Bayesian Methods for Repeated Measures: 1st Edition (Paperback) book cover

Bayesian Methods for Repeated Measures

1st Edition

By Lyle D. Broemeling

Chapman and Hall/CRC

568 pages

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pub: 2018-06-01
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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.

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

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

About the Author

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.

About the Series

Chapman & Hall/CRC Biostatistics Series

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General