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**“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

This book provides a tool in diagnostic decision making by joining applications of information theory to plant disease epidemiology.

**PRINT EDITION**Item No. 44150

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

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#### 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

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#### 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

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#### 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

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#### 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 *g*1(1-*r*)

A test with *n*≥2 outcome categories based on the relative density *g*1(1-*r*)

Grouped data

Summary

## Chapter 5. The Interpretation of Diagnostic Data

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#### 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

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Chapter 7: Appendix B: Relative Entropy and ROC Curves

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#### The shape of ROC curves

Geometric symmetry of ROC curves

Measures of distance between distributions

Asymmetry

Glossary

References

Index

Glossary

References

Index

**“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

Format: 8" x 10" softcover

ISBN: 978-0-89054-415-0

Pages: 158

Images: 29 color images; 16 black and white images

Publication Weight: 2 lbs