因果推断+James M.Robins & Hernan

Causal Inference: What If

Miguel A. Hern´an, James M. Robins

April 26, 2024

ii Causal Inference

Copyright 2020, 2024 Miguel Hern´an and James Robins

All rights reserved. No portion of this book can be reproduced for publi-

cation without express permission from the copyright holders, except as permit-

ted by U.S. copyright law. For permissions, contact miguel hernan@post.harvard.edu

Cover design by Josh McKible

Contents

Introduction: Towards less casual causal inferences vii

I Causal inference without models 1

1 A definition of causal effect 3

1.1 Individual causal effects . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Average causal effects . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Measures of causal effect . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Random variability . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5 Causation versus association . . . . . . . . . . . . . . . . . . . . 10

2 Randomized experiments 13

3.2 Exchangeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3 Positivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4 Consistency: First, define the counterfactual outcome . . . . . . 33

3.5 Consistency: Second, link counterfactuals to the observed data . 37

3.6 The target trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4 Effect modification 43

4.1 Heterogeneity of treatment effects . . . . . . . . . . . . . . . . . 43

4.2 Stratification to identify effect modification . . . . . . . . . . . . 45

4.3 Why care about effect modification . . . . . . . . . . . . . . . . . 47

4.4 Stratification as a form of adjustment . . . . . . . . . . . . . . . 49

5.4 Sufficient causes . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.5 Sufficient cause interaction . . . . . . . . . . . . . . . . . . . . . 65

5.6 Counterfactuals or sufficient-component causes? . . . . . . . . . . 67

iv Causal Inference

6 Graphical representation of causal effects 71

6.1 Causal diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.2 Causal diagrams and marginal independence . . . . . . . . . . . 73

6.3 Causal diagrams and conditional independence . . . . . . . . . . 76

6.4 Positivity and consistency in causal diagrams . . . . . . . . . . . 77

6.5 A structural classification of bias . . . . . . . . . . . . . . . . . . 81

6.6 The structure of effect modification . . . . . . . . . . . . . . . . . 83

7 Confounding 85

7.1 The structure of confounding . . . . . . . . . . . . . . . . . . . . 85

7.2 Confounding and exchangeability . . . . . . . . . . . . . . . . . . 87

7.3 Confounding and the backdoor criterion . . . . . . . . . . . . . . 89

7.4 Confounding and confounders . . . . . . . . . . . . . . . . . . . . 92

7.5 Single-world intervention graphs . . . . . . . . . . . . . . . . . . 95

8.5 How to adjust for selection bias . . . . . . . . . . . . . . . . . . . 111

8.6 Selection without bias . . . . . . . . . . . . . . . . . . . . . . . . 115

9 Measurement bias and “Noncausal” diagrams 119

9.1 Measurement error . . . . . . . . . . . . . . . . . . . . . . . . . . 119

9.2 The structure of measurement error . . . . . . . . . . . . . . . . 120

9.3 Mismeasured confounders and colliders . . . . . . . . . . . . . . . 122

9.4 Causal diagrams without mismeasured variables? . . . . . . . . . 124

9.5 Many proposed causal diagrams include noncausal arrows . . . . 125

9.6 Does it matter that many proposed diagrams include noncausal

arrows? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

II Causal inference with models 145

11.2 Parametric estimators of the conditional mean . . . . . . . . . . 149

11.3 Nonparametric estimators of the conditional mean . . . . . . . 150

11.4 Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

11.5 The bias-variance trade-off . . . . . . . . . . . . . . . . . . . . . 153