# Bayesian Biostatistics

## Lesaffre, E. — Lawson, A.

1ª Edición Julio 2012

Inglés

Tapa dura

536 pags

1800 gr

x x cm

### ISBN 9780470018231

### Editorial WILEY

Recíbelo en un plazo De 7 a 10 días

### Description

The growth of biostatistics has been phenomenal in recent years and has been marked by considerable technical innovation in both methodology and computational practicality. One area that has experienced significant growth is Bayesian methods. The growing use of Bayesian methodology has taken place partly due to an increasing number of practitioners valuing the Bayesian paradigm as matching that of scientific discovery. In addition, computational advances have allowed for more complex models to be fitted routinely to realistic data sets.

Through examples, exercises and a combination of introductory and more advanced chapters, this book provides an invaluable understanding of the complex world of biomedical statistics illustrated via a diverse range of applications taken from epidemiology, exploratory clinical studies, health promotion studies, image analysis and clinical trials.

### Key Features:

- Provides an authoritative account of Bayesian methodology, from its most basic elements to its practical implementation, with an emphasis on healthcare techniques.
- Contains introductory explanations of Bayesian principles common to all areas of application.
- Presents clear and concise examples in biostatistics applications such as clinical trials, longitudinal studies, bioassay, survival, image analysis and bioinformatics.
- Illustrated throughout with examples using software including WinBUGS, OpenBUGS, SAS and various dedicated R programs.
- Highlights the differences between the Bayesian and classical approaches.
- Supported by an accompanying website hosting free software and case study guides.
- Bayesian Biostatistics introduces the reader smoothly into the Bayesian statistical methods with chapters that gradually increase in level of complexity. Master students in biostatistics, applied statisticians and all researchers with a good background in classical statistics who have interest in Bayesian methods will find this book useful.

### Table of Contents

Preface Notation, terminology and some guidance for reading the book**I Basic concepts in Bayesian methods **

**1. Modes of statistical inference**- The frequentist approach: a critical reflection
- The classical statistical approach
- The P-value as a measure of evidence
- The confidence interval as a measure of evidence
- An historical note on the two frequentist paradigms*
- Statistical inference based on the likelihood function
- The likelihood function
- The likelihood principles
- The Bayesian approach: some basic ideas
- Introduction
- Bayes theorem – Discrete version for simple events
- Outlook
**2. Bayes theorem**- Introduction
- Bayes theorem – The binary version
- Probability in a Bayesian context
- Bayes theorem – The categorical version
- Bayes theorem – The continuous version
- The binomial case
- The Gaussian case
- The Poisson case
- The prior and posterior distribution of h(θ)
- Bayesian versus likelihood approach
- Bayesian versus frequentist approach
- The different modes of the Bayesian approach
- An historical note on the Bayesian approach
- Closing remarks
**3. Posterior summary measures**- Introduction
- Summarizing the posterior by probabilities
- Posterior summary measures
- Characterizing the location and variability of the posterior distribution
- Posterior interval estimation
- Predictive distributions
- The frequentist approach to prediction
- The Bayesian approach to prediction
- Applications
- Exchangeability
- A normal approximation to the posterior
- A Bayesian analysis based on a normal approximation to the likelihood
- Asymptotic properties of the posterior distribution
- Numerical techniques to determine the posterior
- Numerical integration
- Sampling from the posterior
- Choice of posterior summary measures
- Bayesian hypothesis testing
- Inference based on credible intervals
- The Bayes factor
- Bayesian versus frequentist hypothesis testing
- Closing remarks
**4. More than one parameter**- Introduction
- Joint versus marginal posterior inference
- The normal distribution with μ and σ2 unknown
- No prior knowledge on μ and σ2 is available
- An historical study is available
- Expert knowledge is available
- Multivariate distributions
- The multivariate normal and related distributions
- The multinomial distribution
- Frequentist properties of Bayesian inference
- Sampling from the posterior distribution: the Method of Composition
- Bayesian linear regression models
- The frequentist approach to linear regression
- A noninformative Bayesian linear regression model
- Posterior summary measures for the linear regression model
- Sampling from the posterior distribution
- An informative Bayesian linear regression model
- Bayesian generalized linear models
- More complex regression models
- Closing remarks
**5. The prior distribution**- Introduction
- The sequential use of Bayes theorem
- Conjugate prior distributions
- Univariate data distributions
- Normal distribution – mean and variance unknown
- Priors for multivariate distributions
- Conditional conjugate and semi-conjugate distributions
- Hyperpriors
- Noninformative prior distributions
- Introduction
- Expressing ignorance
- General principles to choose noninformative priors
- Improper prior distributions
- Weak/vague priors
- Informative prior distributions
- Introduction
- Data-based prior distributions
- Elicitation of prior knowledge
- Archetypal prior distributions
- Prior distributions for regression models
- Normal linear regression
- Generalized linear models
- Specification of priors in Bayesian software
- Modeling priors
- Other regression models
- Closing remarks
**6. Markov chain Monte Carlo sampling**- Introduction
- The Gibbs sampler
- The bivariate Gibbs sampler
- The general Gibbs sampler
- Remarks*
- Review of Gibbs sampling approaches
- The Slice sampler*
- The Metropolis(-Hastings) algorithm
- The Metropolis algorithm
- The Metropolis-Hastings algorithm
- Remarks*
- Review of Metropolis(-Hastings) approaches
- Justification of the MCMC approaches*
- Properties of the MH algorithm
- Properties of the Gibbs sampler
- Choice of the sampler
- The Reversible Jump MCMC algorithm*
- Closing remarks
**7. MCMC convergence**- Introduction
- Assessing convergence of a Markov chain
- Definition of convergence for a Markov chain
- Checking convergence of the Markov chain
- Graphical approaches to assess convergence
- Formal diagnostic tests
- Computing the Monte Carlo standard error
- Practical experience with the formal diagnostic procedures.
- Accelerating convergence
- Introduction
- Acceleration techniques
- Practical guidelines for assessing and accelerating convergence.
- Data augmentation
- Closing remarks
**8. Software**- WinBUGS and related software
- A first analysis
- Assessing and accelerating convergence
- Vector and matrix manipulations
- Working in batch mode
- Troubleshooting
- Directed acyclic graphs
- Add-on modules: GeoBUGS and PKBUGS
- Related software
- Bayesian analysis using SASr
- Analysis using procedure GENMOD
- Analysis using procedure MCMC
- Other Bayesian programs
- Additional Bayesian software and comparisons
- Additional Bayesian software
- Comparison of Bayesian software
- Closing remarks

**II Bayesian tools for statistical modeling **

**9. Hierarchical models**- Introduction
- The Poisson-gamma hierarchical model
- Introduction
- Model specification
- Posterior distributions
- Estimating the parameters
- Posterior predictive distributions
- Full versus Empirical Bayesian approach
- Gaussian hierarchical models
- Introduction
- The Gaussian hierarchical model
- Estimating the parameters
- Posterior predictive distributions
- Comparison of FB and EB approach
- Mixed models
- Introduction
- The linear mixed model
- The generalized linear mixed model
- Nonlinear mixed models
- Some further extensions
- Estimation of the random effects and posterior predictive distributions
- Choice of the level-2 variance prior
- Propriety of the posterior
- Assessing and accelerating convergence
- Comparison with frequentist methods
- Estimating the level-2 variance
- ML and REML estimates compared with Bayesian estimates
- Closing remarks
**10. Model building and assessment**- Introduction
- Measures for model selection
- The Bayes factor
- Information theoretic measures for model selection
- Model selection based on other predictive loss functions
- Model checking
- Introduction
- Model checking procedures
- Sensitivity analysis
- Posterior predictive checks
- Model expansion
- Closing remarks
**11. Variable selection**- Introduction
- Classical variable selection
- Variable selection techniques
- Frequentist regularization
- Bayesian variable selection: concepts and questions
- Introduction to Bayesian variable selection
- Variable selection for K small
- Variable selection for K large
- Variable selection based on Zellner’s g-prior
- Variable selection based on Reversible Jump Markov chain Monte Carlo
- Spike and slab priors
- Stochastic Search Variable Selection (SSVS)
- Gibbs Variable Selection (GVS)
- Dependent variable selection using SSVS
- Bayesian regularization
- Bayesian LASSO regression
- Elastic Net and further extensions of the Bayesian LASSO
- The many regressors case
- Bayesian model selection
- Bayesian model averaging
- Closing remarks

**III Applications **

**12. Bioassay**- Bioassay essentials
- Cell assays
- Animal assays
- A generic in-vitro example
- Ames/Salmonella mutagenic assay
- Mouse lymphoma assay (L5178Y TK+/-)
- Closing remarks
**13. Measurement error**- Continuous measurement error
- Measurement error in a variable
- Two types of measurement error on the predictor in linear and nonlinear models
- Accommodation of predictor measurement error
- Non-additive errors and other extensions
- Discrete measurement error
- Sources of misclassification
- Misclassification in the binary predictor
- Misclassification in a binary response
- Closing remarks
**14. Survival analysis**- Basic terminology
- Endpoint distributions
- Censoring
- Random effect specification
- A general hazard model
- Proportional hazards
- The Cox model with random effects
- The Bayesian model formulation
- A Weibull survival model
- A Bayesian AFT model
- Examples
- The gastric cancer study
- Prostate cancer in Louisiana: a spatial AFT model
- Closing remarks
**15. Longitudinal analysis**- Fixed time periods
- Introduction
- A classical growth curve example
- Alternate data models
- Random event times
- Dealing with missing data
- Introduction
- Response missingness
- Missingness mechanisms
- Bayesian considerations
- Predictor missingness
- Joint modeling of longitudinal and survival responses
- Introduction
- An example
- Closing remarks
**16. Disease mapping & image analysis**- Introduction
- Disease mapping
- Some general spatial epidemiological issues
- Some spatial statistical issues
- Count data models
- A special application area: Disease mapping/risk estimation.
- A special application area: Disease clustering
- A special application area: Ecological analysis
- Image analysis
- fMRI modeling
- A note on software
**17. Final chapter**- What this book covered
- Additional Bayesian developments
- Medical decision making
- Clinical trials
- Bayesian networks
- Bioinformatics
- Missing data
- Mixture models
- Nonparametric Bayesian methods
- Alternative reading
**18. Distributions**- Introduction
- Continuous univariate distributions
- Discrete univariate distributions
- Multivariate distributions

- Bibliography
- Index

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