case Summary... 95
10 Comparison of Variances between Cases With and Without Matching Post data only: Case 1 and Case Post Data with Baseline as Covariable: Case 2 and Case Pre-post differences: Case 3 and Case Discussion of Variance Comparisons Power of test Chapter VII Conclusions and Discussion Summary of Work Contributions Recommendations Recommendations at Design Phase Recommendations Post Data Collection Data Collection Without Pair-Matching Data Collection With Pair.Matching Limitations
11 Chapter VIII Future work Introduction General Grouping Methods to Produce Homogeneous Groups Generalized Error Structure Hierarchical or Deeply Nested Designs Matching on Multiple Baseline Measures Repeated Measures on Clusters Optimal Allocation of Sample Sizes Across Time Points References Appendices -125 A SAS Programs
12 List of Tables Page Table 6.1. Differences in Variances between Cases 1.2. and Table 6.2. Differences in Variances: Comparing Case 1 with Cases 2 and Table 6.3. The Variances for Cases Table 6.4. Differences in Variances Between Cases and Table Schemes Considered for Comparison
13 List of Figures Page Figure 4.1: Data and Parameters from Two Time Points : Paired-Matching on Baseline Data: Order and Induced Order Statistics : Cluster Parameters, Variation, and Time 112 Correlation : Functions of w, by p : Power Curves for 7 Case Scenarios Assuming p=10 N=50 p=o.ol 1y= : Power Curves for 7 Case Scenarios Assuming p=50 N=lO p = 0.01 ~y = : Power Curves for 7 Case Scenarios Assuming p=10 N=50 6.5: Power Curves for 7 Case Scenarios Assuming p=50 N=10 p=o.1 y/=
14 Abstract DESIGN AND ANALYSIS METHODS FOR CLUSTER RANDOMIZED TRIALS WITH PAIR-MATCHING ON BASELINE OUTCOME: REDUCTION OF TREATMENT EFFECT VARIANCE By Misook Park A dissertation submitted in partial hlfillment of the requirements for the degree of Doctor of Philosophy at Virginia Commonwealth University. Virginia Commonwealth University, 2006 Research Director: Dr. Robert E Johnson Associate Professor Department of Biostatistics Cluster randomized trials (CRT) are comparative studies designed to evaluate interventions where the unit of analysis and randomization is the cluster but the unit of observation is individuals within clusters. Typically such designs involve a limited number of clusters and thus the variation between clusters is left uncontrolled. Experimental designs and analysis strategies that minimize this variance are required. In this work we focus on the CRT with pre-post intervention measures. By incorporating the baseline measure into the analysis, we can effectively reduce the variance of the treatment effect. Well known
15 methods such as adjustment for baseline as a covariate and analysis of differences of pre and post measures are two ways to accomplish this. An alternate way of incorporating baseline measures in the data analysis is to order the clusters on baseline means and pair- match the two clusters with the smallest means, pair-match the next two, and so on. Our results show that matching on baseline helps to control the between cluster variation when there is a high correlation between the pre-post measures. Six cases of designs and analysis are evaluated by comparing the variance of the treatment effect and the power of related hypothesis tests. We observed that-given our assunlptions-the adjusted analysis for baseline as a covariate without pair-matching is the best choice in terms of variance. Future work may reveal that other matching schemes that reflect the natural clustering of experimental units could reduce the variance and increase the power over the standard methods... Xlll
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