This book begins with an introduction of pragmatic cluster randomized trials (PCTs) and reviews various pragmatic issues that need to be addressed by statisticians at the design stage. It discusses the advantages and disadvantages of each type of PCT, and provides sample size formulas, sensitivity analyses, and examples for sample size calculation. The generalized estimating equation (GEE) method will be employed to derive sample size formulas for various types of outcomes from the exponential family, including continuous, binary, and count variables. Experimental designs that have been frequently employed in PCTs will be discussed, including cluster randomized designs, matched-pair cluster randomized design, stratified cluster randomized design, stepped-wedge cluster randomized design, longitudinal cluster randomized design, and crossover cluster randomized design. It demonstrates that the GEE approach is flexible to accommodate pragmatic issues such as hierarchical correlation structures, different missing data patterns, randomly varying cluster sizes, etc. It has been reported that the GEE approach leads to under-estimated variance with limited numbers of clusters. The remedy for this limitation is investigated for the design of PCTs. This book can assist practitioners in the design of PCTs by providing a description of the advantages and disadvantages of various PCTs and sample size formulas that address various pragmatic issues, facilitating the proper implementation of PCTs to improve health care. It can also serve as a textbook for biostatistics students at the graduate level to enhance their knowledge or skill in clinical trial design.
Key Features
Discuss the advantages and disadvantages of each type of PCTs, and provide sample size formulas, sensitivity analyses, and examples.
Address an unmet need for guidance books on sample size calculations for PCTs;
A wide variety of experimental designs adopted by PCTs are covered;
The sample size solutions can be readily implemented due to the accommodation of common pragmatic issues encountered in real-world practice;
Useful to both academic and industrial biostatisticians involved in clinical trial design;
Can be used as a textbook for graduate students majoring in statistics and biostatistics.
Author(s): Song Zhang, Chul Ahn, Hong Zhu
Series: Chapman & Hall/CRC Biostatistics Series
Publisher: CRC Press/Chapman & Hall
Year: 2023
Language: English
Pages: 214
City: Boca Raton
Cover
Half Title
Series Page
Title Page
Copyright Page
Table of Contents
Author Biographies
Chapter 1 Pragmatic Randomized Trials
1.1 Introduction
1.1.1 Statistical Issues in Pragmatic Randomization Trials
1.2 Cluster Randomized Designs
1.2.1 Completely Randomized Cluster Trial Design
1.2.2 Restricted Randomized Designs: Strategies to Improve Efficiency for CRTs
1.2.2.1 Matched-Pair Cluster Randomized Design
1.2.2.2 Stratified Cluster Randomized Design
1.2.2.3 Covariate-Constrained Randomized Design
1.2.3 Multiple-Period Cluster Randomized Designs
1.2.3.1 Longitudinal Cluster Randomized Design
1.2.3.2 Crossover Cluster Randomized Design
1.2.3.3 Stepped-Wedge Cluster Randomized Design
References
Chapter 2 Cluster Randomized Trials
2.1 Introduction
2.2 Continuous Outcomes
2.2.1 Standard Two-Sample t-Test
2.2.2 Adjusted Two-Sample t-Test
2.2.3 Generalized Estimating Equation Method
2.2.4 Mixed-Effects Linear Regression Models
2.3 Binary Outcomes
2.3.1 Standard Pearson Chi-Square Test
2.3.2 Adjusted Chi-Square Test
2.3.3 Ratio Estimator Chi-Square Test
2.3.4 Generalized Estimating Equation Approach
2.3.5 Generalized Linear Mixed Model Approach
2.4 Count Outcomes
2.4.1 Adjusted Normality Test
2.4.2 Ratio Estimator Method
2.4.3 Generalized Estimating Equation
2.5 Cluster Size Determination for a Fixed Number of Clusters
References
Chapter 3 Matched-Pair Cluster Randomized Design for Pragmatic Studies
3.1 Introduction of Matched-Pair Cluster Randomized Design
3.2 Considerations for Pragmatic Matched-Pair CRTs
3.2.1 Impact of Correlation
3.2.2 Impact of Missing Data
3.3 Matched-Pair Cluster Randomized Design with Missing Continuous Outcomes
3.3.1 Sample Size Estimation Based on GEE Approach
3.3.2 Relative Efficiency of GEE Approach vs Crude Adjustment
3.3.3 Adjustment of Inflated Type I Error
3.3.4 Sensitivity Analysis
3.3.5 Example
3.4 Matched-Pair Cluster Randomized Design with Missing Binary Outcomes
3.4.1 Sample Size Estimation Based on GEE Approach
3.4.2 Relative Efficiency of GEE Approach vs Crude Adjustment
3.4.3 Adjustment of Inflated Type I Error and Sensitivity Analysis
3.4.4 Example
3.5 Further Readings
Appendix
A.1 Eigenvalues of the Correlation Matrix
A.2 Proof of Theorem 1
References
Chapter 4 Stratified Cluster Randomized Design for Pragmatic Studies
4.1 Introduction of Stratified Cluster Randomized Design
4.2 Considerations for Pragmatic Stratified CRTs
4.3 Stratified Cluster Randomized Design with Continuous Outcomes
4.3.1 Sample Size Estimation Based on GEE Approach
4.3.2 Relative Sample Size Change Due to Varying Cluster Size
4.3.3 Example
4.4 Stratified Cluster Randomized Design with Binary Outcomes
4.4.1 Sample Size Estimation Based on CMH Statistic
4.4.2 Relative Sample Size Change Due to Varying Cluster Size
4.4.3 Estimation of Clustering Parameter
4.4.4 Example
4.5 Further Readings
References
Chapter 5 The GEE Approach for Stepped-Wedge Trial Design
5.1 Introduction
5.2 A Brief Review of GEE
5.3 Design SW trials with a Continuous Outcome
5.3.1 Accounting for Missing Data
5.3.2 Simulation Research
5.3.3 Adjusting for Underestimated Variances for Small Sample Sizes
5.3.4 Consideration of Efficiency and Robustness
5.4 Design SW Trials with a Binary Outcome
5.4.1 Extension to Outcomes from the Exponential Family
5.5 Longitudinal and Crossover Cluster Randomized Trials
5.5.1 Longitudinal cluster randomized trials
5.5.2 Crossover Cluster Randomized Trials
5.5.3 Comparison of and
5.5.4 Adjusting for Small Numbers of Clusters by the -Distribution
5.5.5 Accounting for Randomly Varying Cluster Sizes
Appendix A: Derivation of Equation (5.8)
Appendix B: Derivation of Equations (5.9) and (5.10)
Appendix C: Sample Size for Cross-Sectional SW Trials
Appendix D: Derivation of Equation (5.15)
Appendix E: Proof of Theorem 1
Appendix F: Proof of Theorem 2
References
Chapter 6 The Mixed-Effect Model Approach and Adaptive Strategies for Stepped-Wedge Trial Design
6.1 A Brief Review of Mixed-Effect Models
6.2 Sample Size Calculation Based on Cluster-Step Means
6.2.1 Commonly Used Correlation Structures
6.2.1.1 Exchangeable Correlation Structure
6.2.1.2 Nested Exchangeable Correlation Structure
6.2.1.3 Block Exchangeable Correlation Structure
6.2.1.4 Exponential Decay Correlation Structure
6.2.1.5 Proportional Decay Correlation Structure
6.3 Adaptive Strategies for SW Trials
6.3.1 Group Sequential Design for SW Trials
6.3.1.1 Bayesian Adaptive Design for SW Trials
6.4 Further Readings
References
Index
