Elementary Bayesian Biostatistics

ISBN-13: 9780367388799 / Angielski / Miękka / 2019 / 400 str.

Lemuel A. Moye

Opis

With numerous exercises and a CD-ROM of data sets and computing code, this lucid introduction explores Bayesian principles and illustrates their application to healthcare research. It reviews the interesting and controversial history of the Bayesian concept and enables a balanced comparison of Bayesian tools with standard frequentist approaches. The book also discusses several important implementations of Bayesian procedures in clinical research, including sample size computations, adaptive randomization, and monitoring procedures. In addition, it shows how to evaluate a healthcare research scenario to determine whether a frequentist or Bayesian approach is most appropriate.

Spis treści

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.

O autorze

Moyé, Lemuel A.