1st Edition

Confidence Intervals for Discrete Data in Clinical Research

    240 Pages 2 Color & 52 B/W Illustrations
    by Chapman & Hall

    240 Pages 2 Color & 52 B/W Illustrations
    by Chapman & Hall

    240 Pages 2 Color & 52 B/W Illustrations
    by Chapman & Hall

    Confidence Intervals for Discrete Data in Clinical Research is designed as a toolbox for biomedical researchers. Analysis of discrete data is one of the most used yet vexing areas in clinical research. The array of methodologies available in the literature to address the inferential questions for binomial and multinomial data can be a double-edged sword. On the one hand, these methods open a rich avenue of exploration of data; on the other, the wide-ranging and competing methodologies potentially lead to conflicting inferences, adding to researchers' confusion and frustration and also leading to reporting bias. This book addresses the problems that many practitioners experience in choosing and implementing fit for purpose data analysis methods to answer critical inferential questions for binomial and count data.

    The book is an outgrowth of the authors' collective experience in biomedical research and provides an excellent overview of inferential questions of interest for binomial proportions and rates based on count data, and reviews various solutions to these problems available in the literature. Each chapter discusses the strengths and weaknesses of the methods and suggests practical recommendations. The book's primary focus is on applications in clinical research, and the goal is to provide direct benefit to the users involved in the biomedical field.

    1. A Brief Review of Statistical Inference
     The frequentist approach:          
                    Confidence interval methods               
                    Hypothesis testing methods               
     The Bayesian approach to inference              
     Discussions and conclusions                   

    2. Are we slaves to the p-value: The ASA's Statement on P- value
     ASA statement on statistical significance and p-values     
     Discussion and recommendation                

    3. One Binomial Proportion
     Testing of a hypothesis                     
     Asymptotic Confidence interval methods            
                    Wald Confidence interval                 
                    Wald with continuity corrected Confidence interval  
                    Score interval due to Wilson (1927)          
                    Continuity corrected Wilson interval          
                    Agresti and Coull interval                
                    Second-order corrected interval             
     Bayesian intervals                        
                    Non-informative prior - Jeffreys interval        
                    Non-informative priors - general MCMC approach  
                    Informative prior: Power prior             
     Exact methods                          
                    Clopper and Pearson Confidence interval        
                    Mid-p corrected Clopper-Pearson method       
                    Confidence interval due to Casella (1986)       
                    Confidence interval due to Blaker (2000)        
     Discussion and recommendation                

    4. Two Independent Binomials: Difference of Proportions
     Difference of two proportions: p1-p2             
                    Hypotheses testing problems related to the Difference of proportions                        
                    Asymptotic methods                   
                                    Using Wald Interval              
                                    Using Agresti and Caffo Interval       
                                    Newcombe's method (score)         
                                    Profile likelihood based interval       
                                    Farrington and Manning (score) interval   
                                    Miettinen and Nurminen (score) interval  
                                    MOVER Interval                
                    Exact methods                      
                                    Chan and Zhang interval           
                                    Agresti and Min interval           
                                    Coe and Tamhane interval          
                    Bayesian Intervals                        
     Discussion and recommendation

     5. Two Independent Binomials: Ratio of Proportions
     Hypotheses about the ratio of proportions          
     Asymptotic methods                   
                    Katz et al (KZ) interval           
                    Asymptotic score interval: Koopman     
                    Asymptotic score interval: Farrington and Manning                    
                    Asymptotic score interval: Miettinen and Nurminen
                    Profile likelihood interval           
     Exact Intervals                      
                    Chan and Zhang interval           
                    Agresti and Min interval           
     Bayesian Intervals                        
     Discussion and recommendation                

    6. Paired binomials: Difference of Proportions
     Difference of two paired binomial proportions         
     Hypotheses testing formulation                 
     Asymptotic Intervals                      
                    Wald interval                       
                    Agresti and Min Interval                 
                    MOVER Interval                     
                                    MOVER Wilson Interval           
                                    MOVER Agresti-Coull Interval        
                                    MOVER Jeffreys' Interval           
                    Asymptotic score interval                
                    Weighted profile likelihood method           
                    Confidence interval based on bivariate Copula     
     Bayesian credible intervals                
     Exact Confidence Intervals                    
                    Exact Method by Sidik (2003)             
     Paired binomials with missing data              
                    Confidence interval due to Chang (2011)        
     Likelihood-based Confidence intervals         
                    Likelihood based Wald type intervals    
                    Profile likelihood-based Confidence interval 
     Discussion and recommendation                

    7. One Sample Rates for Count Data
     Poisson Distribution                       
     Confidence interval of Rate Parameter

    Exact Intervals                      
                    Garwood Interval               
                    Blaker's Interval                
                    Mid-P interval                 
     Asymptotic Intervals                   
                    The likelihood ratio Interval         
     Bayesian Interval                     
                    The Jeffreys' interval             
     Remarks on the exact, asymptotic and Bayesian intervals
     Confidence interval for Mean: Other Count Data Models  
                    Negative Binomial distribution             
                    Generalized Poisson distribution            
                    Zero-Inflated Models                   
                                    Confidence Intervals for Zero-Inflated Poisson Distribution (ZIPD)              
                                    Zero-Inflated Generalized Poisson Distribution (ZIGPD)
                                    Zero-Inflated Negative Binomial (ZINB)        
     Bayesian Credible intervals for Poisson Distribution     
     Discussion and recommendation                



    Vivek Pradhan has been working in the industry for more than twenty years. Currently he is a senior director in statistics in Early Clinical Development of Pfizer where he is responsible for managing all the statistical aspects of drug development from pre-clinical to Phase IIB trials. He has been publishing methodological papers on discrete data, and a regular invited speaker in several industry conferences and forums.

    Ashis K Gangopadhyay is an Associate Professor of Statistics in the Department of Mathematics and Statistics at Boston University. His research areas include predictive modeling in clinical research, nonparametric and semiparametric methods, and analysis of financial data. He has authored numerous extensively cited research papers and mentored many Ph.D. students.

    Sandeep Menon is Senior Vice President and the Head of Early Clinical Development at Pfizer Inc. and holds Adjunct faculty positions at Boston University School of Public Health, Tufts University School of Medicine, and the Indian Institute of Management. At Pfizer, he is in the Worldwide Research, Development and Medical Leadership Team and leads a multi-functional global team. Before joining the industry, he practiced medicine in Mumbai and was Resident Medical Officer. Sandeep is an elected fellow of the American Statistical Association (ASA), awarded the Young Scientist Award by the International Indian Statistical Association, the Statistical Excellence Award in Pharmaceutical Industry by Royal Statistical Society, UK and recently awarded the Distinguished Alumni Award by the Department of Biostatistics at Boston University School of Public Health. He received his medical degree from Karnataka University, India, and later completed his Masters in Epidemiology and Biostatistics and Ph.D. in Biostatistics at Boston University and research Assistantship at Harvard Clinical Research Institute. He has published more than 50 scientific original publications and book chapters and co-authored /co-edited six books.

    Cynthia Basu has been involved in research in clinical trials and Bayesian methods. She is currently an associate director of statistics in Early Clinical Development at Pfizer where she works on early phase trials in Oncology. Her research interests include topics in clinical trial designs, Bayesian methods, adaptive trials, and historical borrowing.

    Tathagata Banerjee has been engaged in teaching and research in statistics for more than three decades. Currently, he is a professor at the Indian Institute of Management Ahmedabad, India. His research interest is primarily focused on developing statistical methodologies for drawing inference from different kinds of data. His research is published regularly in peer reviewed journals, and he has given lectures and taught in various universities across the world.

    "Overall speaking, this book delivered what the authors hoped to achieve—"Confidence Intervals for Discrete Data in Clinical Research." This book provides a comprehensive review of existingmethods in constructing confidence intervals for binary and count data because these are the discrete data most frequently used in clinical research. [...] This book not only serves the readers they it intended to serve but can also help potentially a much broader readership. [...] One strength of this book is that it covers a wide range of methods with very good reference articles [...]. This feature makes this book to be one of the very useful references on this topic. For practitioners engaged in clinical research, epidemiology, or public health, this book can be a very helpful tool."
    -Naitee Ting in Biometrics: A Journal of the International Biometric Society, March 2023.