Moyé Elementary Bayesian Biostatistics

1. Auflage 2007
ISBN: 978-1-58488-725-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 400 Seiten

Reihe: Chapman & Hall/CRC Biostatistics Series

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.

Zielgruppe

Advanced undergraduate and graduate students and practitioners in biology and healthcare; biostatisticians and researchers in clinical trials.

Autoren/Hrsg.

Moyé, Lemuel A.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

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.