Hybrid Frequentist/Bayesian Power and Bayesian Power in Planning Clinical Trials

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Table of Contents
List of Figures
List of Tables
Preface
Acknowledgements
Author
List of Acronyms
Chapter 1: Introduction
Chapter 2: All Power Is Conditional Unless It’s Absolute
	2.1 Introduction
	2.2 Expected, Average and Predicted Power
		2.2.1 Averaging Conditional Power with Respect to the Prior – Analytic Calculation
		2.2.2 Calculating the Probability of Achieving “Significance” – Predictive Power
		2.2.3 Averaging Conditional Power with Respect to the Prior – Numerical Integration
		2.2.4 Averaging Conditional Power with Respect to the Prior – Simulation
	2.3 Bounds on Average Power
	2.4 Average Power for a Robust Prior
	2.5 Decomposition of Average Power
	2.6 Average Power – Variance Estimated
		2.6.1 Bound on Average Power when the Variance Is Estimated
Chapter 3: Assurance
	3.1 Introduction
	3.2 Basic Considerations
	3.3 Sample Size for a Given Average Power/Assurance
	3.4 Sample Size for a Given Normalised Assurance
	3.5 Applying Assurance to a Series of Studies
	3.6 A Single Interim Analysis in a Clinical Trial
	3.7 Non-Inferiority Trials
		3.7.1 Fixed Margin
		3.7.2 Synthesis Method
		3.7.3 Bayesian Methods
Chapter 4: Average Power in Non-Normal Settings
	4.1 Average Power Using a Truncated-Normal Prior
	4.2 Average Power When the Variance Is Unknown: (a) Conditional on a Fixed Treatment Effect
	4.3 Average Power When the Variance Is Unknown: (b) Joint Prior on Treatment Effect and Variance
	4.4 Average Power When the Response Is Binary
	4.5 Illustrating the Average Power Bound for a Binary Endpoint
	4.6 Average Power in a Survival Context
		4.6.1 An Asymptotic Approach to Determining the AP
		4.6.2 The Average Power for the Comparison of One Parameter Exponential Distributions
		4.6.3 A Generalised Approach to Simulation of Assurance for Survival Models
	Note
Chapter 5: Bayesian Power
	5.1 Introduction
	5.2 Bayesian Power
	5.3 Sample Size for a Given Bayesian Power
	5.4 Bound on Bayesian Power
	5.5 Sample Size for a Given Normalised Bayesian Power
	5.6 Bayesian Power when the Response Is Binary
	5.7 Posterior Conditional Success Distributions
		5.7.1 Posterior Conditional Success Distributions – Success Defined By Significance
		5.7.2 Posterior Conditional Success Distributions – Success Defined By a Bayesian Posterior Probability
		5.7.3 Use of Simulation to Generate Samples from the Posterior Conditional Success and Failure Distributions
		5.7.4 Use of the Posterior Conditional Success and Failure Distributions to Investigate Selection Bias
Chapter 6: Prior Distributions of Power and Sample Size
	6.1 Introduction
	6.2 Prior Distribution of Study Power – Known Variance
	6.3 Prior Distribution of Study Power – Treatment Effect Fixed, Uncertain Variance
	6.4 Prior Distribution of Study Sample Size – Variance Known
	6.5 Prior Distribution of Sample Size – Treatment Effect Fixed, Uncertain Variance
	6.6 Prior Distribution of Study Power and Sample Size – Uncertain Treatment Effect and Variance
	6.7 Loss Functions and Summaries of Prior Distributions
Chapter 7: Interim Predictions
	7.1 Introduction
	7.2 Conditional and Predictive Power
	7.3 Stopping for Futility Based on Predictive Probability
	7.4 “Proper Bayesian” Predictive Power
Chapter 8: Case Studies in Simulation
	8.1 Introduction
	8.2 Case Study 1 – Proportional Odds Primary Endpoint
		8.2.1 Background
		8.2.2 The Wilcoxon Test for Ordered Categorical Data
		8.2.3 Applying Conditional Power to the Proportional Odds Wilcoxon Test
		8.2.4 Statistical Approach to Control Type I Error
		8.2.5 Simulation Set-Up
		8.2.6 Simulation Results
	8.3 Case Study 2 – Unplanned Interim Analysis
		8.3.1 Background
		8.3.2 Interim Data
		8.3.3 Model for Prediction
Chapter 9: Decision Criteria in Proof-of-Concept Trials
	9.1 Introduction
	9.2 General Decision Criteria for Early Phase Studies
	9.3 Known Variance Case
	9.4 Known Variance Case – Generalised Assurance
	9.5 Bounds on Unconditional Decision Probabilities for Multiple Decision Criteria
	9.6 Bayesian Approach to Multiple Decision Criteria
	9.7 Posterior Conditional Distributions with Multiple Decision Criteria
	9.8 Estimated Variance Case
	9.9 Estimated Variance Case – Generalised Assurance
	9.10 Discussion
Chapter 10: Surety and Assurance in Estimation
	10.1 Introduction
	10.2 An Alternative to Power in Sample Size Determination
	10.3 Should the Confidence Interval Width Be the Sole Determinant of Sample Size?
	10.4 Unconditional Sample Sizing Based on CI Width
		10.4.1 Modified Cook Algorithm
		10.4.2 Harris et al. (1948) Algorithm
	10.5 A Fiducial Interpretation of (10.14)
	Note
References
Appendix 1: Evaluation of a Double Normal Integral
Appendix 2: Besag’s Candidate Formula
Index