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Oftentimes, small groups (called clusters) of individuals (called subunits) are randomized between treatment arms. Typically, clusters are families, classes, communities, surgeons operating patients, and so on. Such trials are called cluster randomization trials (CRTs). The subunits in each cluster share common frailties so that their outcomes tend to be positively correlated. Since clusters are independent, the data in two arms are independent in CRTs.
In a clinical trial, multiple sites (such as teeth or ears) from each subject may be randomized between different treatment arms. In this case, the sites (subunits) of each subject (cluster) share common genetic, physiological, or environmental characteristics so that their observations tend to be positively correlated. This kind of trials are called subunit randomization trials (SRTs). In SRTs, dependency exists both within and between treatment arms.
Individually randomized group treatment (IRGT) trials are composite of traditional independent subject randomization and CRTs. In an IRGT trial, the control arm is to treat patients individually, whereas the experimental arm is to treat patients using a group training, education, or treatment to increase the treatment effect by close interactions among patients. As a result, the outcome data of the control arm are independent as in traditional trials, but those in the experimental arm are correlated within each group (cluster) as in CRTs. Hence, two arms in IRGT trials have different dependency structures. Unlike standard CRTs, clusters of IRGT trials are usually organized after randomization. But statistically, they have identical statistical issues between the two types of trials, i.e., accounting for the dependency within each cluster.
Although this book is entitled Cluster Randomization Trials, it covers all three types of trials (i.e., CRTs, SRTs, and IRGT trials) resulting in clustered data. For outcome variables of binary, continuous, and time-to-event
Preface
Introduction
References
One-Sample Binary Data
Estimation of Binomial Proportions
Modified McNemar's Test for Clustered Paired Binary Data
Clustered McNemar’s Test
Real Data Example
Sample Size Calculations for Clustered Binary Data
Example
NumericalStudies
References
Chi-Square Test for Two-Sample Clustered Binary Data (I): Donner's Adjustment
Donner's Test Statistic
Validation of Donner's Test
Distribution of Donner’s Test Statistic
Numerical Studies
Example
References
Chi-Square Test for Two-Sample Clustered Binary Data (II): GEE Adjustment
Modified Chi-Square Test with GEE-Type Adjustment
Test Statistic based on Optimal Estimators
Efficiency of Weighted Estimators
Sample Size Calculation
Numerical Studies
Example
Simulations
References
Subunit Randomization Trials: GEE-Type Test for Two-Sample Clustered Binary Data
Modified Chi-Square Test with GEE-Type Adjustment
Sample size Calculation
Numerical Studies
Simulations
Real Data Example
References
Random Number Generation of Clustered Binary Data
Lunn-Davies Method
Kang-Jung Method
Basic Algorithm
Beta-Binomial Distribution
Method based on Multivariate Normal Random Variables
Under Cluster Randomization
Under Subunit Randomization
References
Tests for RC Contingency Tables with Clustered Categorical Data
Tests for 2K Contingency Tables with Clustered Ordered Categorical Data
Score Tests for Independent Data
Score Tests for Clustered Data
Simulation Studies
Real Data Examples
Chi-Square Test for RC Contingency Tables with Clustered Categorical Data
Simulation Studies
Real Data Analysis
References
Clustered Continuous Data
Cluster Randomization Trials
Modified t-Test for CRTs
Sample Size Calculation for CRTs
Subunit Randomization Trials
Modified t-Test for SRTs
Sample Size Calculation for SRTs
An Equivalence Test for Clustered Pair Data
Equivalence Test
Example
Inference of Medians for Paired Survival Data
Statistical Testing on Paired Median Survival Times
Sample Size for Testing on Paired Median Survival Times
Confidence Interval of Ratio or Difference of Median Survival Times
Real Data Examples
Simulation Studies
References
Rank Tests for Matched Survival Data and Sample Size Calculation
Weighted Rank Tests for Matched Survival Data
Paired Two-Sample Data Case
Matched K-Sample Data Case
Real Data Examples
Simulation Studies
Sample Size Calculation for the Weighted Rank Tests with Paired Survival Data
Sample Size under Some Practical Settings
When Accrual Rate Is Given Instead of Accrual Period
When Historical Data Are Available with Both of the Paired Subjects Treated by the Same Treatment
Simulation Studies
Examples
Discussion
References
Rank Tests for Clustered Survival Data and Sample Size Calculation under Cluster Randomization
Weighted Rank Tests for Clustered Survival Data
Extension To K Sample Cases
Simulation Studies
Real Example
Sample Size Calculation of the Log-Rank Test for Two-Arm CRTs
Specification of Survival Distribution
Specification of Censoring Distribution
Sample Size Calculation under Practical Design Settings
Sample Size Calculation for given Accrual Rate instead of Accrual Period
Simulation Studies
Examples
References
Rank Tests for Clustered Survival Data and Sample Size Calculation under Subunit Randomization
Two-Sample Weighted Rank Tests for Subunit Randomization Trials
Shared Gamma Frailty Model
Simulation Studies
Examples
Sample Size Calculation of the Log-Rank Test for SRTs
Specification of Survival Distribution
Specification of Censoring Distribution
When Accrual Rate Is Specified Instead of Accrual Period
Subunit Randomization versus Cluster Randomization
Numerical Studies
References
Group Sequential Testing for Cluster Randomized Trials with Time-to-Event Endpoint
Single-Stage Clustered Log-Rank Tests
Group Sequential Testing for the Clustered Log-Rank Statistic
Estimation of Covariance Matrix and Information Times
Maximal Sample Size
Numerical Studies
Comparison of Stopping Boundaries
Simulations
Examples
Discussion
References
Random Number Generation of Clustered Survival Data
Moran's Method
Under Cluster Randomization
Sequential Random Number Generation using Conditional Survival Functions
Under Cluster Randomization
Under Subunit Randomization
Gamma-Exponential Frailty Model
Under Cluster Randomization
Under Subunit Randomization
References
Cox's Regression for Clustered Survival Data
Cox's PHM for Clustered Survival Data
Example
References
Design and Analysis of Individually Randomized Group-Treatment Trials
IRGT Trials with Binary Data
Modified Chi-Squared Test
Sample Size Calculation for the Modified Chi-Squared Test
IRGT Trials with Continuous Data
Modified t-Test
Sample Size Calculation for the Modified t-Test
IRGT Trials with Survival Data
Rank Test for IRGT
Sample Size Calculation for the Log-Rank Test
Distributional Assumptions for Sample Size Calculation
When Number of Clustersis Given
Optimal Designs
Numerical Studies
Discussion
References
Analysis of Medical Tests I: Comparison of Concordance Rates with Clustered Data
Concordance Rates of Clustered Binary Data
Statistical Testing to Compare Concordance Rates
Powerand Sample Size Calculation
Simulation Studies
Example
Concordance Rates of Clustered Categorical Data
Numerical Studies and Results
References
Comparison of Binary Medical Tests and ROC Curves with Clustered Data
Comparison of Binary Tests with Clustered Data
Statistical Testing Methods
Simulations
Example
Comparison of Paired ROC Curves
A Statistical Test for Comparing Two Paired ROC Curves
Sample Size Calculation
Normally Distributed Biomarkers
Numerical Studies
Comparison of Two ROC Curves with Clustered Pair Data
References
Index