1

Introduction, Objectives, and an Alternative

1

Introduction

1

Nonrandomized Epidemiologic Research

1

The Treatment of Uncertainty in Nonrandomized Research

2

Objective

3

An Alternative

4

Heuristics

5

Conclusion

10

2

A Guide to Implementing Quantitative Bias Analysis

13

Introduction

13

Reducing Error

13

Reducing Error by Design

14

Reducing Error in the Analysis

16

Quantifying Error

18

When Is Quantitative Bias Analysis Valuable?

18

Planning for Bias Analysis

20

Creating a Data Collection Plan for Bias Analysis

22

Creating an Analytic Plan for a Bias Analysis

24

Bias Analysis Techniques

27

A Note on Inference

31

Conclusion

32

3

Data Sources for Bias Analysis

33

Bias Parameters

33

Internal Data Sources

33

Selection Bias

34

Unmeasured Confounder

34

Information Bias

35

Limitations of Internal Validation Studies

36

External Data Sources

37

Selection Bias

38

Unmeasured Confounder

39

Information Bias

40

Summary

41

4

Selection Bias

43

Introduction

43

Definitions and Terms

45

Conceptual

45

Motivation for Bias Analysis

48

Sources of Data

48

Simple Correction for Differential Initial Participation

49

Example

49

Introduction to Correction

50

Correction by Projecting the Exposed Proportion Among Nonparticipants

51

Correction Using Selection Proportions

52

Simple Correction for Differential Loss-to-Follow-up

54

Example

54

Correction

55

5

Unmeasured and Unknown Confounders

59

Introduction

59

Definition and Terms

60

Conceptual

60

Motivation for Bias Analysis

61

Sources of Data

62

Introduction to Simple Bias Analysis

63

Approach

63

Introduction to the Example

63

Bias Parameters

64

Implementation of Simple Bias Analysis

65

Ratio Measures

65

Example

68

Difference Measures

71

Unmeasured Confounder in the Presence of Effect Modification

72

Polytomous Confounders

75

Bounding the Bias Limits of Unmeasured Confounding

76

Analytic Approach

77

6

Misclassification

79

Introduction

79

Definitions and Terms

80

Conceptual

80

Calculating Classification Bias Parameters from Validation Data

82

Sources of Data

83

Bias Analysis of Exposure Misclassification

85

Corrections Using Sensitivity and Specificity: Nondifferential and Independent Errors

87

Corrections Using Predictive Values

89

Corrections Using Sensitivity and Specificity: Differential Independent Errors

91

Corrections Using Sensitivity and Specificity: Internal Validation Data

91

Overreliance on Nondifferential Misclassification Biasing Toward the Null

93

Disease Misclassification

94

Corrections with Sensitivity and Specificity Nondifferential and Idependent Errors

94

Overreliance on Nondifferential Misclassification Biasing Toward the Null

96

Covariate Misclassification

100

Corrections with Sensitivity and Specificity Nondifferential and Idependent Errors

100

Overreliance on Nondifferential Misclassification Biasing Toward the Null

101

Dependent Misclassification

103

Adjusting Standard Errors for Corrections

106

Standard Errors When Sensitivity and Specificity Are Used

106

Standard Errors When Predictive Values Are Used

107

Conclusions

107

Extensions

107

Limitations

108

7

Multidimensional Bias Analysis

109

Introduction

109

Selection Bias

110

Unmeasured Confounder

112

Misclassification

113

Limitations

116

8

Probabilistic Bias Analysis

117

Introduction

117

Probability Distributions

119

Uniform Distribution

119

Trapezoidal Distribution

121

Triangular Distribution

123

Normal Distribution

124

Beta Distribution

126

Other Probability Distributions

132

Analytic Approach

132

Exposure Misclassification Implementation

132

Misclassification Implementation Alternative: Predictive Values

138

Unmeasured Confounding Implementation

138

Confounding Implementation Alternative: Relative Risk Due to Confounding

141

Selection Bias Implementation

142

Correlated Distributions

144

Impossible Values for Bias Parameters

146

Combining Systematic and Random Error

147

Record Level Correction

149

Conclusions

149

Appendix

150

9

Multiple Bias Modeling

151

Introduction

151

Multiple Bias Analysis Example

153

Multiple Bias Analysis, Simple Methods

154

Simple Misclassification Bias Analysis

154

Simple Selection Bias Analysis

155

Simple Unmeasured Confounder Analysis

158

Multiple Bias Analysis, Multidimensional Methods

160

Misclassification Scenarios

160

Selection Bias Scenarios

160

Unmeasured Confounder Scenarios

161

Multiple Bias Analysis, Probabilistic Methods

162

Probabilistic Misclassification Bias Analysis

163

Probabilistic Selection Bias Analysis

168

Probabilistic Unmeasured Confounder Bias Analysis

169

Probabilistic Multiple Bias Analysis

171

10

Presentation and Inference

175

Introduction

175

Presentation

175

Methods

175

Results

176

Inference

178

Inferential Framework

178

Caveats and Cautions

179

Utility

180

References

183

Index

191