Elementary Bayesian Biostatistics

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.

PREFACEINTRODUCTIONPROLOGUE: OPENING SALVOSBASIC PROBABILITY AND BAYES THEOREMProbability's RoleObjective and Subjective Probability Relative Frequency and Collections of EventsCounting and CombinatoricsSimple Rules in ProbabilityLaw of Total Probability and Bayes TheroemCOMPOUNDING AND THE LAW OF TOTAL PROBABILITYIntroduction The Law of Total Probability: CompoundingProportions and the Binomial DistributionNegative Binomial DistributionThe Poisson ProcessThe Uniform Distribution Exponential Distribution ProblemsINTERMEDIATE COMPOUNDING AND PRIOR DISTRIBUTIONS Compounding and Prior DistributionsThe Force of Effect SizeEpidemiology 101Computing Distributions of Deaths The Gamma Distribution and ER Arrivals The Normal DistributionProblemsCOMPLETING YOUR FIRST BAYESIAN COMPUTATIONS Compounding and Bayes ProceduresIntroduction to a Simple Bayes Procedure Including a Continuous Conditional Distribution Working with Continuous Conditional Distributions Continuous Conditional and Prior Distributions ProblemsWHEN WORLDS COLLIDEIntroductionDEVELOPING PRIOR PROBABILITYIntroduction Prior Knowledge and Subjective BeliefThe Counterintuitive Prior Prior Information from Different InvestigatorsMeta Analysis and Prior DistributionsPriors and Clinical TrialsConclusionsProblemsUSING POSTERIOR DISTRIBUTIONS: LOSS AND RISK IntroductionThe Role of Loss and RiskDecision Theory Dichotomous LossGeneralized Discrete Loss FunctionsContinuous Loss FunctionsThe Need for Realistic Loss FunctionsProblemsPUTTING IT ALL TOGETHER Introduction Illustration 1: Stroke TreatmentIllustration 2: Adverse Event RatesConclusionsBAYESIAN SAMPLE SIZEIntroduction The Real Purpose of Sample Size Discussions Hybrid Bayesian-Frequentist Sample SizesComplete Bayesian Sample Size Computations Conclusions ProblemsPREDICTIVE POWER AND ADAPTIVE PROCEDURESIntroduction Predictive PowerAdaptive Bayes ProceduresConclusionsIS MY PROBLEM A BAYES PROBLEM? IntroductionUnidimensional versus Multidimensional Problems Ovulation TimingBuilding Community IntuitionCONCLUSIONS AND COMMENTARY Validity of the Key IngredientsDark Clouds RecommendationsAPPENDICESCompound Poisson Distribution Evaluations Using the Uniform DistributionComputations for the Binomial-Uniform DistributionBinomial-Exponential Compound DistributionPoisson-Gamma ProcessesGamma and Negative Binomial DistributionGamma Compounding with Gamma Distribution Standard Normal Distribution Compound and Conjugate Normal DistributionsUniform Prior and Conditional Normal DistributionBeta DistributionCalculations for Chapter 8Sample Size PrimerPredictive Power ComputationsINDEXReferences appear at the end of each chapter.

Moyé, Lemuel A.