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# Sample Sizes for Clinical Trials

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## Book Description

Drawing on various real-world applications, **Sample Sizes for Clinical Trials** takes readers through the process of calculating sample sizes for many types of clinical trials. It provides descriptions of the calculations with a practical emphasis.

Focusing on normal, binary, ordinal, and survival data, the book explores a range of trials, including superiority, equivalence, non-inferiority, bioequivalence, and precision for both parallel group and crossover designs. The author discusses how trial objectives impact the study design with respect to the derivation of formulae for sample size calculations. He uses real-life studies throughout to show how the concepts and calculations can be employed.

This work underscores the importance of sample size calculation in the design of a clinical trial. With useful calculation tables throughout, it enables readers to quickly find an appropriate formula, formula application, and associated worked example.

Watch the author speak about this book at JSM 2012 in San Diego.

## Table of Contents

**Introduction**

Background to Randomized Controlled Trials

Types of Clinical Trial

Assessing Evidence from Trials

Superiority Trials

Equivalence Trials

Non-Inferiority Trials

As-Good-as-or-Better Trials

Assessment of Bioequivalence

Estimation to a Given Precision

**Seven Key Steps to Cook up a Sample Size**

Introduction

Step 1: Deciding on the Trial Objective

Step 2: Deciding on the Endpoint

Step 3: Determining the Effect Size (or Margin)

Step 4: Assessing the Population Variability

Step 5: Type I Error

Step 6: Type II Error

Step 7: Other Factors

**Sample Sizes for Parallel Group Superiority Trials with Normal Data**

Introduction

Sample Sizes Estimated Assuming the Population Variance to Be Known

Design Considerations

Revisiting Worked Example

Sensitivity Analysis

Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations

Interim Analyses and Sample Size Re-Estimation

Cluster Randomized Trials

**Sample Size Calculations for Superiority Crossover Trials with Normal Data**

Introduction

Sample Sizes Estimated Assuming the Population Variance to Be Known

Sensitivity Analysis about the Variance Used in the

Sample Size Calculations

Calculations Taking Account of the Imprecision of the Variance Used in the Sample Size Calculations

**Sample Size Calculations for Equivalence Clinical Trials with Normal Data**

Introduction

Parallel Group Trials

Crossover Trials

**Sample Size Calculations for Non-Inferiority Clinical Trials with Normal Data**

Introduction

Parallel Group Trials

Crossover Trials

As-Good-as-or-Better Trials

**Sample Size Calculations for Bioequivalence Trials**

Introduction

Crossover Trials

Parallel Group Studies

**Sample Size Calculations for Precision-Based Clinical Trials with Normal Data**

Introduction

Parallel Group Trials

Crossover Trials

**Sample Size Calculations for Parallel Group Superiority Clinical Trials with Binary Data**

Introduction

Inference and Analysis of Clinical Trials with Binary Data

Sample Sizes with the Population Effects Assumed Known

Inclusion of Baselines or Covariates

Sample Size Re-Estimation

Sensitivity Analysis about the Estimates of the Population Effects Used in the Sample Size Calculations

Calculations Taking Account of the Imprecision of the Estimates of the Population Effects Used in the Sample Size Calculations

Calculations Taking Account of the Imprecision of the Estimates Used in the Sample Size Calculations: Bayesian Methods

**Sample Size Calculations for Superiority Crossover Clinical Trials with Binary Data**

Introduction

Analysis of a Trial

Analysis of a Trial Revisited

Sensitivity Analysis about the Estimates of the Population Effects Used in the Sample Size Calculations

Calculations Taking Account of the Imprecision of the Estimates of the Population Effects Used in the Sample Size Calculations

Calculations Taking Account of the Imprecision of the Estimates Used in the Sample Size Calculations: Bayesian Methods

**Sample Size Calculations for Non-Inferiority Trials with Binary Data**

Introduction

Choice of Non-Inferiority Limit

Parallel Group Trials Sample Size with the Population Effects Assumed Known

As-Good-as-or-Better Trials

**Sample Size Calculations for Equivalence Trials with Binary Data**

Introduction

Parallel Group Trials

Crossover Trials

**Sample Size Calculations for Precision-Based Trials with Binary Data**

Introduction

Parallel Group Trials

Crossover Trials

**Sample Size Calculations for Clinical Trials with Ordinal Data**

Introduction

The Quality-of-Life Data

Superiority Trials

Non-Inferiority Trials

As-Good-as-or-Better Trials

Equivalence Trials

Estimation to a Given Precision

**Sample Size Calculations for Clinical Trials with Survival Data**

Introduction

Superiority Trials

Non-Inferiority Trials

Equivalence Trials

Precision-Based Trials

**References**

**Appendix**

## Author(s)

### Biography

**Steven A. Julious** is a Senior Lecturer in Medical Statistics at the University of Sheffield. His research interests include clinical trials, clinical trial design, early phase trials, and the development of new methodologies related to clinical trials.

## Reviews

"… a useful compendium that takes the reader through the process of calculating sample sizes and addresses many points to consider for the most common types of clinical trials and data. … this book provides a good introduction to the most common trial design scenarios for comparing two treatments. With a lot of hints, tips, and numeric examples, it is easy to read for statisticians and non-statisticians."

—ISCB News, December 2015"… it is lively, peppered with opinions and advice, and full of methods. … the book has many useful formulas for a variety of designs. It is well organized, so users can easily find the section relevant to their needs. And the plethora of worked examples is very helpful. … a useful introduction to the clinical researcher and as a reference for the statistician interested in sample size formulae for specific designs."

—Janet T. Wittes,Biometrics, February 2012"The book’s author is an expert and experienced researcher of clinical trial design and conduct. … True to its purpose as a reference book (or manual) for sample size calculation, the book covers all relevant formulas for sample size calculation. It also includes examples to demonstrate the implementation of the formulas, and even has boxed texts to highlight major ideas and "to do lists" for users. The demonstrations of the methods and formulas using study examples are a very helpful feature of the book. For each type of response (including even ordinal and survival responses), formulas for various types of clinical trials, including equivalent trials and design with interim analysis, are covered."

—Debajyoti Sinha,Journal of the American Statistical Association, September 2011, Vol. 106"The book should be useful as a reference work for statisticians or other researchers that are interested in quickly finding an appropriate formula for a sample size calculation problem. Although the worked examples may be quite short, they are useful for understanding the discussed methods and for the reader to apply the methods by himself or herself. Each chapter also ends with a valuable short summary that gives the key messages to be learned from the chapter in question."

—International Statistical Review,2010, 78, 3"… fairly comprehensive in its description of sample size calculations across a multitude of trial designs and analytical approaches. … It is worth noting that the accumulation of references to the author’s published work in a multitude of journals as one reads through the text is demonstrative of the level of contributions he has made to the topic of this book. He clearly has a comprehensive knowledge of the literature that contributes to the body of knowledge in this area of methodology. … this is an extremely useful reference book that does not require a large investment of time to be able to put it to good use. The nomenclature used is clear and not overly complex, and key points are highlighted both within the chapter contents as well as in tabular format at the end of each chapter. … he also covers some less common topics, … which are very useful in practice and somewhat unique as topics for a text on this subject matter."

—Christopher A. Assaid,Journal of Biopharmaceutical Statistics, Issue 4, 2010