Advanced Bayesian Methods for Medical Test Accuracy

By Lyle D. Broemeling

© 2011 – CRC Press

487 pages | 52 B/W Illus.

Purchasing Options:
Hardback: 9781439838785
pub: 2011-08-01

e–Inspection Copy

About the Book

Useful in many areas of medicine and biology, Bayesian methods are particularly attractive tools for the design of clinical trials and diagnostic tests, which are based on established information, usually from related previous studies. Advanced Bayesian Methods for Medical Test Accuracy begins with a review of the usual measures such as specificity, sensitivity, positive and negative predictive value, and the area under the ROC curve. Then the scope expands to cover the more advanced topics of verification bias, diagnostic tests with imperfect gold standards, and those for which no gold standard is available.

Promoting accuracy and efficiency of clinical trials, tests, and the diagnostic process, this book:

  • Enables the user to efficiently apply prior information via a WinBUGS package
  • Presents many ideas for the first time and goes far beyond the two standard references
  • Integrates reader agreement with different modalities—X-ray, CT Scanners, and more—to study their effect on medical test accuracy
  • Provides practical chapter-end problems

Useful for graduate students and consulting statisticians working in the various areas of diagnostic medicine and study design, this practical resource introduces the fundamentals of programming and executing BUGS, giving readers the tools and experience to successfully analyze studies for medical test accuracy.


"… very thorough coverage of topics that are commonly encountered in practice as well as numerous examples. This book is particularly appropriate for graduate students in statistics who have interests in diagnostic medicine. It is also valuable to consulting statisticians who have some basic knowledge of Bayesian methods and need such a reference to solve practical problems. … a great introduction to Bayesian methods specifically focused on solving medical test accuracy-related problems. It addresses popular topics in medical accuracy studies via Bayesian statistical methods to take advantage of prior information. Some complex problems, such as situations without a gold standard and partial verification bias, are also discussed. I recommend this book to graduate students in statistics or biostatistics and applied statisticians who are interested in medical diagnostic test accuracy."

—Xiaoye Ma, Journal of the American Statistical Association, December 2013

"Dr. Broemeling places all these considerations associated with test accuracy determinations into a pure Bayesian perspective. His book can be, in some sense, considered as a Bayesian counterpart to the books of Pepe and Zhou et al. The presentation is quite detailed and supported by a significant number of applications. … The literature review supporting the theoretical concepts about accuracy and the practical aspects associated with the applications is without a doubt extensive. … a good overview of the methods currently used to assess the accuracy of a medical test and their transposition to the Bayesian framework."

—Benoît Beck, CHANCE, August 2013

"It covers extensively most aspects of applied problems one can encounter when dealing with diagnostic accuracy studies. An attractive feature is that WinBUGS code needed for the implementation of the described methodologies is given in every chapter (also available on the author’s blog). A set of exercises is given at the end of each chapter. … a carefully written book. It will be useful for consulting biostatisticians, graduate students and teachers using methods for the assessment of diagnostic accuracy from a Bayesian viewpoint. The book is a must have for the interested audience."

—Christos Nakas, ISCB Newsletter, June 2013

Table of Contents



Statistical Methods in Medical Test Accuracy

Datasets for This Book


Bayesian Approach


Medical Tests and Preliminary Information


Medical Imaging Tests

Other Medical Tests

Activities Involved in Medical Testing

Accuracy and Agreement

Developmental Trials for Medical Devices



Preview of the Book


Preliminary Information

Fundamentals of Test Accuracy

Advanced Methods for Test Accuracy


Fundamentals of Diagnostic Accuracy


Study Design

Bayesian Methods for Test Accuracy: Binary and Ordinal Data

Clustered Data: Detection and Localization

Comparing Accuracy between Modalities with Ordinal Scores



Regression and Medical Test Accuracy


Audiology Study

Receiver Operating Characteristic Area and Patient Covariates

Regression Methods for Continuous Test Scores



Agreement and Test Accuracy


Ordinal Scores with a Gold Standard

Continuous Scores with a Gold Standard

Agreement with Ordinal Scores and No Gold Standard

Other Measures of Agreement

Agreement and Test Accuracy

Kappa and Association


Agreement with Multiple Raters and Ordinal Scores—No Gold Standard

Conclusions for Agreement and Accuracy



Estimating Test Accuracy with an Imperfect Reference Standard


Two Binary Tests

Posterior Distribution for Two Binary Tests

Posterior Distribution without Conditional Independence

Posterior Distribution Assuming Conditional Independence

Example of Accuracy for Diagnosing a Bacterial Infection

Accuracies of Two Binary Tests for Several Populations with Conditional Independence

Accuracies of Two Binary Tests without Conditional Independence: Two Populations

Multiple Tests in a Single Population

Multiple Tests without Conditional Independence

Two Ordinal Tests and the Receiver Operating

Characteristic Area



Verification Bias and Test Accuracy


Verification Bias and Binary Tests

Two Binary Tests

Ordinal Tests and Verification Bias

Two Ordinal Tests and Verification Bias

Two Ordinal Tests and Covariates

Inverse Probability Weighting

Without the Missing at Random Assumption

One Ordinal Test and the Receiver Operating Characteristic Area

Comments and Conclusions



Test Accuracy and Medical Practice


Choice of Optimal Threshold

Test Accuracy with Bayesian Decision Curves

Test Accuracy and Clinical Trials

Summary and Conclusions



Accuracy of Combined Tests


Two Binary Tests

Two Binary Tests and Several Readers

Accuracy of Combined Binary Tests with Verification Bias

Likelihood Ratio, the Risk Score, the Neyman–Pearson Lemma, and the Accuracy of Multiple Ordinal Tests

Accuracy of the Combined Test for Continuous Scores

Observations and Conclusions



Bayesian Methods for Meta-Analysis


Summary Receiver Operating Characteristic Curve and Bilogistic Regression

Bayesian Analysis for Summary Accuracy

Meta-Analysis with Two Tests

Meta-Analysis with Study Covariates and One Test

Meta-Analysis with Covariates for Several Tests

Other Meta-Analyses

Comments and Conclusions



Appendix: Introduction to WinBUGS





Another Example



About the Author

Lyle D. Broemeling, Ph.D., is Director of Broemeling and Associates Inc., and is a consulting biostatistician. He has been involved with academic health science centers for about 20 years and has taught and been a consultant at the University of Texas Medical Branch in Galveston, The University of Texas MD Anderson Cancer Center and the University of Texas School of Public Health. His main interest is in developing Bayesian methods for use in medical and biological problems and in authoring textbooks in statistics. His previous books are Bayesian Analysis of Linear Models, Econometrics and Structural Change(written with Hiraki Tsurumi), Bayesian Biostatistics and Diagnostic Medicine, and Bayesian Methods for Agreement.

About the Series

Chapman & Hall/CRC Biostatistics Series

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General
MEDICAL / Clinical Medicine
MEDICAL / Radiology & Nuclear Medicine