1st Edition
Confidence Intervals for Discrete Data in Clinical Research
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
Introduction
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
Introduction
ASA statement on statistical significance and p-values
Discussion and recommendation
3. One Binomial Proportion
Introduction
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
Introduction
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
Introduction
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
Introduction
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
Introduction
Poisson Distribution
Confidence interval of Rate Parameter
Exact Intervals
Garwood Interval
Blaker's Interval
Mid-P interval
Asymptotic Intervals
Wald-Interval
Score-Interval
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
Biography
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.
