Statistical Testing Strategies in the Health Sciences provides a compendium of statistical approaches for decision making, ranging from graphical methods and classical procedures through computationally intensive bootstrap strategies to advanced empirical likelihood techniques. It bridges the gap between theoretical statistical methods and practical procedures applied to the planning and analysis of health-related experiments.
The book is organized primarily based on the type of questions to be answered by inference procedures or according to the general type of mathematical derivation. It establishes the theoretical framework for each method, with a substantial amount of chapter notes included for additional reference. It then focuses on the practical application for each concept, providing real-world examples that can be easily implemented using corresponding statistical software code in R and SAS. The book also explains the basic elements and methods for constructing correct and powerful statistical decision-making processes to be adapted for complex statistical applications.
With techniques spanning robust statistical methods to more computationally intensive approaches, this book shows how to apply correct and efficient testing mechanisms to various problems encountered in medical and epidemiological studies, including clinical trials. Theoretical statisticians, medical researchers, and other practitioners in epidemiology and clinical research will appreciate the book’s novel theoretical and applied results. The book is also suitable for graduate students in biostatistics, epidemiology, health-related sciences, and areas pertaining to formal decision-making mechanisms.
Table of Contents
Preliminaries: Welcome to the Statistical Inference Club: Some Basic Concepts in Experimental Decision Making
Overview: Essential Elements of Defining Statistical Hypotheses and Constructing Statistical Tests
Errors Related to the Statistical Testing Mechanism
Components for Constructing Test Procedures
Parametric Approach and Modeling
Warning and Advice: Limitations of Parametric Approaches: Detour to Nonparametric Approaches
Large Sample Approximate Tests
When All Else Fails: Bootstrap?
Permutation Testing versus Bootstrap Methodology
Atlas of the Book
Statistical Software: R and SAS
Descriptive Plots of Raw Data
Empirical Distribution Function Plot
Probability Plots as Informal Auxiliary Information to Inference
A Brief Ode to Parametric Likelihood
Likelihood Ratio Test and Its Optimality
Likelihood Ratio Based on the Likelihood Ratio Test Statistic Is the Likelihood Ratio Test Statistic
Maximum Likelihood: Is It the Likelihood?
Tests on Means of Continuous Data
Univariate and p-Dimensional Likelihood Ratio Tests of Location Given Normally Distributed Data
Exact Likelihood Ratio Test for Equality of Two Normal Populations
Classical Empirical Likelihood Methods
Techniques for Analyzing Empirical Likelihoods
Density-Based Empirical Likelihood Methods
Combining Likelihoods to Construct Composite Tests and Incorporate the Maximum Data-Driven Information
Bayesians and Empirical Likelihood: Are They Mutually Exclusive?
Three Key Arguments That Support the Empirical Likelihood Methodology as a Practical Statistical Analysis Tool
Bayes Factor–Based Test Statistics
Integrated Most Powerful Tests
The Fundamentals of Receiver Operating Characteristic Curve Analyses
ROC Curve Inference
Area under the ROC Curve
ROC Analysis and Logistic Regression: Comparison and Overestimation
Best Combinations Based on Values of Multiple Biomarkers
Notes Regarding Treatment Effects
Nonparametric Comparisons of Distributions
Wilcoxon Rank-Sum Test
Kolmogorov–Smirnov Two-Sample Test
Density-Based Empirical Likelihood Ratio Tests
Density-Based Empirical Likelihood Ratio Based on Paired Data
Dependence and Independence: Structures, Testing, and Measuring
Tests of Independence
Indices of Dependence
Structures of Dependence
Monte Carlo Comparisons of Tests of Independence
Goodness-of-Fit Tests (Tests for Normality)
Shapiro–Wilk Test for Normality
Statistical Change-Point Analysis
Common Change-Point Models
Simple Change-Point Model
Problems in Regression Models
A Brief Review of Sequential Testing Methods
Sequential Probability Ratio Test
Adaptive Sequential Designs
Appendix: Determination of Sample Sizes Based on the Errors' Control of SPRT
A Brief Review of Multiple Testing Problems in Clinical Experiments
Definitions of Error Rates
Some Statistical Procedures for Biomarker Measurements Subject to Instrumental Limitations
Monte Carlo Experiments
Calculating Critical Values and p-Values for Exact Tests
Methods of Calculating Critical Values of Exact Tests
Available Software Packages
Bootstrap and Permutation Methods
Resampling Data with Replacement in SAS
Theoretical Quantities of Interest
Bootstrap Confidence Intervals
Simple Two-Group Comparisons
Simple Regression Modeling
Relationship between Empirical Likelihood and Bootstrap Methodologies
Appendix: Bootstrap-t Example Macro
Albert Vexler is a tenured professor in the Department of Biostatistics at the State University of New York (SUNY) at Buffalo. Dr. Vexler is the associate editor of Biometrics and BMC Medical Research Methodology. He is the author and coauthor of various publications that contribute to the theoretical and applied aspects of statistics in medical research. Many of his papers and statistical software developments have appeared in statistical and biostatistical journals that have top-rated impact factors and are historically recognized as leading scientific journals. Dr. Vexler was awarded a National Institutes of Health grant to develop novel nonparametric data analysis and statistical methodology. His research interests include receiver operating characteristic curve analysis, measurement error, optimal designs, regression models, censored data, change point problems, sequential analysis, statistical epidemiology, Bayesian decision-making mechanisms, asymptotic methods of statistics, forecasting, sampling, optimal testing, nonparametric tests, empirical likelihoods, renewal theory, Tauberian theorems, time series, categorical analysis, multivariate analysis, multivariate testing of complex hypotheses, factor and principal component analysis, statistical biomarker evaluations, and best combinations of biomarkers.
Alan D. Hutson is the chair of biostatistics and bioinformatics at Roswell Park Cancer Institute. He is also the biostatistical, epidemiological, and research design director for SUNY’s National Institutes of Health–funded Clinical and Translational Research Award. Dr. Hutson is a fellow of the American Statistical Association, the associate editor of Communications in Statistics and the Sri Lankan Journal of Applied Statistics, and a New York State NYSTAR Distinguished Professor. He has written more than 200 peer-reviewed publications. Dr. Hutson’s methodological work focuses on nonparametric methods for biostatistical applications as they pertain to statistical functionals. He also has several years of experience in the design and analysis of clinical trials.
Xiwei Chen is a biostatistician at Johnson & Johnson Vision Care, Inc. She obtained her PhD in biostatistics from SUNY at Buffalo, where her advisor was Dr. Albert Vexler. Dr. Chen is the author or coauthor of more than 10 papers and several book chapters on biostatistical areas concerning statistical approaches related to disease diagnoses. She is also very active as a reviewer for statistical journals. Her research interests include empirical likelihood methods, the receiver operating characteristic curve methodology, and statistical diagnosis and its applications.
"This book covers a wide range of statistical approaches to hypothesis testing for decision-making in various health science research fields. It provides not only refreshing information on many routinely used statistical methods but also a good review of more advanced methods such as empirical likelihood (EL) methods… For clinicians or medical researchers with some training in statistics, many chapters can serve as references. For research statisticians, the book provides important properties and theoretical elaborations for the methods. For pharmaceutical drug trial statisticians in particular, the book on one hand offers a systematic account of many methods and on another hand exposes them to the methods used in some related research fields (e.g., diagnosis identification and testing) that lead one to see the interrelations across such research fields. Throughout the book, the authors transfer the statistical concepts and methods to real-world applications, with emphasis on implementing the methods in R and SAS program code and on interpreting the results…Another great feature of the book is that the authors provide supplemental materials on the evolution of the methodology with additional research notes in each chapter. These give research-oriented statisticians a comprehensive list of references which would be quite helpful for their research. The supplemental materials are also entertaining for the general readers to learn the chronology of statistical theory and methods."
—X. Daniel Jia, published in Journal of Biopharmaceutical Statistics, April 2017
"With techniques spanning robust statistical methods to more computationally intensive approaches, this book shows how to apply correct and efficient testing mechanisms to various problems encountered in medical and epidemiological studies, including clinical trials."
—TLT Magazine, September 2016
"This comprehensive book takes the reader from the underpinnings of statistical inference through to cutting-edge modern analytical techniques. Along the way, the authors explore graphical representations of data, a key component of any data analysis; standard procedures such as the t-test and tests for independence; and modern methods, including the bootstrap and empirical likelihood method. The presentation focuses on practical applications interwoven with theoretical rationale, with an emphasis on how to carry out procedures and interpret the results. Numerous software examples (R and SAS) are provided, such that the readers should be able to reproduce plots and other analyses on their own. A wealth of examples from real data sets, web resources, supplemental notes, and plentiful references are provided, which round out the materials."
—From the Foreword by Nicole Lazar, Department of Statistics, University of Georgia