Elementary Bayesian Biostatistics: 1st Edition (Hardback) book cover

Elementary Bayesian Biostatistics

1st Edition

By Lemuel A. Moyé

Chapman and Hall/CRC

400 pages | 123 B/W Illus.

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Description

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.

Reviews

"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

Table of Contents

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.

About the Author/Editor

Moyé, Lemuel A.

About the Series

Chapman & Hall/CRC Biostatistics Series

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MED071000
MEDICAL / Pharmacology
MED090000
MEDICAL / Biostatistics