In Applications of Information Theory to Epidemiology, author Gareth Hughes gathers together epidemiological applications of information theory and presents them in a manner that makes them accessible to plant disease epidemiologists and others in the field of plant pathology and beyond. He provides a summary of basic concepts, methods, and results that is not only understandable to newcomers to the topic, but is immediately useful and applicable for those using data for making diagnostic determinations.

This is the first book written on information theory applications explicitly for plant disease epidemiology. Few, if any, plant disease epidemiologists have followed closely the epidemiological applications of information theory. One reason for this is that applications of information theory to epidemiology have been devised almost exclusively by clinical epidemiologists. The author’s key methodologies related to diagnostic decision making as it relates to plant diseases are drawn from his career work which includes the epidemiology and modeling of diseases. Dr. Hughes has been honored for his work using real-world disease problems in fruit crops as model systems for the development of methodology for basic research in epidemiology and plant disease losses. The breakthrough results of these basic studies have provided innovative approaches for the management of diseases and have made a substantial impact on our knowledge in this area of science.

Applications of Information Theory to Epidemiology uses original clinical epidemiology examples as well as phytopathological applications to illustrate theory, citing a wide range of literature. This permits the examples in the book to be used by many diverse groups of scientists. This book is ideally suited for plant pathologists and others with an interest in the quantitative basis for diagnostic decision making. Epidemiologists (botanical, also clinical and veterinary) will find it useful as well. Those who have enjoyed The Study of Plant Disease Epidemics by Larry Madden and colleagues will welcome this title as a continuation of the applied knowledge in this area. The author includes a helpful glossary of terms for those new to the nomenclature.

Applications of Information Theory to Epidemiology

Chapter 1. Introduction

Disease management
Potato late blight
Sclerotinia stem rot of oil seed rape in Sweden
Sensitivity and specificity
Prior and posterior probabilities
Low prior probabilities
Combining probabilistic data
Summary

Chapter 2. The Information Content of Predictions

The information content of a message
Expected information content
Benish’s information graph
Mutual information
Expected information and ROC curves
Expected information for tests with n>2 outcome categories
Relative entropy as weighted average information content
Summary

Chapter 3. Information Characteristics of Predictors

Lee’s analysis of a 2x2 decision table
Interval likelihood ratios
Lee’s analysis of an nx2 decision table
Comparison of tests
Relative entropy as weighted average log-likelihood ratio
Summary

Chapter 4. Indicator Scores and the Relative Distribution

Properties of the distributions of indicator scores
The continuous relative distribution
The relative distribution and the ROC curve
A binary test based on the relative density g1(1-r)
A test with n≥2 outcome categories based on the relative density g1(1-r)
Grouped data
Summary

Chapter 5. The Interpretation of Diagnostic Data

Sclerotinia stem rot of oil seed rape in France
Relative entropy and Biggerstaff’s likelihood ratios graph
Variability in the prior probability of disease
Classification errors in a binomial sampling process
An approximate posterior probability distribution
The exact posterior probability distribution
Comparing the exact and approximate posterior distributions
A phytopathological example with a beta prior and classification errors
Summary

Chapter 6: Appendix A: Relative Entropy Between Bernoulli Distributions

Chapter 7: Appendix B: Relative Entropy and ROC Curves

The shape of ROC curves
Geometric symmetry of ROC curves
Measures of distance between distributions
Asymmetry

“Disease management is all about making decisions, possibly based on diagnostic tests or disease predictors. This book elegantly and rigorously shows how the field of information theory can be used to evaluate the accuracy of decision tools and therefore make better control decisions.”
—Larry Madden, Distinguished Professor in Plant Protection at Ohio State University (Wooster) and Former President and APS Fellow