1st Edition

Bayesian Methods for Repeated Measures

By Lyle D. Broemeling Copyright 2016
    568 Pages
    by Chapman & Hall

    568 Pages 86 B/W Illustrations
    by Chapman & Hall

    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.

    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

    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.

    "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