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."
Author(s): Paul Gustafson
Edition: 1
Publisher: Chapman and Hall/CRC
Year: 2004
Language: English
Pages: 193
Measurement Error and Misclassifications in Statistics and Epidemiolgy......Page 1
Dedication......Page 5
Table of Contents......Page 6
Preface......Page 8
Guide to Notation......Page 10
1.1 Examples of Measurements......Page 11
Table of Contents......Page 0
1.2 The Mismeasurement Phenomenon......Page 13
1.3 What is Ahead?......Page 16
2.1 The Archetypical Scenario......Page 19
2.2 More General Impact......Page 21
2.3 Multiplicative Measurement Error......Page 25
2.4 Multiple Mismeasured Predictors......Page 28
2.5 What about Variability and Small Samples?......Page 31
2.6 Logistic Regression......Page 34
2.7 Beyond Nondiferential and Unbiased Measurement Error......Page 36
2.8 Summary......Page 39
2.9.1 A Generalization of Result 2.1......Page 40
2.9.2 Proof of Result 2.2 from Section 2.3......Page 41
2.9.3 A Result on the Impact of Measurement Error in Logistic Regression......Page 42
3.1 The Linear Model Case......Page 44
3.2 More General Impact......Page 46
3.3 Inferences on Odds-Ratios......Page 48
3.4 Logistic Regression......Page 53
3.5 Differential Misclassification......Page 55
3.6 Polychotomous Variables......Page 56
3.8 Mathematical Details......Page 58
4.1 Posterior Distributions......Page 60
4.2 A Simple Scenario......Page 65
4.3 Nonlinear Mixed Effects Model: Viral Dynamics......Page 71
4.4 Logistic Regression I: Smoking and Bladder Cancer......Page 78
4.5 Logistic Regression II: Framingham Heart Study......Page 81
4.6 Issues in Specifying the Exposure Model......Page 83
4.7 More Flexible Exposure Models......Page 88
4.8 Retrospective Analysis......Page 92
4.9 Comparison with Non-Bayesian Approaches......Page 97
4.11.1 Full Conditional Distributions in the Example of Section 4.2......Page 101
4.11.3 Proof of Result 4.1......Page 103
4.11.4 Proof of Result 4.2......Page 104
5.1 A Simple Scenario......Page 107
5.2 Partial Knowledge of Misclassi......Page 112
5.3 Dual Exposure Assessment......Page 119
5.3.1 Relaxing the Conditional Independence Assumption......Page 122
5.3.2 Example......Page 125
5.4 Models with Additional Explanatory Variables......Page 127
5.4.1 Example......Page 130
5.4.2 Beyond Nondifferential and Conditionally Independent Dual Exposure Assessment......Page 132
5.4.3 Dual Exposure Assessment in Three Populations......Page 134
5.6.1 Gibbs Sampling for the AWU Model of Section 5.2......Page 139
5.6.2 A Tailored MCMC Algorithm for the AWU Model of Section 5.2......Page 140
5.6.3 Comparing MCMC Algorithms for the AWU Model of Section 5.2......Page 142
5.6.4 MCMC Fitting for the DUAL-DEP Model of Section 5.3......Page 143
5.6.5 Gibbs Sampling for the Model of Section 5.4.3......Page 145
6.1 Dichotomization of Mismeasured Continuous Variables......Page 146
6.2 Mismeasurement Bias and Model Misspeci......Page 154
6.2.1 Further Consideration of Dichotomization......Page 156
6.2.2 Other Examples......Page 157
6.3 Identifiability in Mismeasurement Models......Page 159
6.3.1 Estimator Performance in Nonidenti......Page 160
6.3.2 Example: Partial Knowledge of Misclassi......Page 162
6.3.3 Linear and Normal Models Revisited......Page 165
6.3.4 Dual Exposure Assessment in One Population......Page 169
6.4 Further Remarks......Page 171
References......Page 172
A.1 Bayes Theorem......Page 180
A.2 Point and Interval Estimates......Page 183
A.3 Markov Chain Monte Carlo......Page 184
A.4 Prior Selection......Page 191
A.5 MCMC and Unobserved Structure......Page 192
