Statistics Applied to Clinical Studies

Transcription

1 Statistics Applied to Clinical Studies

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3 Ton J. Cleophas Aeilko H. Zwinderman Statistics Applied to Clinical Studies Fifth Edition With the help from Toine F. Cleophas, Eugene P. Cleophas, and Henny I. Cleophas-Allers

4 Ton J. Cleophas Past-President American College of Angiology Co-Chair Module Statistics Applied to Clinical Trials European Interuniversity College of Pharmaceutical Medicine, Lyon France Department of Medicine Albert Schweitzer Hospital, Dordrecht Netherlands Aeilko H. Zwinderman President-Elect International Society of Biostatistics Co-Chair Module Statistics Applied to Clinical Trials European Interuniversity College of Pharmaceutical Medicine, Lyon France Department of Biostatistics and Epidemiology, Academic Medical Center, Amsterdam Netherlands ISBN e-isbn DOI / Springer Dordrecht Heidelberg London New York Library of Congress Control Number: Springer Science+Business Media B.V No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 Foreword In clinical medicine appropriate statistics has become indispensable to evaluate treatment effects. Randomized controlled trials are currently the only trials that truly provide evidence-based medicine. Evidence based medicine has become crucial to optimal treatment of patients. We can define randomized controlled trials by using Christopher J. Bulpitt s definition a carefully and ethically designed experiment which includes the provision of adequate and appropriate controls by a process of randomization, so that precisely framed questions can be answered. The answers given by randomized controlled trials constitute at present the way how patients should be clinically managed. In the setup of such randomized trial one of the most important issues is the statistical basis. The randomized trial will never work when the statistical grounds and analyses have not been clearly defined beforehand. All endpoints should be clearly defined in order to perform appropriate power calculations. Based on these power calculations the exact number of available patients can be calculated in order to have a sufficient quantity of individuals to have the predefined questions answered. Therefore, every clinical physician should be capable to understand the statistical basis of well performed clinical trials. It is therefore a great pleasure that Drs. T. J. Cleophas, A. H. Zwinderman, and T. F. Cleophas have published a book on statistical analysis of clinical trials. The book entitled Statistics Applied to Clinical Trials is clearly written and makes complex issues in statistical analysis transparent. Apart from providing the classical issues in statistical analysis, the authors also address novel issues such as interim analyses, sequential analyses, and meta-analyses. The book is composed of 18 chapters, which are nicely structured. The authors have deepened our insight in the applications of statistical analysis of clinical trials. We would like to congratulate the editors on this achievement and hope that many readers will enjoy reading this intriguing book. Professor of Cardiology, President Netherlands Association of Cardiology, Leiden, Netherlands E.E. van der Wall, M.D., Ph.D. v

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7 Preface to First Edition The European Interuniversity Diploma of Pharmaceutical Medicine is a postacademic course of 2 3 years sponsored by the Socrates program of the European Community. The office of this interuniversity project is in Lyon and the lectures are given there. The European Community has provided a building and will remunerate lecturers. The institute which provides the teaching is called the European College of Pharmaceutical Medicine, and is affiliated with 15 universities throughout Europe, whose representatives constitute the academic committee. This committee supervises educational objectives. Start lectures February There are about 20 modules for the first 2 years of training, most of which are concerned with typically pharmacological and clinical pharmacological matters including pharmacokinetics, pharmacodynamics, phase III clinical trials, reporting, communication, ethics and, any other aspects of drug development. Subsequent training consists of practice training within clinical research organisations, universities, regulatory bodies etc., and finally of a dissertation. The diploma, and degree are delivered by the Claude Bernard University in Lyon as well as the other participating universities. The module Statistics applied to clinical trials will be taught in the form of a 3 6 day yearly course given in Lyon and starting February Lecturers have to submit a document of the course (this material will be made available to students). Three or four lecturers are requested to prepare detailed written material for students as well as to prepare examination of the students. The module is thus an important part of a postgraduate course for physicians and pharmacists for the purpose of obtaining the European diploma of pharmaceutical medicine. The diploma should make for leading positions in pharmaceutical industry, academic drug research, as well as regulatory bodies within the EC. This module is mainly involved in the statistics of randomized clinical trials. The Chaps. 1 9, 11, 17, and 18 of this book are based on the module Medical statistics applied to clinical trials and contain material that should be mastered by the students before their exams. The remaining chapters are capita selecta intended for excellent students and are not included in the exams. vii

8 viii Preface to First Edition The authors believe that this book is innovative in the statistical literature because, unlike most introductory books in medical statistics, it provides an explanatory rather than mathematical approach to statistics, and, in addition, emphasizes nonclassical but increasingly frequently used methods for the statistical analyses of clinical trials, e.g., equivalence testing, sequential analyses, multiple linear regression analyses for confounding, interaction, and synergism. The authors are not aware of any other work published so far that is comparable with the current work, and, therefore, believe that it does fill a need. August 1999 Dordrecht, Leiden Delft

9 Preface to Second Edition In this second edition the authors have removed textual errors from the first edition. Also seven new chapters (Chaps. 8, 10, 13, 15 18) have been added. The principles of regression analysis and its resemblance to analysis of variance was missing in the first edition, and have been described in Chap. 8. Chapter 10 assesses curvilinear regression. Chapter 13 describes the statistical analyses of crossover data with binary response. The latest developments including statistical analyses of genetic data and quality-of-life data have been described in Chaps. 15 and 16. Emphasis is given in Chaps. 17 and 18 to the limitations of statistics to assess non-normal data, and to the similarities between commonly-used statistical tests. Finally, additional tables including the Mann-Whitney and Wilcoxon rank sum tables have been added in the Appendix. December 2001 Dordrecht, Amsterdam Delft ix

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11 Preface to the Third Edition The previous two editions of this book, rather than having been comprehensive, concentrated on the most relevant aspects of statistical analysis. Although wellreceived by students, clinicians, and researchers, these editions did not answer all of their questions. This called for a third, more comprehensive, rewrite. In this third edition the 18 chapters from the previous edition have been revised, updated, and provided with a conclusions section summarizing the main points. The formulas have been re-edited using the Formula-Editor from Windows XP 2004 for enhanced clarity. Thirteen new chapters (Chaps. 8 10, 14, 15, 17, 21, 25 29, 31) have been added. The Chaps give methods to assess the problems of multiple testing and data testing closer to expectation than compatible with random. The Chaps. 14 and 15 review regression models using an exponential rather than linear relationship including logistic, Cox, and Markow models. Chapter 17 reviews important interaction effects in clinical trials and provides methods for their analysis. In Chap. 21 study designs appropriate for medicines from one class are discussed. The Chaps review respectively (1) methods to evaluate the presence of randomness in the data, (2) methods to assess variabilities in the data, (3) methods to test reproducibility in the data, (4) methods to assess accuracy of diagnostic tests, and (5) methods to assess random rather than fixed treatment effects. Finally, Chap. 31 reviews methods to minimize the dilemma between sponsored research and scientific independence. This updated and extended edition has been written to serve as a more complete guide and reference-text to students, physicians, and investigators, and, at the same time, preserves the common sense approach to statistical problem-solving of the previous editions. August 2005 Dordrecht, Amsterdam Delft xi

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13 Preface to Fourth Edition In the past few years many important novel methods have been applied in published clinical research. This has made the book again rather incomplete after its previous edition. The current edition consists of 16 new chapters, and updates of the 31 chapters from the previous edition. Important methods like Laplace transformations, log likelihood ratio statistics, Monte Carlo methods, and trend testing have been included. Also novel methods like superiority testing, pseudo-r2 statistics, optimism corrected c-statistic, I-statistics, and diagnostic meta-analyses have been addressed. The authors have given special efforts for all chapters to have their own introduction, discussion, and references section. They can, therefore, be studied separately and without need to read the previous chapters first. September 2008 Dordrecht, Amsterdam, Gorinchem, and Delft xiii

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15 Preface to Fifth Edition Thanks to the omnipresent computer, current statistics can include data files of many thousands of values, and can perform any exploratory analysis in less than seconds. This development, however fascinating, generally does not lead to simple results. We should not forget that clinical studies are, mostly, for confirming prior hypotheses based on sound arguments, and the simplest tests provide the best power and are adequate for such purposes. In the past few years the authors of this 5th edition, as teachers and research supervisors in academic and top-clinical facilities, have been able to closely observe the latest developments in the field of clinical data analysis, and they have been able to assess their performance. In this 5th edition the 47 chapters of the previous edition have been maintained and upgraded according to the current state of the art, and 20 novel chapters have been added after strict selection of the most valuable and promising novel methods. The novel methods are explained using practical examples and step-by-step analyses readily accessible not only to statisticians but also to non-mathematicians. In order to keep up with the forefront of statistical analysis it was unavoidable to also include more complex data modeling and computationally intensive statistical methods. These methods include, e.g., multistage regression, neural networks, fuzzy modeling, mixed linear and non linear models, item response modeling, non linear regression methods, propensity score matching, Bhattacharya modeling and various regression models with multiple outcome variables. However, the authors have given every effort to review these methods in an explanatory rather than mathematical manner. We should add that the authors are well-qualified in their field. Professor Zwinderman is president-elect of the International Society of Biostatistics, and Professor Cleophas is past-president of the American College of Angiology. From their expertise they should be able to make adequate selections of modern methods for clinical data analysis for the benefit of physicians, students, and investigators. The authors have been working and publishing together for over 10 years, and their research of statistical methodology can be characterized as a continued effort to demonstrate that statistics is not mathematics but rather a discipline at the interface of biology and mathematics. September 2011 Dordrecht, Amsterdam, Lyon xv

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17 Contents 1 Hypotheses, Data, Stratification General Considerations Two Main Hypotheses in Drug Trials: Efficacy and Safety Different Types of Data: Continuous Data Different Types of Data: Proportions, Percentages and Contingency Tables Different Types of Data: Correlation Coefficient Stratification Issues Randomized Versus Historical Controls Factorial Designs Conclusions References The Analysis of Efficacy Data Overview The Principle of Testing Statistical Significance The t-value = Standardized Mean Result of Study Unpaired t-test Null-Hypothesis Testing of Three or More Unpaired Samples Three Methods to Test Statistically a Paired Sample First Method Second Method Third Method Null-Hypothesis Testing of Three or More Paired Samples Null-Hypothesis Testing with Complex Data Paired Data with a Negative Correlation Studies Testing Significance of Differences Studies Testing Equivalence Rank Testing Paired Test: Wilcoxon Signed Rank Test Unpaired Test: Mann-Whitney Test xvii

18 xviii Contents 11 Rank Testing for Three or More Samples The Friedman Test for Paired Observations The Kruskall-Wallis Test for Unpaired Observations Conclusions References The Analysis of Safety Data Introduction, Summary Display Four Methods to Analyze Two Unpaired Proportions Method Method Method Method Chi-square to Analyze More Than Two Unpaired Proportions McNemar s Test for Paired Proportions Multiple Paired Binary Data (Cochran s Q Test) Survival Analysis Survival Analysis Testing Significance of Difference Between Two Kaplan-Meier Curves Odds Ratio Method for Analyzing Two Unpaired Proportions Odds Ratios for One Group, Two Treatments Conclusions Log Likelihood Ratio Tests for Safety Data Analysis Introduction Numerical Problems with Calculating Exact Likelihoods The Normal Approximation and the Analysis of Clinical Events Log Likelihood Ratio Tests and the Quadratic Approximation More Examples Discussion Conclusions References Equivalence Testing Introduction Overview of Possibilities with Equivalence Testing Calculations Equivalence Testing, a New Gold Standard? Validity of Equivalence Trials Special Point: Level of Correlation in Paired Equivalence Studies Conclusions Statistical Power and Sample Size What Is Statistical Power Emphasis on Statistical Power Rather Than Null-Hypothesis Testing... 78

19 Contents xix 3 Power Computations For t-distributions of Continuous Data For Proportions For Equivalence Testing of Samples with t-distributions and Continuous Data Examples of Power Computation Using the t-table First Example Second Example Third Example Calculation of Required Sample Size, Rationale Calculations of Required Sample Size, Methods A Simple Method A More Accurate Method Is the Power Index Method Power Calculation for Parallel-Group Studies Required Sample Size Equation for Studies with Proportions Required Sample Size Formula for Equivalence Testing Testing Inferiority of a New Treatment (Type III Error) Conclusions Reference Interim Analyses Introduction Monitoring Interim Analysis Group-Sequential Design of Interim Analysis Continuous Sequential Statistical Techniques Conclusions References Controlling the Risk of False Positive Clinical Trials Introduction Bonferroni Test Least Significant Difference (LSD) Test Other Tests for Adjusting the p-values Composite Endpoint Procedures No Adjustments at all, and Pragmatic Solutions Conclusions References Multiple Statistical Inferences Introduction Multiple Comparisons Multiple Variables Conclusions References

20 xx Contents 10 The Interpretation of the p-values Introduction Renewed Attention to the Interpretation of the Probability Levels, Otherwise Called the p-values Standard Interpretation of p-values Common Misunderstandings of the p-values Renewed Interpretations of p-values, Little Difference Between p = 0.06 and p = The Real Meaning of Very Large p-values Like p > p-values Larger than 0.95, Examples (Table 10.2) The Real Meaning of Very Small p-values Like p < p-values Smaller than , Examples (Table 10.3) Discussion Recommendations Conclusions References Research Data Closer to Expectation than Compatible with Random Sampling Introduction Methods and Results Discussion Conclusions References Statistical Tables for Testing Data Closer to Expectation than Compatible with Random Sampling Introduction Statistical Tables of Unusually High p-values How to Calculate the p-values Yourself t-test Chi-square Test F-Test Additional Examples Simulating Real Practice, Multiple Comparisons Discussion Conclusions References Data Dispersion Issues Introduction Data Without Measure of Dispersion Numbers Needed to Treat in Clinical Trials Reproducibility of Quantitative Diagnostic Tests Sensitivity and Specificity Markov Predictors Risk Profiles from Multiple Logistic Models

21 Contents xxi 3 Data with Over-Dispersion Discussion Conclusions References Linear Regression, Basic Approach Introduction More on Paired Observations Using Statistical Software for Simple Linear Regression Multiple Linear Regression Multiple Linear Regression, Example Purposes of Linear Regression Analysis Another Real Data Example of Multiple Linear Regression (Exploratory Purpose) It May Be Hard to Define What Is Determined by What, Multiple and Multivariate Regression Limitations of Linear Regression Conclusions Linear Regression for Assessing Precision, Confounding, Interaction, Basic Approach Introduction Example Model (I.) Increased Precision of Efficacy (II.) Confounding (III.) Interaction and Synergism Estimation, and Hypothesis Testing Goodness-of-Fit Selection Procedures Main Conclusions References Curvilinear Regression Introduction Methods, Statistical Model Reproducibility of Means of the Population Reproducibility of Individual Data Results Reproducibility of Means of Population Reproducibility of Individual Data Discussion Conclusions References

22 xxii Contents 17 Logistic and Cox Regression, Markov Models, Laplace Transformations Introduction Linear Regression Logistic Regression Logistic Regression Analysis for Predicting the Probability of an Event Logistic Regression for Efficacy Data Analysis Cox Regression Markov Models Regression-Analysis with Laplace Transformations Discussion Conclusions References Regression Modeling for Improved Precision Introduction Regression Modeling for Improved Precision of Clinical Trials, the Underlying Mechanism Regression Model for Parallel-Group Trials with Continuous Efficacy Data Regression Model for Parallel-Group Trials with Proportions or Odds as Efficacy Data Discussion Conclusions References Post-hoc Analyses in Clinical Trials, A Case for Logistic Regression Analysis Multiple Variables Methods Examples Logistic Regression Equation Conclusions References Multistage Regression Introduction An Example, Usual Linear Regression Modeling Path Analysis Multistage Least Squares Method Bivariate Analysis Using Path Analysis Discussion Conclusions References

23 Contents xxiii 21 Categorical Data Introduction Races as a Categorical Variable Numbers of Co-medications as a Categorical Variable Discussion Multinomial Logistic Regression Conclusions References Missing Data Introduction Current Methods for Missing Data Imputation A Proposed Novel Approach to Regression-Substitution Example Discussion Conclusions Appendix References Poisson Regression Introduction Example Example Discussion Conclusions References More on Non Linear Relationships, Splines Introduction Logit or Probit Transformation Trial and Error Method, Box Cox Transformation, ACE/AVAS Packages Curvilinear Data Spline Modeling Discussion Conclusions Appendix References Multivariate Analysis Introduction Multivariate Regression Analysis Using Path Analysis Multiple Analysis of Variance, First Example Multiple Analysis of Variance, Second Example Multivariate Probit Regression Discussion Conclusions References

24 xxiv Contents 26 Bhattacharya Modeling Introduction Unmasking Normal Values Improving the p-values of Data Testing Objectively Searching Subsets in the Data Discussion Conclusions References Trend-Testing Introduction Binary Data, the Chi-Square-Test-for-Trends Continuous Data, Linear-Regression-Test-for-Trends Discussion Conclusions References Confounding Introduction First Method for Adjustment of Confounders: Subclassification on One Confounder Second Method for Adjustment of Confounders: Regression Modeling Third Method for Adjustment of Confounders: Propensity Scores Discussion Conclusions References Propensity Score Matching Introduction Calculation of Propensity-Scores Propensity-Scores for Adjusting Covariates Propensity-Scores for Matching Discussion Conclusions Appendix References Interaction Introduction What Exactly Is Interaction, a Hypothesized Example How to Test Interaction Statistically, a Real Data Example with a Concomitant Medication as Interacting Factor: Incorrect Method

25 Contents xxv 4 Three Analysis Methods First Method, t-test Second Method, Analysis of Variance (ANOVA) Third Method, Regression Analysis Using a Regression Model for Testing Interaction, Another Real Data Example Analysis of Variance for Testing Interaction, Other Real Data Examples Parallel-Group Study with Treatment Health Center Interaction Crossover Study with Treatment Subjects Interaction Discussion Conclusions References Time-Dependent Factor Analysis Introduction Cox Regression Without Time-Dependent Predictors Cox Regression with a Time-Dependent Predictor Cox Regression with a Segmented Time-Dependent Predictor Multiple Cox Regression with a Time-Dependent Predictor Discussion Conclusions References Meta-analysis, Basic Approach Introduction Examples Clearly Defined Hypotheses Thorough Search of Trials Strict Inclusion Criteria Uniform Data Analysis Individual Data Continuous Data, Means and Standard Errors of the Mean (SEMs) Proportions: Relative Risks (RRs), Odds Ratios (ORs), Differences Between Relative Risks (RDs) Publication Bias Heterogeneity Robustness Discussion, Where Are We Now? Conclusions References

26 xxvi Contents 33 Meta-analysis, Review and Update of Methodologies Introduction Four Scientific Rules Clearly Defined Hypothesis Thorough Search of Trials Strict Inclusion Criteria Uniform Data Analysis General Framework of Meta-analysis Pitfalls of Data Analysis Publication Bias Heterogeneity Investigating the Cause for Heterogeneity Lack of Robustness New Developments Conclusions References Meta-regression Introduction An Example of a Heterogeneous Meta-analysis Discussion Conclusions References Crossover Studies with Continuous Variables Introduction Mathematical Model Hypothesis Testing Statistical Power of Testing Discussion Analysis of Covariance (ANCOVA) Conclusion References Crossover Studies with Binary Responses Introduction Assessment of Carryover and Treatment Effect Statistical Model for Testing Treatment and Carryover Effects Results Calculation of p c Values Just Yielding a Significant Test for Carryover Effect Power of Paired Comparison for Treatment Effect Examples Discussion Conclusions References

27 Contents xxvii 37 Cross-Over Trials Should Not Be Used to Test Treatments with Different Chemical Class Introduction Examples from the Literature in Which Cross-Over Trials Are Correctly Used Examples from the Literature in Which Cross-Over Trials Should Not Have Been Used Estimate of the Size of the Problem by Review of Hypertension Trials Published Discussion Conclusions References Quality-Of-Life Assessments in Clinical Trials Introduction Some Terminology Defining QOL in a Subjective or Objective Way? The Patients Opinion Is an Important Independent-Contributor to QOL Lack of Sensitivity of QOL-Assessments Odds Ratio Analysis of Effects of Patient Characteristics on QOL Data Provides Increased Precision Discussion Conclusions References Item Response Modeling Introduction Item Response Modeling, Principles Quality Of Life Assessment Clinical and Laboratory Diagnostic-Testing Discussion Conclusions References Statistical Analysis of Genetic Data Introduction Some Terminology Genetics, Genomics, Proteonomics, Data Mining Genomics Conclusions References Relationship Among Statistical Distributions Introduction Variances The Normal Distribution

28 xxviii Contents 4 Null-Hypothesis Testing with the Normal or t-distribution Relationship Between the Normal Distribution and Chi-Square Distribution, Null-Hypothesis Testing with Chi-Square Distribution Examples of Data Where Variance Is More Important Than Mean Chi-Square Can Be Used for Multiple Samples of Data Contingency Tables Pooling Relative Risks or Odds Ratios in a Meta-analysis of Multiple Trials Analysis of Variance (ANOVA) Discussion Conclusions Reference Testing Clinical Trials for Randomness Introduction Individual Data Available Method 1: The Chi-Square Goodness of Fit Test Method 2: The Kolmogorov-Smirnov Goodness of Fit Test Randomness of Survival Data Individual Data Not Available Studies with Single Endpoints Studies with Multiple Endpoints Discussion Conclusions References Clinical Trials Do Not Use Random Samples Anymore Introduction Non-normal Sampling Distributions, Giving Rise to Non-normal Data Testing the Assumption of Normality What to Do in case of Non-normality Discussion Conclusions References Clinical Data Where Variability Is More Important Than Averages Introduction Examples Testing Drugs with Small Therapeutic Indices Testing Variability in Drug Response Assessing Pill Diameters or Pill Weights

29 Contents xxix 2.4 Comparing Different Patient Groups for Variability in Patient Characteristics Assessing the Variability in Duration of Clinical Treatments Finding the Best Method for Patient Assessments An Index for Variability in the Data How to Analyze Variability, One Sample c 2 Test Confidence Interval Equivalence Test How to Analyze Variability, Two Samples F Test Confidence Interval Equivalence Test How to Analyze Variability, Three or More Samples Bartlett s Test Levene s Test Discussion Conclusions References Testing Reproducibility Introduction Testing Reproducibility of Quantitative Data (Continuous Data) Method 1, Duplicate Standard Deviations (Duplicate SDs) Method 2, Repeatability Coefficients Method 3, Intraclass Correlation Coefficients (ICCS) Testing Reproducibility of Qualitative Data (Proportions and Scores) Cohen s Kappas Incorrect Methods to Assess Reproducibility Testing the Significance of Difference Between Two or More Sets of Repeated Measures Calculating the Level of Correlation Between Two Sets of Repeated Measures Additional Real Data Examples Reproducibility of Ambulatory Blood Pressure Measurements (ABPM) Two Different Techniques to Measure the Presence of Hypertension Discussion Conclusions References

30 xxx Contents 46 Validating Qualitative Diagnostic Tests Introduction Overall Accuracy of a Qualitative Diagnostic Test Perfect and Imperfect Qualitative Diagnostic Tests Determining the Most Accurate Threshold for Positive Qualitative Tests Discussion Conclusions References Uncertainty of Qualitative Diagnostic Tests Introduction Example Example Example Example Discussion Conclusion Appendix Appendix References Meta-Analysis of Qualitative Diagnostic Tests Introduction Diagnostic Odds Ratios (DORS) Constructing Summary ROC Curves Discussion Conclusions References c-statistic Versus Logistic Regression for Assessing the Performance of Qualitative Diagnostic Accuracy Introduction The Performance of c-statistics The Performance of Logistic Regression Discussion Conclusions Conclusions References Validating Quantitative Diagnostic Tests Introduction Linear Regression Testing a Significant Correlation Between the New Test and the Control Test Linear Regression Testing the Hypotheses That the a-value = and the b-value =

31 Contents xxxi 4 Linear Regression Using a Squared Correlation Coefficient (r 2 -Value) of > Alternative Methods Discussion Conclusions References Summary of Validation Procedures for Diagnostic Tests Introduction Qualitative Diagnostic Tests Accuracy Reproducibility Precision Quantitative Diagnostic Tests Accuracy Reproducibility Precision Additional Methods Discussion Conclusions References Validating Surrogate Endpoints of Clinical Trials Introduction Some Terminology Surrogate Endpoints and the Calculation of the Required Sample Size in a Trial Validating Surrogate Markers Using 95% Confidence Intervals Validating Surrogate Endpoints Using Regression Modeling Discussion Conclusions References Binary Partitioning Introduction Example ROC (Receiver Operating Characteristic) Method for Finding the Best Cut-Off Level Entropy Method for Finding the Best Cut-Off Level Discussion Conclusions References Methods for Repeated Measures Analysis Introduction Summary Measures

32 xxxii Contents 3 Repeated Measures ANOVA Without Between-Subjects Covariates Repeated Measures ANOVA with Between-Subjects Covariates Conclusions References Mixed Linear Models for Repeated Measures Introduction A Placebo-Controlled Parallel Group Study of Cholesterol Treatment A Three Treatment Crossover Study of the Effect of Sleeping Pills on Hours of Sleep Discussion Conclusion References Advanced Analysis of Variance, Random Effects and Mixed Effects Models Introduction Example 1, a Simple Example of a Random Effects Model Example 2, a Random Interaction Effect Between Study and Treatment Efficacy Example 3, a Random Interaction Effect Between Health Center and Treatment Efficacy Example 4, a Random Effects Model for Post-hoc Analysis of Negative Crossover Trials Discussion Conclusions References Monte Carlo Methods for Data Analysis Introduction Principles of the Monte Carlo Method Explained from a Dartboard to Assess the Size of P The Monte Carlo Method for Analyzing Continuous Data The Monte Carlo Method for Analyzing Proportional Data Discussion Conclusions References Artificial Intelligence Introduction Historical Background The Back Propagation (BP) Neural Network: The Computer Teaches Itself to Make Predictions

33 Contents xxxiii 4 A Real Data Example Discussion Conclusions References Fuzzy Logic Introduction Some Fuzzy Terminology First Example, Dose Response Effects of Thiopental on Numbers of Responders Second Example, Time-Response Effect of Propranolol on Peripheral Arterial Flow Discussion Conclusions References Physicians Daily Life and the Scientific Method Introduction Example of Unanswered Questions of a Physician During a Single Busy Day How the Scientific Method Can Be Implied in a Physician s Daily Life Falling Out of Bed Evaluation of Fundic Gland Polyps Physicians with a Burn-Out Patients Letters of Complaints Discussion Conclusions References Incident Analysis and the Scientific Method Introduction The Scientific Method in Incident-Analysis Discussion Conclusions References Clinical Trials: Superiority-Testing Introduction Examples of Studies Not Meeting Their Expected Powers How to Assess Clinical Superiority Discussion Conclusions References

34 xxxiv Contents 63 Noninferiority Testing Introduction A Novel Approach Basing the Margins of Noninferiority on Counted Criteria Testing the Presence of Both Noninferiority and a Significant Difference from Zero Testing the New Treatment Versus Historical Placebo Data Including Prior Sample Size Calculations and p-values Examples Example Example Example Example Discussion Conclusions References Time Series Introduction Autocorrelation Cross Correlation Change Points Discussion Conclusions References Odds Ratios and Multiple Regression Models, Why and How to Use Them Introduction Understanding Odds Ratios (ORS) Odds Ratios (ORs) as an Alternative Method to c 2 -Tests for the Analysis of Binary Data How to Analyze Odds Ratios (ORs) Real Data Examples of Simple OR Analyses Real Data Examples of Advanced OR Analyses Multiple Regression Models to Reduce the Spread in the Data A Linear Regression Model for Increasing Precision A Logistic Regression Model for Increasing Precision Discussion Conclusions References

35 Contents xxxv 66 Statistics Is No Bloodless Algebra Introduction Statistics Is Fun Because It Proves Your Hypothesis Was Right Statistical Principles Can Help to Improve the Quality of the Trial Statistics Can Provide Worthwhile Extras to Your Research Statistics Is Not Like Algebra Bloodless Statistics Can Turn Art into Science Statistics for Support Rather Than Illumination? Statistics Can Help the Clinician to Better Understand Limitations and Benefits of Current Research Limitations of Statistics Conclusions References Bias Due to Conflicts of Interests, Some Guidelines Introduction The Randomized Controlled Clinical Trial as the Gold Standard Need for Circumspection Recognized The Expanding Commend of the Pharmaceutical Industry Over Clinical Trials Flawed Procedures Jeopardizing Current Clinical Trials The Good News Further Solutions to the Dilemma Between Sponsored Research and the Independence of Science Conclusions References Appendix Index

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