Handbook of Statistical Methods for Randomized Controlled Trials

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Preface
List of Figures
List of Tables
Contributors
I. Introduction to Randomized Controlled Trials
	1. Introduction
		1.1. Historical Background
		1.2. Statistical Concepts
		1.3. Organization of the Handbook
		Bibliography
II. Analytic Methods for Randomized Controlled Trials
	2. Binary and Ordinal Outcomes
		2.1. Introduction
		2.2. Analysis of 2 x 2 Contingency Tables
		2.3. Analysis of R x C Contingency Tables
		2.4. Analysis of Stratified 2 x 2 Contingency Tables
		2.5. Regression Models for Binary Outcomes
			2.5.1. Logistic regression
			2.5.2. Estimation and inference for logistic regression
			2.5.3. Exact logistic regression
			2.5.4. Example
		2.6. Regression Models for Ordinal Outcomes
			2.6.1. Proportional odds model
			2.6.2. Some alternative models for ordinal outcomes
			2.6.3. Example
		2.7. Adjustment for Baseline Response
		2.8. Concluding Remarks
		Bibliography
	3. Continuous Outcomes
		3.1. Introduction
		3.2. The t-Test (One Population)
		3.3. The t-Test (Two Populations)
		3.4. Mann-Whitney U-Test
		3.5. Paired Tests
			3.5.1. Paired t-test
			3.5.2. Wilcoxon signed rank test
		3.6. Multiple Comparisons
		3.7. Regression
			3.7.1. Residuals
			3.7.2. Inference for linear regression
			3.7.3. ANCOVA models
			3.7.4. Nonlinear regression
		3.8. Conclusion
		Bibliography
	4. Time to Event Data
		4.1. Introduction
		4.2. ACTG 320
		4.3. Mathematical Fundamentals
			4.3.1. Notation
			4.3.2. Hazard
			4.3.3. Censoring and observed data
		4.4. Estimation of Survival Distribution
		4.5. Hypothesis Testing
		4.6. Cox Regression Model
		4.7. Informative Censoring
		4.8. Conclusion
		Bibliography
	5. Count Data
		5.1. Introduction
		5.2. Regression Analysis of Simple Count Data
			5.2.1. Poisson regression for count
			5.2.2. Negative binomial regression for count
			5.2.3. Poisson and negative binomial regression for rate
			5.2.4. Other models for simple count data
		5.3. Regression Analysis of Correlated Count Data: Likelihood-Based Approaches
			5.3.1. Maximum pseudo-likelihood estimation for the Poisson model
			5.3.2. Maximum likelihood estimation for the Poisson model
			5.3.3. Maximum likelihood estimation for the negative binomial model
		5.4. Regression Analysis of Correlated Count Data: Distribution-Free Approaches
			5.4.1. Conditional estimating equation method
			5.4.2. Unconditional estimating equation method
			5.4.3. Analysis of the National Cooperative Gallstone Study
		5.5. Discussion and Concluding Remarks
		Bibliography
	6. Longitudinal Data
		6.1. Introduction
		6.2. Generalized Linear Models
		6.3. Generalized Estimating Equations
			6.3.1. Notations
			6.3.2. Asymptotic properties
			6.3.3. Efficiency
			6.3.4. Model selection criterion in GEE
		6.4. Generalized Linear Mixed Models
			6.4.1. Notations
			6.4.2. Population average versus subject-specific model
			6.4.3. Estimation procedures
				6.4.3.1. Marginal likelihood
				6.4.3.2. Conditional likelihood
		6.5. Test Statistics Under Randomization
			6.5.1. Notations
			6.5.2. Score-type test for GEE under randomization
			6.5.3. Score test for GLMMs under randomization
		6.6. Handling Missing Data in Clinical Trials
			6.6.1. Missing data in GEE
			6.6.2. Missing data in GLMMs
		6.7. Case Study
		Bibliography
	7. Recurrent Events
		7.1. Introduction
			7.1.1. Recurrent event data
			7.1.2. Data from a cystic fibrosis Trial
		7.2. Notation and Model Formulation
			7.2.1. Analysis considerations with recurrent event data
			7.2.2. Methods based on rate and mean functions
			7.2.3. Censoring, Likelihood, and Marginal Methods
			7.2.4. Assessment based on exacerbations in cystic fibrosis
		7.3. Sample Size Based on Proportional Rate Functions
			7.3.1. Derivations under a negative binomial model
			7.3.2. Illustrative sample size calculation
		7.4. Other Considerations in Recurrent Event Analyses
			7.4.1. Issues regarding causal inference
			7.4.2. Marginal multivariate failure times models
			7.4.3. Adaptive two-stage sample size estimation
			7.4.4. Recurrent and terminal events
		7.5. Discussion
		Acknowledgments
		Bibliography
III. Design of Randomized Controlled Trials
	8. Cross-Over Designs
		8.1. Introduction
		8.2. Some Examples
			8.2.1. Example 1 : An AB/BA design
			8.2.2. Example 2: A design in three treatments, three periods, and six sequences
			8.2.3. Example 3: An incomplete blocks design with fewer periods than treatments
			8.2.4. Example 4: A replicate cross-over design with more periods than treatments
			8.2.5. Example 5: A replicate bioequivalence study comparing two formulations in four periods
		8.3. General Considerations
			8.3.1. Phase of drug development
			8.3.2. Suitable indications
		8.4. Issues in Analysis
			8.4.1. Models for cross-over trials
			8.4.2. Patient effects and variance structures
			8.4.3. Carry-over effects
			8.4.4. Residual degrees of freedom and error estimation
		8.5. Examples of Analysis
			8.5.1. Basic estimator approach
			8.5.2. Two-sample t-test approach
			8.5.3. Linear and mixed models
			8.5.4. Testing for carry-over
			8.5.5. 8.5.5. An unbiased estimate of the treatment effect
			8.5.6. The two-stage procedure
		8.6. Issues in Design
			8.6.1. Choosing sequences
			8.6.2. Other issues
			8.6.3. Planning the sample size
		8.7. N-of-1 trials
		8.8. Conclusion
		8.9. Further reading
		8.10. Acknowledgement
		Bibliography
	9. Factorial Designs
		9.1. Introduction
		9.2. Different Usages of Factorial Designs
			9.2.1. Efficiency of confirmatory trials: Evaluation of more than one Intervention in a single study
			9.2.2. Screening trials: Developing multicomponent interventions
			9.2.3. Situations where factorial designs are not suitable
		9.3. Full Factorial Designs: A Theoretical Background
		9.4. Fractional Factorial Designs
		9.5. Analysis Strategies
		9.6. Follow-up Studies: Developing Multicomponent Interventions
		9.7. Power and Sample Size Considerations
		9.8. Discussion
		Bibliography
	10. Cluster Randomized Designs
		10.1. What is a Cluster Randomized Trial?
		10.2. The Problem of Clustering
		10.3. Summary Statistics
		10.4. The Intra-Cluster Correlation Coefficient and the Design Effect
		10.5. Baseline and Other Adjustments
		10.6. Robust Standard Errors
		10.7. Multilevel Modeling
		10.8. Generalized Estimating Equations (GEE) Models
		10.9. Stepped Wedge Designs
		10.10. Sample Size Estimation
		10.11. Practical Problems of Cluster Randomized Trials
		Bibliography
	11. Randomization, Stratification, and Outcome-Adaptive Allocation
		11.1. Introduction
		11.2. Simple and Restricted Randomization
		11.3. Stratified and Covariate-Adaptive Randomization
		11.4. Outcome-Adaptive Randomization
		11.5. Concluding Remarks
		Bibliography
	12. Background to Sample Size Calculations
		12.1. Introduction
		12.2. Types of Trials
			12.2.1. Parallel group trials
			12.2.2. Cross-over trials
		12.3. Continuous Outcomes
			12.3.1. Superiority trials
				12.3.1.1. Parallel group trials
				12.3.1.2. Quick results
				12.3.1.3. Worked example 1
				12.3.1.4. Cross-over trials
				12.3.1.5. Quick results
				12.3.1.6. Worked example 2
			12.3.2. Equivalence trials
				12.3.2.1. Parallel group trials
				12.3.2.2. Worked example 3
				12.3.2.3. Cross-over trials
				12.3.2.4. Worked example 4
			12.3.3. Non-inferiority trials
				12.3.3.1. Parallel group trials
				12.3.3.2. Worked example 5
				12.3.3.3. Cross-over trials
				12.3.3.4. Worked example 6
		12.4. Binary Outcomes
			12.4.1. Superiority trials
				12.4.1.1. Parallel group trials
				12.4.1.2. Method 2
				12.4.1.3. Worked example 7
				12.4.1.4. Cross-over trials
				12.4.1.5. Worked example 8
			12.4.2. Equivalence trials
				12.4.2.1. Parallel group trials
				12.4.2.2. Worked example 9
				12.4.2.3. Cross-over trials
			12.4.3. Non-inferiority trials
				12.4.3.1. Parallel group trials
				12.4.3.2. Worked example 10
		12.5. Final Remarks
		Bibliography
	13. Sample Size Estimation and Power Analysis: Time to Event Data
		13.1. Introduction
		13.2. Methods for Sample Size Estimation and Power Analysis
			13.2.1. Approaches relating to acquisition of events
			13.2.2. Estimation of required number of events: no accounting of other design parameters
			13.2.3. Estimation of required number of events: with accounting of other design parameters
		13.3. Case Studies
			13.3.1. Rare events with non-proportional hazard ratio
				13.3.1.1. The study as designed
				13.3.1.2. The study as it unfolded
				13.3.1.3. Insights gleaned from the study
				13.3.1.4. Alternative strategies
				13.3.1.5. Alternative strategy example
			13.3.2. An oncology study
			13.3.3. A diabetes noninferiority study
		13.4. Special Topics and Recent Developments
			13.4.1. Treatment effects beyond hazard ratios
			13.4.2. Sample size re-estimation
		Bibliography
	14. Sample Size Estimation and Power Analysis: Longitudinal Data
		14.1. Introduction
		14.2. Generalized Estimating Equations (GEE) Method
			14.2.1. Continuous outcome variable case
			14.2.2. Binary outcome variable case
		14.3. Power Analysis and Sample Size Estimation
			14.3.1. Continuous outcome variable case
			14.3.2. Binary outcome variable case
		14.4. Modelling Missing Pattern and Correlation Structure
			14.4.1. Missing pattern
			14.4.2. Correlation structure
		14.5. Examples
			14.5.1. Labor pain study (Continuous outcome case)
			14.5.2. Design of an RCT based on GENISOS (binary outcome case)
		14.6. Discussions
		Bibliography
IV. Monitoring of Randomized Controlled Trials
	15. Group Sequential Methods
		15.1. Group Sequential Methods
			15.1.1. A unified framework
			15.1.2. Boundaries
		15.2. The Effect of Monitoring on Power
		15.3. Futility/Stochastic Curtailment
		15.4. Problems with Post-Trial Inference
		15.5. Conclusions
		Bibliography
	16. Sample Size Re-Estimation
		16.1. Introduction
		16.2. Nuisance Parameter Based Sample Size Re-Estimation
			16.2.1. Sample size re-estimation for normal data
				16.2.1.1. Motivating example
				16.2.1.2. Statistical model and sample size re-estimation
				16.2.1.3. Unblinded nuisance parameter estimation
				16.2.1.4. Blinded nuisance parameter estimation
				16.2.1.5. Comparison of sample size re-estimation procedures
			16.2.2. Sample size re-estimation for count data
				16.2.2.1. Motivating example
				16.2.2.2. Negative binomial outcomes
			16.2.3. Further issues and recent developments
				16.2.3.1. Non-inferiority trials
				16.2.3.2. Controlling the type I error rate
				16.2.3.3. Size of the internal pilot study
				16.2.3.4. Covariates
				16.2.3.5. Other endpoints and more complex designs
				16.2.3.6. Multi-arm trials
				16.2.3.7. Incorporating historical data into the sample size re-estimation
		16.3. Effect-Based Sample Size Re-Estimation
			16.3.1. Controlling the type I error rate
			16.3.2. Sample size adaptation
			16.3.3. Further issues and recent developments
		16.4. Discussion
		Acknowledgements
		Bibliography
	17. Adaptive Designs
		17.1. Introduction
		17.2. General Principles
			17.2.1. The combination testing principle
			17.2.2. The closed testing principle
			17.2.3. Adaptive designs for multiple hypotheses
			17.2.4. Assessing the performance of an adaptive design
		17.3. Treatment Arm Selection Designs
			17.3.1. The procedure
			17.3.2. Binary and survival endpoints
			17.3.3. Case studies
		17.4. Population Enrichment Designs
			17.4.1. The procedure
			17.4.2. Effect specification
			17.4.3. Binary and survival endpoints
			17.4.4. Case studies
		17.5. Discussion and Further Developments
		Acknowledgment
		Bibliography
V. Practical Issues in Analysis of Randomized Controlled Trials
	18. Multiple Testing
		18.1. Error Rates in Multiple Comparisons
		18.2. Principles of Multiple Testing
			18.2.1. Partitioning principle
			18.2.2. Closed testing principle
		18.3. A Simple Example
		18.4. Shortcutting
			18.4.1. Holm's method is a shortcut
			18.4.2. Hochberg's method is also a shortcut
		18.5. Paths in Decision-Making
			18.5.1. Decision path respecting principle
			18.5.2. A specific dose x endpoint example
		18.6. Setting Priorities in Multiple Testing for Each Study
			18.6.1. The graphical approach
		18.7. Logical Relationships Among Parameters Tested
			18.7.1. Logic induced in multiple test construction
			18.7.2. Logic inherent in scientific parameters
		18.8. Going Forward
		Bibliography
	19. Subgroup Analysis
		19.1. Introduction
		19.2. Methods for Conducting Subgroup Analyses
			19.2.1. Commonly used methods
			19.2.2. Qualitative interaction
			19.2.3. Graphical methods
			19.2.4. Multivariate tests of interaction
		19.3. Power Consideration of Subgroup Analysis
		19.4. Subgroup Analysis Reporting and Interpretation
		19.5. Final Remarks
		Bibliography
	20. Competing Risks
		20.1. Introduction
		20.2. Cumulative Incidence Function in the Presence of Competing Risks
			20.2.1. Cumulative incidence function
			20.2.2. Estimation of CIF in the presence of competing risks
		20.3. Testing for Differences between Cumulative Incidence Curves in the Presence of Competing Risks
			20.3.1. Gray test
			20.3.2. Estimation of Gray statistic
		20.4. Competing Risks Regression Analysis
			20.4.1. Cause-specific hazard regression model
			20.4.2. Fine and Gray model
			20.4.3. Klein and Andersen model
			20.4.4. Remarks
		20.5. Conclusion
		20.6. Computing Tools
		Acknowledgements
		Bibliography
	21. Joint Models for Longitudinal and Time to Event Data
		21.1. Introduction
		21.2. Illustrative Example
		21.3. Joint Shared Random-Effect Models
			21.3.1. Model definition for Gaussian markers
			21.3.2. Model definition for discrete markers
			21.3.3. Estimation
				21.3.3.1. Likelihood
				21.3.3.2. Bayesian estimation
				21.3.3.3. Model diagnostic
			21.3.4. Joint shared random-effect models for clinical trials
				21.3.4.1. Distinguishing direct and indirect treatment effects
				21.3.4.2. Incomplete data
		21.4. Joint Latent Class Models
			21.4.1. Model definition
			21.4.2. Estimation
				21.4.2.1. Likelihood
				21.4.2.2. Model diagnostic
			21.4.3. Joint latent class models for clinical trials
		21.5. Conclusion and Recent Developments
		Acknowledgements
		Bibliography
VI. Miscellaneous Topics in Randomized Controlled Trials
	22. Design and Analysis Methods for Developing Personalized Treatment Rules
		22.1. Introduction
		22.2. Study Design
		22.3. Analysis Techniques: Single Stage
		22.4. Analysis Techniques: Multiple Stages
		22.5. Related Topics
			22.5.1. Variable selection
			22.5.2. Multiple outcomes
			22.5.3. DTRs for observational data
		22.6. Conclusion
		Bibliography
	23. Safety Evaluation in Clinical Trials
		23.1. Introduction
		23.2. Elements of a Systematic Approach to Clinical Trial Safety Data Evaluation
			23.2.1. The program safety analysis plan (PSAP)
			23.2.2. Facilitating combining data across studies, including planning meta-analyses (be prepared)
		23.3. Approaches to Characterizing the Product Safety Profile
			23.3.1. Known or pre-specified safety issues
				23.3.1.1. Specific safety issues that should always be considered for all products
				23.3.1.2. Product-specific adverse events of special interest (AESIs)
				23.3.1.3. Adverse events not specified in advance
			23.3.2. Data sources for safety evaluation including specific safety studies
		23.4. Planning for Clinical Data Collection and Standardization
			23.4.1. Definition of safety outcomes and adjudication
			23.4.2. Standardization of safety data collection
		23.5. Safety Data Analysis and Reporting
			23.5.1. Considerations for individual studies
				23.5.1.1. Defining the safety analysis set
				23.5.1.2. Accounting for time on or off treatment
			23.5.2. Meta-analysis of adverse event data
			23.5.3. Multiplicity
			23.5.4. Signal detection for common events
			23.5.5. Descriptive analysis of infrequent adverse events
			23.5.6. Reporting
		23.6. Conclusions
		Bibliography
	24. Non-Inferiority Trials
		24.1. Background and History
		24.2. Basics
			24.2.1. Historical studies
			24.2.2. Parameters and margins
			24.2.3. Study design and conduct
			24.2.4. Test statistics, confidence intervals and decision rules
			24.2.5. Reporting and interpretation
			24.2.6. Power and sample size assessment
			24.2.7. Equivalence and non-inferiority
		24.3. Issues and Evolving Ideas
			24.3.1. Analysis sets
			24.3.2. Missing data
			24.3.3. Adaptive designs
		24.4. Conclusions
		Bibliography
	25. Incorporating Historical Data into Randomized Controlled Trials
		25.1. Introduction
		25.2. Case Study
		25.3. Meta-Analytic-Predictive Approach
			25.3.1. Hierarchical model
			25.3.2. Mixture approximation for priors
			25.3.3. Robustness to a prior-data conflict
			25.3.4. Prior effective sample size
			25.3.5. Operating characteristics
			25.3.6. Analysis
		25.4. Other Approaches
			25.4.1. Meta-analytic-combined approach
			25.4.2. Bias models
			25.4.3. Commensurate priors
			25.4.4. Power priors
			25.4.5. Test-then-pool
			25.4.6. How much borrowing?
		25.5. Extensions
			25.5.1. Individual patient data and aggregate data
			25.5.2. Non-inferiority trials
		25.6. Discussion
		25.7. Appendix
			25.7.1. WinBUGS code
			25.7.2. SAS code
		Bibliography
	26. Evaluation of Surrogate Endpoints
		26.1. Introduction
		26.2. Data from a Single Trial
			26.2.1. Definition and criteria
			26.2.2. The proportion explained
			26.2.3. The relative effect
		26.3. A Meta-analytic Framework for Normally Distributed Outcomes
			26.3.1. A meta-analytic approach
		26.4. Non-Gaussian Endpoints
			26.4.1. Two binary endpoints
			26.4.2. Two failure-time endpoints
			26.4.3. An ordinal surrogate and a survival endpoint
			26.4.4. Binary and normally distributed endpoints
			26.4.5. Longitudinal endpoints
		26.5. Alternatives and Extensions
		26.6. Prediction and Design Aspects
		26.7. Case Studies
			26.7.1. A meta-analysis of five clinical trials in schizophrenia
				26.7.1.1. Analysis of continuous endpoints
				26.7.1.2. Analysis of the categorical endpoints
			26.7.2. Prostate-specific antigen (PSA)
				26.7.2.1. PSA as a surrogate in multiple trials
			26.7.3. Surrogate endpoints in gastric cancer
				26.7.3.1. Resectable gastric cancer: can DFS be used a surrogate for OS?
				26.7.3.2. Advanced gastric cancer: can PFS be used as a surrogate for OS?
				26.7.3.3. Contrasting conclusions about DFS and PFS
		26.8. Concluding Remarks
		Acknowledgment
		Bibliography
Index