1st Edition

Elementary Bayesian Biostatistics

By Lemuel A. Moyé Copyright 2007
    400 Pages 123 B/W Illustrations
    by Chapman & Hall

    400 Pages 123 B/W Illustrations
    by Chapman & Hall

    Bayesian analyses have made important inroads in modern clinical research due, in part, to the incorporation of the traditional tools of noninformative priors as well as the modern innovations of adaptive randomization and predictive power. Presenting an introductory perspective to modern Bayesian procedures, Elementary Bayesian Biostatistics explores Bayesian principles and illustrates their application to healthcare research.

    Building on the basics of classic biostatistics and algebra, this easy-to-read book provides a clear overview of the subject. It focuses on the history and mathematical foundation of Bayesian procedures, before discussing their implementation in healthcare research from first principles. The author also elaborates on the current controversies between Bayesian and frequentist biostatisticians. The book concludes with recommendations for Bayesians to improve their standing in the clinical trials community. Calculus derivations are relegated to the appendices so as not to overly complicate the main text.

    As Bayesian methods gain more acceptance in healthcare, it is necessary for clinical scientists to understand Bayesian principles. Applying Bayesian analyses to modern healthcare research issues, this lucid introduction helps readers make the correct choices in the development of clinical research programs.

    PREFACE
    INTRODUCTION

    PROLOGUE: OPENING SALVOS

    BASIC PROBABILITY AND BAYES THEOREM
    Probability's Role
    Objective and Subjective Probability
    Relative Frequency and Collections of Events
    Counting and Combinatorics
    Simple Rules in Probability
    Law of Total Probability and Bayes Theroem

    COMPOUNDING AND THE LAW OF TOTAL PROBABILITY
    Introduction
    The Law of Total Probability: Compounding
    Proportions and the Binomial Distribution
    Negative Binomial Distribution
    The Poisson Process
    The Uniform Distribution
    Exponential Distribution
    Problems

    INTERMEDIATE COMPOUNDING AND PRIOR DISTRIBUTIONS
    Compounding and Prior Distributions
    The Force of Effect Size
    Epidemiology 101
    Computing Distributions of Deaths
    The Gamma Distribution and ER Arrivals
    The Normal Distribution
    Problems

    COMPLETING YOUR FIRST BAYESIAN COMPUTATIONS
    Compounding and Bayes Procedures
    Introduction to a Simple Bayes Procedure
    Including a Continuous Conditional Distribution
    Working with Continuous Conditional Distributions
    Continuous Conditional and Prior Distributions
    Problems

    WHEN WORLDS COLLIDE
    Introduction

    DEVELOPING PRIOR PROBABILITY
    Introduction
    Prior Knowledge and Subjective Belief
    The Counterintuitive Prior
    Prior Information from Different Investigators
    Meta Analysis and Prior Distributions
    Priors and Clinical Trials
    Conclusions
    Problems

    USING POSTERIOR DISTRIBUTIONS: LOSS AND RISK
    Introduction
    The Role of Loss and Risk
    Decision Theory Dichotomous Loss
    Generalized Discrete Loss Functions
    Continuous Loss Functions
    The Need for Realistic Loss Functions
    Problems

    PUTTING IT ALL TOGETHER
    Introduction
    Illustration 1: Stroke Treatment
    Illustration 2: Adverse Event Rates
    Conclusions

    BAYESIAN SAMPLE SIZE
    Introduction
    The Real Purpose of Sample Size Discussions
    Hybrid Bayesian-Frequentist Sample Sizes
    Complete Bayesian Sample Size Computations
    Conclusions
    Problems

    PREDICTIVE POWER AND ADAPTIVE PROCEDURES
    Introduction
    Predictive Power
    Adaptive Bayes Procedures
    Conclusions

    IS MY PROBLEM A BAYES PROBLEM?
    Introduction
    Unidimensional versus Multidimensional Problems
    Ovulation Timing
    Building Community Intuition

    CONCLUSIONS AND COMMENTARY
    Validity of the Key Ingredients
    Dark Clouds
    Recommendations

    APPENDICES
    Compound Poisson Distribution
    Evaluations Using the Uniform Distribution
    Computations for the Binomial-Uniform Distribution
    Binomial-Exponential Compound Distribution
    Poisson-Gamma Processes
    Gamma and Negative Binomial Distribution
    Gamma Compounding with Gamma Distribution
    Standard Normal Distribution
    Compound and Conjugate Normal Distributions
    Uniform Prior and Conditional Normal Distribution
    Beta Distribution
    Calculations for Chapter 8
    Sample Size Primer
    Predictive Power Computations

    INDEX

    References appear at the end of each chapter.

    Biography

    Moyé, Lemuel A.

    "This is a fun book for teaching oneself (or others) both some fundamental principles of epidemiology and clinical trials and fundamental principles of probability and statistical inference from the point of view of a practising clinical scientist who is also a very knowledgeable, no-nonsense Bayesian. What makes it very different from common textbooks is its blending of history, controversy (about probability, statistics, and clinical studies), real-life examples, and wise practical advice. … a very readable introduction to basic probability models, inference questions, and Bayesian answers without calculus and Markov chain Monte Carlo. …"
    International Statistical Review, 2008

    ". . . provides a very clear exposition of Bayesian thinking for applications in biostatistics. The book’s strengths lie in its careful discussions of Bayesian thinking or problems in health care research, including the constructions of priors and loss functions . . . a welcome addition to the growing number of books that describe Bayesian modeling from an applied perspective."

    –Jim Albert, Bowling Green State University, in JASA, December 2008