Confidence Intervals for Discrete Data in Clinical Research  book cover
1st Edition

Confidence Intervals for Discrete Data in Clinical Research

ISBN 9781138048980
Published November 15, 2021 by Chapman and Hall/CRC
240 Pages 2 Color & 52 B/W Illustrations

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Book Description

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.

Table of Contents

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                


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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.