1st Edition

# Measurement Error and Misclassification in Statistics and Epidemiology Impacts and Bayesian Adjustments

200 Pages 39 B/W Illustrations
by Chapman & Hall

200 Pages
by Chapman & Hall

Also available as eBook on:

Mismeasurement of explanatory variables is a common hazard when using statistical modeling techniques, and particularly so in fields such as biostatistics and epidemiology where perceived risk factors cannot always be measured accurately. With this perspective and a focus on both continuous and categorical variables, Measurement Error and Misclassification in Statistics and Epidemiology: Impacts and Bayesian Adjustments examines the consequences and Bayesian remedies in those cases where the explanatory variable cannot be measured with precision.

The author explores both measurement error in continuous variables and misclassification in discrete variables, and shows how Bayesian methods might be used to allow for mismeasurement. A broad range of topics, from basic research to more complex concepts such as "wrong-model" fitting, make this a useful research work for practitioners, students and researchers in biostatistics and epidemiology."

INTRODUCTION
Examples of Mismeasurement
The Mismeasurement Phenomenon
THE IMPACT OF MISMEASURED CONTINUOUS VARIABLES
The Archetypical Scenario
More General Impact
Multiplicative Measurement Error
Multiple Mismeasured Predictors
What about Variability and Small Samples?
Logistic Regression
Beyond Nondifferential and Unbiased Measurement Error
Summary
Mathematical Details
THE IMPACT OF MISMEASURED CATEGORICAL VARIABLES
The Linear Model Case
More General Impact
Inferences on Odds-Ratios
Logistic Regression
Differential Misclassification
Polychotomous Variables
Summary
Mathematical Details
Posterior Distributions
A Simple Scenario
Nonlinear Mixed Effects Model: Viral Dynamics
Logistic Regression I: Smoking and Bladder Cancer
Logistic Regression II: Framingham Heart Study
Issues in Specifying the Exposure Model
More Flexible Exposure Models
Retrospective Analysis
Comparison with Non-Bayesian Approaches
Summary
Mathematical Details
A Simple Scenario
Partial Knowledge of Misclassification Probabilities
Dual Exposure Assessment
Summary
Mathematical Details
FURTHER TOPICS
Dichotomization of Mismeasured Continuous Variables
Mismeasurement Bias and Model Misspecification Bias
Identifiability in Mismeasurement Models
Further Remarks
APPENDIX: BAYES-MCMC INFERENCE
Bayes Theorem
Point and Interval Estimates
Markov Chain Monte Carlo
Prior Selection
MCMC and Unobserved Structure
REFERENCES

### Biography

Paul Gustafson (University of British Columbia, Vancouver, Canada) (Author)

"The topic addressed by this book is an important one. … This book shows that error-prone measurements may create serious biases and offers Bayesian approaches to attempt unbiased estimation, or 'adjustments'. … This is a useful book if you have data containing errors or if you have an interest in statistical theory of errors of measurement. As nearly all data is in some way erroneous, it is a useful book for all statisticians and mathematically inclined epidemiologists. …"
-Statistics in Medicine, Vol. 24, 2005

"This book provides a good overview of recent topics in measurement error models in the linear and logistic regression context using the Bayesian paradigm… . "
-Technometrics

" … a welcome addition for anyone who is interested in the topic of mismeasurement and in particular the issue of Bayesian adjustment methods. Although it does not shy away from the theoretical issues surrounding this subject, it remains accessible for practical applied statisticians. The book has two real highlights for me: firstly, the author's focus on the problems that mismeasurement creates in a variety of complex situations, reflecting what practical statisticians deal with regularly. Secondly, the book gives almost equal treatment to the problem of mismeasurement of continuous and discrete variable; it is quite rare to see such extensive treatment of both situations in one place …The examples that are used throughout the book offer great insight, as they highlight the complexities of real life data analysis when mismeasurement is an issue …"
-Journal of the Royal Statistical Society, Series A, Vol. 157(3)

"This is a well-written book and contains a great deal of information on the impact of measurement error in explanatory variables, as well as details of methods to adjust for mismeasurement. Considering measurement error in both continuous and categorical variables, as well as using Bayesian methods to adjust for mismeasurement, make this an excellent resource for epidemiologists or medical statisticians."
-Zoe Fewell, International Journal of Epidemiology

"This book is an ambitious undertaking by a prolific, creative, and relatively young researcher. As a non-Bayesian researcher in the field on measurement error and misclassification, I found the book to be clearly written, well organized, and much interest. In fact, I enjoyed reading it. … I found this to be an interesting and clearly written text of high technical quality that would be of interest to statistical researchers in the measurement error and misclassification area as well as to Bayesian statisticians interested in a somewhat novel area of application for Bayesian statistics. All of us working in these areas should find this book a worthwhile read."
- Donna Spiegelman (Harvard School of Public Health), Journal of the American Statistical Association