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

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.