Bayesian Methods for Repeated Measures

About this book

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.

Bayesian Methods for Repeated Measures 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, Bayesian Methods for Repeated Measures 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.

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

Customer Reviews

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.