1st Edition

Bayesian Methods for Repeated Measures





ISBN 9781138894044
Published June 1, 2018 by Chapman and Hall/CRC
568 Pages

USD $67.95

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Book Description

Analyze Repeated Measures Studies Using Bayesian Techniques

Going beyond standard non-Bayesian books, Bayesian Methods for Repeated Measures presents the main ideas for the analysis of repeated measures and associated designs from a Bayesian viewpoint. It describes many inferential methods for analyzing repeated measures in various scientific areas, especially biostatistics.

The author takes a practical approach to the analysis of repeated measures. He bases all the computing and analysis on the WinBUGS package, which provides readers with a platform that efficiently uses prior information. The book includes the WinBUGS code needed to implement posterior analysis and offers the code for download online.

Accessible to both graduate students in statistics and consulting statisticians, the book introduces Bayesian regression techniques, preliminary concepts and techniques fundamental to the analysis of repeated measures, and the most important topic for repeated measures studies: linear models. It presents an in-depth explanation of estimating the mean profile for repeated measures studies, discusses choosing and estimating the covariance structure of the response, and expands the representation of a repeated measure to general mixed linear models. The author also explains the Bayesian analysis of categorical response data in a repeated measures study, Bayesian analysis for repeated measures when the mean profile is nonlinear, and a Bayesian approach to missing values in the response variable.

Table of Contents

Introduction to the Analysis of Repeated Measures
Introduction
Bayesian Inference
Bayes's Theorem
Prior Information
Posterior Information
Posterior Inference
Estimation
Testing Hypotheses
Predictive Inference
The Binomial
Forecasting from a Normal Population
Checking Model Assumptions
Sampling from an Exponential, but Assuming a Normal Population
Poisson Population
Measuring Tumor Size
Testing the Multinomial Aßumption
Computing
Example of a Cross-Sectional Study
Markov Chain Monte Carlo
Metropolis Algorithm
Gibbs Sampling
Common Mean of Normal Populations
An Example
Additional Comments about Bayesian Inference
WinBUGS
Preview
Exercises
Review of Bayesian Regression Methods
Introduction
Logistic Regression
Linear Regression Models
Weighted Regression
Nonlinear Regression
Repeated Measures Model
Remarks about Review of Regression
Exercises
Foundation and Preliminary Concepts
Introduction
An Example
Notation
Descriptive Statistics
Graphics
Sources of Variation
Bayesian Inference
Summary Statistics
Another Example
Basic Ideas for Categorical Variables
Summary
Exercises
Linear Models for Repeated Measures and Bayesian Inference
Introduction
Notation for Linear Models
Modeling the Mean
Modeling the Covariance Matrix
Historical Approaches
Bayesian Inference
Another Example
Summary and Conclusions
Exercises
Estimating the Mean Profile of Repeated Measures
Introduction
Polynomials for Fitting the Mean Profile
Modeling the Mean Profile for Discrete Observations
Examples
Conclusions and Summary
Exercises
Correlation Patterns for Repeated Measures
Introduction
Patterns for Correlation Matrices
Choosing a Pattern for the Covariance Matrix
More Examples
Comments and Conclusions
Exercises
General Mixed Linear Model
Introduction and Definition of the Model
Interpretation of the Model
General Linear Mixed Model Notation
Pattern of the Covariance Matrix
Bayesian Approach
Examples
Diagnostic Procedures for Repeated Measures
Comments and Conclusions
Exercises
Repeated Measures for Categorical Data
Introduction to the Bayesian Analysis with a Dirichlet Posterior Distribution
Bayesian GEE
Generalized Mixed Linear Models for Categorical Data
Comments and Conclusions
Exercises
Nonlinear Models and Repeated Measures
Nonlinear Models and a Continuous Response
Nonlinear Repeated Measures with Categorical Data
Comments and Conclusion
Exercises
Bayesian Techniques for Missing Data
Introduction
Missing Data and Linear Models of Repeated Measures
Missing Data and Categorical Repeated Measures
Comments and Conclusions
Exercises
References

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Author(s)

Biography

Lyle D. Broemeling has 30 years of experience as a biostatistician. He has been a professor at the University of Texas Medical Branch at Galveston, the University of Texas School of Public Health at Houston, and the University of Texas MD Anderson Cancer Center. He is also the author of several books, including Bayesian Methods in Epidemiology. His research interests include the analysis of repeated measures and Bayesian methods for assessing medical test accuracy and inter-rater agreement.

Reviews

"The book will be especially useful for clinical researchers, epidemiologists, and other researchers focused on data analysis and seeking to apply Bayesian methods. Useful computer codes and worked examples are provided. Moreover, the book also has utility as a general exposition of data and graph analytic approaches to longitudinal data."
~Peter Congdon, Biometric Journal

"This book is rich in illustrative examples and detailed WinBUGS code for analyzing real-world data, while providing thorough insight in the underlying theory of Bayesian methods for the analysis of repeated measures data. This makes the book a practical guide, and a great resource for learning the theory and practice of Bayesian methods for repeated measures for students and applied statisticians."
~Hao Zhang