Success Probability Estimation with Applications to Clinical Trials E-Book

Daniele De Martini

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 290

Veröffentlichungsjahr: 2013

Beschreibung

Provides an introduction to the various statistical techniques involved in medical research and drug development with a focus on estimating the success probability of an experiment Success Probability Estimation with Applications to Clinical Trials details the use of success probability estimation in both the planning and analyzing of clinical trials and in widely used statistical tests. Devoted to both statisticians and non-statisticians who are involved in clinical trials, Part I of the book presents new concepts related to success probability estimation and their usefulness in clinical trials, and each section begins with a non-technical explanation of the presented concepts. Part II delves deeper into the techniques for success probability estimation and features applications to both reproducibility probability estimation and conservative sample size estimation. Success Probability Estimation with Applications to Clinical Trials: * Addresses the theoretical and practical aspects of the topic and introduces new and promising techniques in the statistical and pharmaceutical industries * Features practical solutions for problems that are often encountered in clinical trials * Includes success probability estimation for widely used statistical tests, such as parametric and nonparametric models * Focuses on experimental planning, specifically the sample size of clinical trials using phase II results and data for planning phase III trials * Introduces statistical concepts related to success probability estimation and their usefulness in clinical trials Success Probability Estimation with Applications to Clinical Trials is an ideal reference for statisticians and biostatisticians in the pharmaceutical industry as well as researchers and practitioners in medical centers who are actively involved in health policy, clinical research, and the design and evaluation of clinical trials.

Leseprobe

Contents

Cover

Half Title page

Title page

Copyright page

Dedication

Preface

Acknowledgments

Acronyms

Introduction: Clinical Trials, Success Rates, and Success Probability

I.1 Overview of clinical trials

I.2 Success rates of clinical trials

I.3 Success probability

I.4 Starting from practice

Part I: Success Probability Estimation in Planning and Analyzing Clinical Trials

Chapter 1: Basic Statistical Tools

1.1 Pointwise estimation

1.2 Confidence interval estimation, conservative estimation

1.3 The statistical hypotheses, the statistical test and the type I error for one-tailed tests

1.4 The power function and the type II error

1.5 The p-value

1.6 The success probability and its estimation

1.7 Basic statistical tools for two-tailed tests

1.8 Other statistical hypotheses and tests

Chapter 2: Reproducibility Probability Estimation

2.1 Pointwise RP estimation

2.2 RP-testing

2.3 The RP estimate and the p-value

2.4 Statistical lower bounds for the RP

2.5 The γ-stability criterion for statistical significance

2.6 Other stability criteria for statistical significance

2.7 Comparing stability criteria

2.8 Regulatory agencies and the single study

2.9 The RP for two-tailed tests

2.10 Discussing Situation I in Section 1.4.1

Chapter 3: Sample Size Estimation

3.1 The classical paradigm of sample size determination

3.2 SP estimation for adapting the sample size

3.3 Launching the trial in practice

3.4 Practical aspects of SSE

3.5 Frequentist conservative SSE

3.6 Optimal frequentist CSSE

3.7 Bayesian CSSE

3.8 A comparison of CSSE strategies

3.9 Discussing Situations I and II in Section 1.4

3.10 Sample size estimation for the two-tailed setting

Chapter 4: Robustness and Corrections in Sample Size Estimation

4.1 CSSE strategies with different effect sizes in phases II and III

4.2 Comparing CSSE strategies in different scenarios

4.3 Corrections for CSSE strategies

4.4 A comparison among corrected CSSE strategies

Part II: Success Probability Estimation for Some Widely Used Statistical Tests

Chapter 5: General Parametric SP Estimation

5.1 The parametric model

5.2 Power, SP and noncentrality parameter estimation

5.3 RP estimation and testing

5.4 Sample size estimation

5.5 Statistical tests included in the model

Chapter 6: SP Estimation for Student’s t Statistical Tests

6.1 Test for two means − equal variances

6.2 Test for two means − unequal variances

6.3 On Student’s t RP estimates

Chapter 7: SP Estimation for Gaussian Distributed test Statistics

7.1 Test for two proportions

7.2 Test for survival: the log-rank test

Chapter 8: SP Estimation for Chi-Square Statistical Tests

8.1 Test for two multinomial distributions: 2 × C comparative trial

8.2 Test for S couples of binomial distributions: the Mantel-Haenszel test

8.3 On chi-square RP estimates

Chapter 9: General Nonparametric SP Estimation - with Applications to the Wilcoxon Test

9.1 The nonparametric model

9.2 General nonparametric SP estimation

9.3 The Wilcoxon rank-sum test

Appendix A: Tables of Quantiles

Appendix B: Tables of RP Estimates for the One-Tailed Z-Test

References

Topic Index

Author Index

Success Probability Estimation with Applications to Clinical Trials

Copyright © 2013 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, [phone], fax [phone], or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, [phone], fax [phone], or online at http://www.wiley.com/go/permission.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at [phone], outside the United States at [phone] or fax [phone].

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com.

Library of Congress Cataloging-in-Publication Data:

De Martini, Daniele, 1965–  Success probability estimation with applications to clinical trials / Daniele De Martini,      p. ; cm.  Includes bibliographical references and indexes.  ISBN 978-1-118-33578-9 (cloth)  I. Title.  [DNLM: 1. Clinical Trials as Topic. 2. Probability. 3. Pharmaceutical Preparations. 4. Statistics as Topic. QV 771.4]  610.72′4—dc23 2013001310

To my family

PREFACE

This book aims to provide a simple and understandable introduction to the statistical techniques of success probability estimation.

Success probability estimation offers an original and practical perspective to the two problems: 1) evaluating the statistical significance and the stability of an experiment whose data analysis is based on a statistical test (e.g. a phase III trial), in order to avoid, if possible, further confirmatory studies; and 2) planning experiments on the basis of pilot data (e.g. phase III trials on the basis of phase II data), taking into account the variability of pilot data.

It is worth noting that these two problems have a common mathematical core, that is, the estimation of the true power of the test, namely the success probability. Usually, the power of statistical tests is viewed as a mathematical function, and it is studied analytically to compare these tests. Here, the new perspective is to estimate the true power of the tests, in other words, to estimate the success probability of experiments based on statistical tests.

The introduction, regarding clinical trials in general and reporting of some remarkable numbers related to them, opens the book. Then, the book is divided into two Parts: I) Success Probability Estimation in Planning and Analyzing Clinical Trials; and II) Success Probability Estimation for Some Widely Used Statistical Tests.

The first part presents the concepts related to success probability estimation and their usefulness in applied statistics, and in clinical trials in particular. Part I is devoted to both statisticians and non-statisticians (for example, clinicians who are involved in clinical trials).

The second part is mainly of interest to statisticians. An in depth analysis is provided on the techniques for success probability estimation, with applications both to reproducibility probability estimation and to conservative sample size estimation of some widely used statistical tests.

D. DE MARTINI

Genoa, ItalyMarch, 2013

ACKNOWLEDGMENTS

I would like to thank the Department of Statistics of Stanford University, where I visited several times, for the exceptional intellectual atmosphere I breathed there. I would also like to thank the Department of Statistics and Quantitative Methods (DiSMeQ) of the Università degli Studi di Milano-Bicocca for supporting this book.

With regards to single individuals, I wish to warmly thank Dr. Maurizio Rainisio and Dr. Lucio De Capitani, who revised the manuscript and gave me some useful suggestions.

D.D.M.

ACRONYMS

1SES

One Standard Error Strategy

3QS

Third Quartile Strategy

AN

Asymptotic Normality

AP

Average Power

BAS

Bayesian Strategy

BAT

Bayesian Truncated Strategy

COS

Calibrated Optimal Strategy

CSSE

Conservative Sample Size Estimation

dfs

Degrees of Freedom

edf

Empirical Distribution Function

iff

If and Only if

MC

Monte Carlo

MSE

Mean Square Error

OP

Overall Power

PWS

PointWise Strategy

RP

Reproducibility Probability

SP

Success Probability

SS

Single Study

SSE

Sample Size Estimation

WRS

Wilcoxon Rank-Sum

INTRODUCTION: CLINICAL TRIALS, SUCCESS RATES, AND SUCCESS PROBABILITY

This book considers experiments whose data are analyzed through statistical tests. A significant outcome of a test is considered a success, whereas a non-significant one is a failure.

Data are supposed to be collected with a certain amount of randomness, which implies the adoption of statistical tests for data analysis. Consequently, also the outcomes of the tests, i.e. success/failure, are affected by randomness. So, the probability of a successful outcome in these experiments, i.e. the probability of a significant outcome, is of great interest to researchers, sponsors of research and users of research results.

Focus is placed on large experiments that have been preceded by pilot ones. A pilot experiment is often performed in order to achieve data for deciding whether or not to launch the successive, important study and, if this is the case, to adequately plan the latter.

One of the contexts in which the framework above can be found is that of clinical trials. Here, large experiments are phase III trials, and previous phase II studies can be considered pilot studies in view of the subsequent phase III studies. A brief introduction to clinical trials follows, together with some data on their success rates and an introduction to their individual probability of success.

To conclude, in order to introduce applied problems related to success probability estimation, and to motivate the latter, two practical situations often encountered in clinical trials are presented, which can also be understood by those owning minimal statistical skills.