Measurement Error and Misclassification in Statistics and Epidemiology: Impacts and Bayesian Adjustments
INTRODUCTION Examples of Mismeasurement The Mismeasurement Phenomenon What is Ahead? 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 ADJUSTMENT FOR MISMEASURED CONTINUOUS VARIABLES 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 ADJUSTMENT FOR MISMEASURED CATEGORICAL VARIABLES A Simple Scenario Partial Knowledge of Misclassification Probabilities Dual Exposure Assessment Models with Additional Explanatory Variables 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