Sample Sizes for Clinical Trials

✍ Scribed by Steven A. Julious

• Publisher: Chapman and Hall/CRC
• Year: 2023
• Tongue: English
• Leaves: 421
• Edition: 2
• Category: Library

✦ Synopsis

Sample Sizes for Clinical Trials, Second Edition is a practical book that assists researchers in their estimation of the sample size for clinical trials. Throughout the book there are detailed worked examples to illustrate both how to do the calculations and how to present them to colleagues or in protocols. The book also highlights some of the pitfalls in calculations as well as the key steps that lead to the final sample size calculation.

Features:

• Comprehensive coverage of sample size calculations, including Normal, binary, ordinal, and survival outcome data
• Covers superiority, equivalence, non-inferiority, bioequivalence and precision objectives for both parallel group and crossover designs
• Highlights how trial objectives impact the study design with respect to both the derivation of sample formulae and the size of the study
• Motivated with examples of real-life clinical trials showing how the calculations can be applied
• New edition is extended with all chapters revised, some substantially, and four completely new chapters on multiplicity, cluster trials, pilot studies, and single arm trials

The book is primarily aimed at researchers and practitioners of clinical trials and biostatistics, and could be used to teach a course on sample size calculations. The importance of a sample size calculation when designing a clinical trial is highlighted in the book. It enables readers to quickly find an appropriate sample size formula, with an associated worked example, complemented by tables to assist in the calculations.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Preface to the First Edition
1. Introduction
1.1. Background to Randomised Controlled Trials
1.2. Types of Clinical Trial
1.3. Assessing Evidence from Trials
1.3.1. The Normal Distribution
1.3.2. The Central Limit Theorem
1.3.3. Frequentist Approaches
1.3.3.1. Hypothesis Testing and Estimation
1.3.3.2. Hypothesis Testing – Superiority Trials
1.3.3.3. Statistical and Clinical Significance or Importance
1.4. Sample Size Calculations for a Clinical Trial
1.4.1. Why to Do a Sample Size Calculation?
1.4.2. Why Not to Do a Sample Size Calculation?
1.5. Superiority Trials
1.5.1. CACTUS Example
1.6. Equivalence Trials
1.6.1. General Case
1.6.2. Special Case of No Treatment Difference
1.7. Worked Example
1.8. Non-Inferiority Trials
1.8.1. Worked Example
1.9. As Good as or Better Trials
1.9.1. A Test of Non-Inferiority and One-Sided Test of Superiority
1.9.2. A Test of Non-Inferiority and Two-Sided Test of Superiority
1.10. Assessment of Bioequivalence
1.10.1. Justification for Log Transformation
1.10.2. Rationale for Using Coefficients of Variation
1.11. Estimation to a Given Precision
1.12. Summary
2. Seven Key Steps to Cook up a Sample Size
2.1. Introduction
2.2. Step 1: Deciding on the Trial Objective
2.3. Step 2: Deciding on the Endpoint
2.4. Step 3: Determining the Effect Size (or Margin)
2.4.1. Estimands
2.4.2. Quantifying an Effect Size
2.4.3. Obtaining an Estimate of the Treatment Effect
2.4.4. Worked Example with a Binary Endpoint
2.4.5. Worked Example with Normal Endpoint
2.4.6. Issues in Quantifying an Effect Size from Empirical Data
2.4.7. Further Issues in Quantifying an Effect Size from Empirical Data
2.4.8. A Worked Example Using the Anchor Method
2.4.9. Choice of Equivalence or Non-Inferiority Limit
2.4.9.1. Considerations for the Active Control
2.4.9.2. Considerations for the Retrospective Placebo Control
2.5. Step 4: Assessing the Population Variability
2.5.1. Binary Data
2.5.1.1. Worked Example of a Variable Control Response with Binary Data
2.5.2. Normal Data
2.5.2.1. Worked Example of Assessing Population Differences with Normal Data
2.6. Step 5: Type I Error
2.6.1. Superiority Trials
2.6.2. Non-Inferiority and Equivalence Trials
2.7. Step 6: Type II Error
2.8. Step 7: Other Factors
2.9. Summary
3. Sample Sizes for Parallel Group Superiority Trials with Normal Data
3.1. Introduction
3.2. Sample Sizes Estimated Assuming the Population Variance to Be Known
3.3. Worked Example 3.1
3.3.1. Initial Wrong Calculation
3.3.2. Correct Calculations
3.3.3. Accounting for Dropout
3.4. Worked Example 3.2
3.5. Design Considerations
3.5.1. Inclusion of Baselines or Covariates
3.5.2. Post-Dose Measures Summarised by Summary Statistics
3.5.3. Inclusion of Baseline or Covariates as Well as Post-Dose Measures Summarised by Summary Statistics
3.6. Revisiting Worked Example 3.1
3.6.1. Re-Investigating the Type II Error
3.7. Sensitivity Analysis
3.7.1. Worked Example 3.3
3.8. Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations
3.8.1. Worked Example 3.4.
3.9. Summary
4. Sample Size Calculations for Superiority Cross-Over Trials with Normal Data
4.1. Introduction
4.2. Sample Sizes Estimated Assuming the Population Variance to Be Known
4.2.1. Analysis of Variance (ANOVA)
4.2.2. Paired t-tests
4.2.3. Period Adjusted t-tests
4.2.4. Summary of Statistical Analysis Approaches
4.2.5. Sample Size Calculations
4.2.6. Worked Example 4.1
4.2.7. Worked Example 4.2
4.2.8. Worked Example 4.3
4.3. Sensitivity Analysis about the Variance Used in the Sample Size Calculations
4.3.1. Worked Example 4.4
4.4. Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations
4.5. Summary
5. Sample Sizes for Cluster Randomised Trials
5.1. Introduction
5.2. Context of the Chapter
5.3. Sample Size Calculations
5.3.1. Quantifying the Effect of Clustering
5.3.2. Sample Size Requirements for Cluster Randomised Designs
5.3.2.1. Worked Example 5.1
5.3.3. Sample Size Requirements for Cluster Trials with Baseline Data
5.3.3.1. Worked Example 5.2 – Worked Example 5.1 Revisited
5.4. Clustering in One-Arm of a Trial
5.4.1. Worked Example 5.3
5.4.2. Sample Size Requirements for Cluster Randomised Cross-Over Designs
5.4.2.1. Worked Example 5.4
5.5. Do Cluster Trials Need More People?
5.5.1. Worked Example 5.5
5.6. Stepped Wedge Trials
5.6.1. Sample Size Calculations
5.6.2. Worked Example 5.6 – Worked Example 5.1 Revisited Again
5.7. Summary
6. Allowing for Multiplicity in Sample Size Calculations for Clinical Trials
6.1. Introduction
6.2. Context of the Chapter
6.3. Multiple Treatment Comparisons
6.3.1. Multiplicity Adjustments for Independent Comparisons
6.3.1.1. Bonferroni
6.3.1.2. Hochberg Procedures
6.3.1.3. Holm Procedures
6.3.1.4. Gatekeeping through Sequential Testing
6.3.2. Multiplicity Adjustments for Correlated Comparisons
6.3.2.1. Hochberg Procedures
6.3.2.2. Dunnett’s Test
6.3.3. Sample Size Calculations Allowing for Multiplicity in the Endpoints
6.3.4. Worked Example 6.1 – Three Endpoints for the Sample Size Estimation
6.4. Allowing for Multiple Must-Win in Treatment Comparisons
6.4.1. Sample Size Calculations for Multiple Must-Win Trials Ignoring the Multiplicity in Type II Error
6.4.1.1 Worked Example 6.2 – Worked Example 6.1 Revisited as a Multiple Must-Win Trial but Ignoring the Multiplicity
6.4.2. Sample Sizes Accounting for the Multiplicity in Type II Error with Two Endpoints
6.4.2.1. Worked Example 6.3 – Worked Example 6.1 Revisited as a Multiple Must-Win Using Two Endpoints for the Sample Size Estimation
6.4.3. Sample Sizes for Multiple Must-Win Trials with More Than Two Endpoints
6.4.3.1. Worked Example 6.1 Revisited as a Multiple Must-Win Using Three Endpoints for the Sample Size Estimation
6.4.3.2. Non-Constant Treatment Effects
6.5. Summary
7. Sample Size Calculations for Non-Inferiority Clinical Trials with Normal Data
7.1. Introduction
7.2. Parallel-Group Trials
7.2.1. Sample Size Estimated Assuming the Population Variance to Be Known
7.2.2. Non-Inferiority Versus Superiority Trials
7.2.3. Worked Example 7.1
7.2.4. Sensitivity Analysis about the Mean Difference Used in the Sample Size Calculations
7.2.5. Worked Example 7.2
7.2.6. Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations
7.3. Cross-Over Trials
7.3.1. Sample Size Estimated Assuming the Population Variance to Be Known
7.3.2. Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations
7.4. As Good as or Better Trials
7.4.1. Worked Example 7.3
7.5. Summary
8. Sample Size Calculations for Equivalence Clinical Trials with Normal Data.
8.1. Introduction
8.2. Parallel Group Trials
8.2.1. Sample Sizes Estimated Assuming the Population Variance to Be Known
8.2.1.1. General Case
8.2.1.2. Special Case of No Treatment Difference
8.2.1.3. Worked Example 8.1
8.2.1.4. Worked Example 8.2
8.2.2. Sensitivity Analysis for the Assumed Mean Difference Used in the Sample Size Calculations
8.2.2.1. Worked Example 8.3
8.2.3. Calculations Taking Account of the Imprecision of the Variances Used in the Sample Size Calculations
8.2.3.1. General Case
8.2.3.2. Special Case of No Treatment Difference
8.3. Cross-Over Trials
8.3.1. Sample Size Estimated Assuming the Population Variance to Be Known
8.3.1.1. General Case
8.3.1.2. Special Case of No Treatment Difference
8.3.2. Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations
8.3.2.1. General Case
8.3.2.2. Special Case of No Treatment Difference
8.4. Summary
9. Sample Size Calculations for Bioequivalence Trials
9.1. Introduction
9.2. Cross-Over Trials
9.2.1. Sample Sizes Estimated Assuming the Population Variance to Be Known
9.2.1.1. General Case
9.2.1.2. Special Case of the Mean Ratio Equalling Unity
9.2.2. Replicate Designs
9.2.3. Worked Example 9.1
9.2.4. Sensitivity Analysis about the Variance Used in the Sample Size Calculations
9.2.5. Worked Example 9.2
9.2.6. Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations
9.2.6.1. General Case
9.2.6.2. Special Case of the Mean Ratio Equalling Unity
9.3. Parallel-Group Studies
9.3.1. Sample Size Estimated Assuming the Population Variance to Be Known
9.3.1.1. General Case
9.3.1.2. Special Case of the Ratio Equalling Unity
9.3.2. Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations
9.3.2.1. General Case
9.3.2.2. Special Case of the Mean Ratio Equalling Unity
9.4. Summary
10. Sample Size Calculations for Precision Clinical Trials with Normal Data
10.1. Introduction
10.2. Parallel Group Trials
10.2.1. Sample Size Estimated Assuming the Population Variance to Be Known
10.2.1.1. Worked Example 10.1 – Standard Results
10.2.1.2. Worked Example 10.2 – Using Results from Superiority Trials
10.2.1.3. Worked Example 10.3 – Sample Size Is Based on Feasibility
10.2.2. Sensitivity Analysis about the Variance Used in the Sample Size Calculations
10.2.3. Worked Example 10.4
10.2.4. Accounting for the Imprecision of the Variance in the Future Trial
10.2.4.1. Worked Example 10.5 – Accounting for the Imprecision in the Variance in the Future Trial
10.2.5. Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations
10.2.5.1. Worked Example 10.6 – Accounting for the Imprecision in the Variance Used in Calculations
10.2.6. Allowing for the Imprecision in the Variance Used in the Sample Size Calculations and in Future Trials
10.2.6.1. Worked Example 10.7 – Allowing for the Imprecision in the Variance Used in the Sample Size Calculations and in Future Trials
10.3. Cross-Over Trials
10.3.1. Sample Size Estimated Assuming the Population Variance to Be Known
10.3.2. Sensitivity Analysis about the Variance Used in the Sample Size Calculations
10.3.3. Accounting for the Imprecision of the Variance in the Future Trial
10.3.4. Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations
10.3.5. Allowing for the Imprecision in the Variance Used in the Sample Size Calculations and in Future Trials
10.4. Summary
11. Sample Sizes for Pilot Studies
11.1. Introduction
11.2. Minimum Sample Size for a Pilot Study
11.2.1. Reason 1: Feasibility
11.2.2. Reason 2: Precision about the Mean and Variance
11.2.2.1. Precision about the Mean
11.2.2.2. Precision about the Variance
11.2.3. Reason 3: Regulatory Considerations
11.2.4. Discussion of Minimum Sample Size
11.3. Recruiting on t and Not on n
11.4 Optimising the Sample Size for a Pilot Trial
11.5. Rules of Thumb Revisited
11.6. Summary
12. Sample Size Calculations for Parallel Group Superiority Clinical Trials with Binary Data
12.1. Introduction
12.2 Inference and Analysis of Clinical Trials with Binary Data
12.3. πs or ps
12.3.1. Absolute Risk Difference
12.3.1.1. Calculation of Confidence Intervals
12.3.1.2. Normal Approximation
12.3.1.3. Normal Approximation with Continuity Correction
12.3.1.4. Exact Confidence Intervals
12.3.2. Odds Ratio
12.3.2.1. Calculation of Confidence Intervals
12.4. Sample Sizes with the Population Effects Assumed Known
12.4.1. Odds Ratio
12.4.2. Absolute Risk Difference
12.4.2.1. Method 1 – Using the Anticipated Responses
12.4.2.2. Method 2 – Using the Responses under the Null and Alternative Hypotheses
12.4.2.3. Accounting for Continuity Correction and Exact Methods
12.4.2.4. Fisher’s Exact Test
12.4.3. Worked Example 12.1 – Sample Size Calculation for a Parallel Group Superiority Trial with Binary Response
12.4.4. Discussion of the Sample Size Calculations
12.4.5. Equating Odds Ratios with Absolute Risks
12.4.6. Equating Odds Ratios with Absolute Risks – Revisited
12.4.7. Worked Example 12.2
12.4.8. Worked Example 12.3
12.4.9. Worked Example 12.4
12.5. Inclusion of Baselines or Covariates
12.5.1. Methods for Allowing for Covariates
12.5.2. Comparison of Adjusted and Unadjusted Estimates
12.5.3. Reflections on Allowing for Covariates
12.5.4. Further Considerations – The Impact on Non-Inferiority and Equivalence Studies
12.6. Sensitivity Analysis about the Estimates of the Population
12.6.1. Worked Example 12.5
12.6.2. Worked Example 12.6
12.7. Calculations Taking Account of the Imprecision of the Estimates of the Population Effects Used in the Sample Size Calculations
12.7.1. Odds Ratio
12.7.2. Absolute Risk Difference
12.7.3. Worked Example 12.7
12.8. Summary
13. Sample Size Calculations for Superiority Cross-Over Clinical Trials with Binary Data
13.1. Introduction
13.2. Analysis of a Trial
13.2.1. Sample Size Estimation with the Population Effects Assumed Known
13.2.1.1. Worked Example 13.1
13.2.1.2. Worked Example 13.2
13.2.2. Comparison of Cross-Over and Parallel-Group Results
13.2.2.1. Worked Example 13.3
13.2.2.2. Worked Example 13.4
13.3. Analysis of a Trial Revisited
13.4. Sensitivity Analysis about the Estimates of the Population Effects Used in the Sample Size Calculations
13.5 Calculations Taking Account of the Imprecision of the Estimates of the Population Effects Used in the Sample Size Calculations
13.6. Summary
14. Sample Size Calculations for Non-Inferiority Trials with Binary Data
14.1. Introduction
14.2. Choice of Non-Inferiority Limit
14.3. Parallel Group Trials Sample Size with the Population Effects Assumed Known
14.3.1. Absolute Risk Difference
14.3.1.1. Method 1 – Using Anticipated Responses
14.3.2. Worked Example 1 – Sample Size Calculation for a Parallel Group Non-Inferiority Trial with Binary Response
14.3.2.1. Method 2 – Using Anticipated Responses in Conjunction with the Non-Inferiority Limit
14.3.2.2. Method 3 – Using Maximum Likelihood Estimates
14.3.2.3. Comparison of the Three Methods of Sample Size Estimation
14.3.3. Odds Ratio
14.3.3.1. Worked Example 14.1
14.3.4. Superiority Trials Re-Visited
14.3.5. Sensitivity Analysis about the Estimates of the Population Effects Used in the Sample Size Calculations
14.3.5.1. Worked Example 14.2
14.3.6. Absolute Risk Difference Versus Odds Ratios – Revisited
14.3.7. Calculations Taking Account of the Imprecision of the Estimates of the Population Effects Used in the Sample Size Calculations
14.3.7.1. Worked Example 14.3
14.3.8. Calculations Taking Account of the Imprecision of the Estimates of the Population Effects with Respect to the Assumptions about the Mean Difference and the Variance Used in the Sample Size Calculations
14.3.8.1. Worked Example 14.5
14.3.9. Cross-Over Trials
14.4. As Good as or Better Trials
14.4.1. A Test of Non-Inferiority and a One-Sided Test of Superiority
14.4.2. A Test of Non-Inferiority and a Two-Sided Test of Superiority
14.4.3. Sample Size Estimation
14.5. Summary
15. Sample Size Calculations for Equivalence Trials with Binary Data
15.1. Introduction
15.2. Parallel Group Trials
15.2.1. Sample Sizes with the Population Effects Assumed Known – General Case
15.2.1.1. Absolute Risk Difference
15.2.1.2. Method 1 – Using Anticipated Responses
15.2.2. Worked Example 1 – Sample Size Calculation for a Parallel Group Equivalence Trial with Binary Response
15.2.2.1. Method 2 – Using Anticipated Responses in Conjunction with the Equivalence Limit
15.2.2.2. Method 3 – Using Maximum Likelihood Estimates
15.2.2.3. Comparison of the Three Methods
15.2.2.4. Odds Ratio
15.2.2.5. Worked Example 15.1
15.2.3. Sensitivity Analysis about the Estimates of the Population Effects Used in the Sample Size Calculations
15.2.3.1. Worked Example 15.2
15.2.4. Calculations Taking Account of the Imprecision of the Estimates of the Populations Effects Used in the Sample Size Calculations
15.2.4.1. Worked Example 15.3
15.2.5. Calculations Taking Account of the Imprecision of the Population Effects with Respect to the Assumptions about the Mean Difference and the Variance Used in the Sample Size Calculations
15.2.5.1. Worked Example 15.4
15.3. Cross-Over Trials
15.4. Summary
16. Sample Size Calculations for Precision Trials with Binary Data
16.1. Introduction
16.2. Parallel Group Trials
16.2.1. Absolute Risk Difference
16.2.2. Worked Example 1 – Sample Size Calculation for a Parallel Group Estimation Trial with Binary Response
16.2.3 Odds Ratio
16.2.4. Equating Odds Ratios with Proportions
16.2.5. Worked Example 16.1
16.2.6. Sensitivity Analysis about the Estimates of the Population Effects Used in the Sample Size Calculations
16.2.6.1. Worked Example 16.2
16.3. Cross-Over Trials
16.4. Summary
17. Sample Size Calculations for Single-Arm Clinical Trials
17.1. Introduction
17.2. Single Proportion
17.2.1. Confidence Interval Calculation
17.2.1.1. Normal Approximation
17.2.1.2. Exact Confidence Intervals
17.2.2. One-Tailed or Two-Tailed?
17.2.3 Sample Size Calculation
17.2.3.1. Worked Example 1 – Sample Size Calculation for a Single Binary Response
17.2.4. Sample Size Calculation Re-Visited – Sample Size Based on Feasibility
17.2.4.1. Precision-Based Approach
17.2.4.2. Probability of Seeing an Event
17.2.4.3. Worked Example 2 – Calculating a Probability of Observing an Adverse Event
17.3. Finite Population Size
17.3.1. Practical Example
17.3.1.1. Worked Example Ignoring the Finite Population Sample
17.3.2. Methods for Accounting for Finite Populations
17.3.2.1. Normal Approximation
17.3.2.2. Beta Distribution
17.3.2.3. Worked Example Accounting for the Finite Population Sample
17.3.2.4. Extending the Results for a Normal Outcome
17.4. Sample Size Calculations
17.4.1. Standard Methods Ignoring the Finite Population Size
17.4.1.1. Worked Example Ignoring the Finite Population Sample
17.4.2. Methods for Accounting for Finite Populations
17.4.2.1. Worked Example Accounting for the Finite Population Sample
17.5. Summary
18. Sample Sizes for Clinical Trials with an Adaptive Design
18.1. Introduction
18.2. Adaptive Designs
18.2.1. Case Study
18.3. Sample Size Re-Estimation for Normal Data
18.3.1. Sample Sizes for Internal Pilot Trials – Assuming the Variance Is Known
18.3.2. Sample Size Re-Estimation with a Restriction on the Sample Size
18.3.2.1. Worked Example
18.3.2.2. Worked Example
18.3.3. Allowing for the Variance to Be Unknown
18.4. Sample Size Re-Estimation for Binary Data
18.5. Interim Analyses
18.6. Allowing for an Assessment of Futility
18.7. Sample Size Re-Estimation and Promising Zone
18.7.1. Worked Example
18.7.1.1. Discussion of Promising Zone
18.8. Efficacy Interim Analyses
18.8.1. Pocock Approach
18.8.2. O’Brien-Fleming Approach
18.8.3. Wang-Tsiatis Approach
18.8.4. Special Case of One Interim Analysis
18.8.5. Worked Example 18.1
18.8.6. More than One Interim Analysis
18.9. Summary
19. Sample Size Calculations for Clinical Trials with Ordinal Data
19.1. Introduction
19.2. The Quality of Life Data
19.3. Superiority Trials
19.3.1. Parallel Group Trials
19.3.2. Whitehead’s Method
19.3.2.1. Worked Example 19.1 – Full Ordinal Scale
19.3.2.2. Worked Example 19.2 – Effects of Dichotomisation
19.3.2.3. Worked Example 19.3 – Additional Categories
19.3.2.4. Worked Example 19.4 – Quick Result
19.3.3. Noether’s Method
19.3.3.1. Worked Example 19.5 – Illustrative Example
19.3.3.2. Worked Example 19.6 – MRC Example Revisited – Full Ordinal Scale
19.3.3.3. Worked Example 19.7 – Four Categories
19.3.4. Comparison of Methods
19.3.5. Sensitivity Analysis of the Estimates of the Population Effects Used in the Sample Size Calculations
19.3.5.1. Worked Example 19.8 – Full Ordinal Scale
19.3.6. Calculations Taking Account of the Imprecision of the Estimates of the Population Effects Used in the Sample Size Calculations
19.3.6.1. Worked Example 19.9 – Full Ordinal Scale
19.3.7. Cross-Over Trials
19.3.7.1. Worked Example 19.10 – Full Ordinal Scale
19.3.7.2. Worked Example 19.11 – Applying Parallel Group Methodology
19.3.7.3. Worked Example 19.12 – Applying Binary Methodology
19.3.8. Sensitivity Analysis of the Estimates of the Population Effects Used in the Sample Size Calculations
19.3.8.1. Worked Example 19.13
19.3.9. Calculations Taking Account of the Imprecision of the Estimates of the Population Effects Used in the Sample Size Calculations
19.3.9.1. Worked Example 19.14
19.4. Non-Inferiority Trials
19.4.1. Parallel Group Trials
19.4.1.1. Sensitivity Analysis of the Variance Used in the Sample Size Calculations
19.4.1.2. Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations
19.4.2 Cross-Over Trials
19.4.2.1. Sensitivity Analysis of the Variance Used in the Sample Size Calculations
19.4.2.2. Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations
19.5. As Good As or Better Trials
19.6. Equivalence Trials
19.6.1. Parallel Group Trials
19.6.1.1. Sensitivity Analysis of the Variance Used in the Sample Size Calculations
19.6.1.2. Calculations Taking Account of the Imprecision of the Variances Used in the Sample Size Calculations
19.6.2. Cross-Over Trials
19.6.2.1. Sensitivity Analysis of the Variance Used in the Sample Size Calculations
19.6.2.2. Calculations Taking Account of the Imprecision of the Variances Used in the Sample Size Calculations
19.7. Estimation to a Given Precision
19.7.1. Parallel Group Trials
19.7.1.1. Worked Example 19.17
19.7.1.2. Sensitivity Analysis of the Variance Used in the Sample Size Calculations
19.7.1.3. Worked Example 19.18
19.7.2. Cross-Over Trials
19.8. Summary
20. Estimating the Number of Events for Clinical Trials with Survival Data for a Negative Outcome
20.1. Introduction
20.2. Superiority Trials
20.2.1. Method 1 – Assuming Exponential Survival
20.2.2. Method 2 – Proportional Hazards Only
20.2.2.1. Worked Example 20.1
20.3. Delayed Treatment Effects
20.4. Non-Inferiority Trials
20.5. Equivalence Trials
20.6. Precision Trials
20.7. Summary
21. Sample Size Calculations for Clinical Trials with Survival Data and a Positive Outcome
21.1. Introduction
21.2. Methods for Estimating the Number of Events
21.2.1. Method of Whitehead
21.2.2. Method of Noether
21.2.2.1. Worked Example 21.1 – Estimating Number of Events Using Noether’s Approach
21.2.3. Assuming the Data Are Log-Normal
21.2.3.1. Worked Example 21.2 – Normal Approximation Approach
21.2.4. Assuming the Data Are Normal (Revisited)
21.2.4.1. Worked Example 21.3 – Normal Approach (Revisited)
21.2.5. Summary of the Approaches So Far
21.3. Assuming a Weibull Distribution
21.3.1. Superiority Trials
21.3.1.1. Worked Example 21.4 – Estimating Number of Events for a Weibull Model
21.3.2. Non-Inferiority Trials
21.3.3. Equivalence Trials
21.3.4. Precision Trials
21.4. Summary
22. Sample Size Calculations for Clinical Trials with Survival Data Allowing for Recruitment and Loss and Follow-up
22.1. Introduction
22.2. Initial Estimation of Total Sample Size
22.3. Loss to Follow-Up
22.3.1. Worked Example 22.1 – Estimating Total Sample Size
22.3.2. Summary of Simple Calculations
22.4. Total Sample Size Re-Visited
22.4.1. Worked Example 22.2 – Estimating Total Sample Size with a Uniform Pattern of Recruitment
22.4.2. Worked Example 22.3 – Truncated Exponential Recruitment
22.5. Summary of Worked Examples in the Chapter
22.5.1. Worked Example 22.4 – Estimating Study Duration for a Fixed Total Sample
22.6. Summary
Appendix
References
Index