ハーバードの因果推論の教科書の目次をメモ

ハーバードの人たちが因果推論の教科書を書いてドラフトを公開している。
http://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/
とりあえず現段階の全容を把握したいので目次をメモ。

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

2.1 Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Conditional randomization . . . . . . . . . . . . . . . . . . . . . 16
2.3 Standardization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Inverse probability weighting . . . . . . . . . . . . . . . . . . . . 20

3 Observational studies 25

3.1 The randomized experiment paradigm . . . . . . . . . . . . . . . 25
3.2 Exchangeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 Positivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4 Well-defined interventions . . . . . . . . . . . . . . . . . . . . . . 31
3.5 Well-defined interventions are a pre-requisite for causal inference 35
3.6 Causation or prediction? . . . . . . . . . . . . . . . . . . . . . . . 37

4 Effect modification 41

4.1 Definition of effect modification . . . . . . . . . . . . . . . . . . . 41
4.2 Stratification to identify effect modification . . . . . . . . . . . . 43
4.3 Reasons to care about effect modification . . . . . . . . . . . . . 45
4.4 Stratification as a form of adjustment . . . . . . . . . . . . . . . 47
4.5 Matching as another form of adjustment . . . . . . . . . . . . . . 49
4.6 Effect modification and adjustment methods . . . . . . . . . . . 50

5 Interaction 55

5.1 Interaction requires a joint intervention . . . . . . . . . . . . . . 55
5.2 Identifying interaction . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3 Counterfactual response types and interaction . . . . . . . . . . . 58
5.4 Sufficient causes . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.5 Sufficient cause interaction . . . . . . . . . . . . . . . . . . . . . 63
5.6 Counterfactuals or sufficient-component causes? . . . . . . . . . . 65

6 Graphical representation of causal effects 69

6.1 Causal diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2 Causal diagrams and marginal independence . . . . . . . . . . . 72
6.3 Causal diagrams and conditional independence . . . . . . . . . . 73
6.4 Graphs, counterfactuals, and interventions . . . . . . . . . . . . . 75
6.5 A structural classification of bias . . . . . . . . . . . . . . . . . . 77
6.6 The structure of effect modification . . . . . . . . . . . . . . . . . 78

7 Confounding 83

7.1 The structure of confounding . . . . . . . . . . . . . . . . . . . . 83
7.2 Confounding and identifiability of causal effects . . . . . . . . . . 85
7.3 Confounders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
7.4 Confounding and exchangeability . . . . . . . . . . . . . . . . . . 89
7.5 How to adjust for confounding . . . . . . . . . . . . . . . . . . . 92

8 Selection bias 95

8.1 The structure of selection bias . . . . . . . . . . . . . . . . . . . 95
8.2 Examples of selection bias . . . . . . . . . . . . . . . . . . . . . . 97
8.3 Selection bias and confounding . . . . . . . . . . . . . . . . . . . 99
8.4 Selection bias and identifiability of causal effects . . . . . . . . . 101
8.5 How to adjust for selection bias . . . . . . . . . . . . . . . . . . . 102
8.6 Selection without bias . . . . . . . . . . . . . . . . . . . . . . . . 106

9 Measurement bias 109

9.1 Measurement error . . . . . . . . . . . . . . . . . . . . . . . . . . 109
9.2 The structure of measurement error . . . . . . . . . . . . . . . . 110
9.3 Mismeasured confounders . . . . . . . . . . . . . . . . . . . . . . 111
9.4 Adherence to treatment in randomized experiments . . . . . . . 113
9.5 The intention-to-treat effect and the per-protocol effect . . . . . 115

10 Random variability 119

10.1 Identification versus estimation . . . . . . . . . . . . . . . . . . 119
10.2 Estimation of causal effects . . . . . . . . . . . . . . . . . . . . 122
10.3 The myth of the super-population . . . . . . . . . . . . . . . . . 123
10.4 The conditionality “principle” . . . . . . . . . . . . . . . . . . . 124
10.5 The curse of dimensionality . . . . . . . . . . . . . . . . . . . . 126

II Causal inference with models 1

11 Why model? 3

11.1 Data cannot speak for themselves . . . . . . . . . . . . . . . . . 3
11.2 Parametric estimators . . . . . . . . . . . . . . . . . . . . . . . 5
11.3 Nonparametric estimators . . . . . . . . . . . . . . . . . . . . . 6
11.4 Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
11.5 The bias-variance trade-off ..................... 8

12 IP weighting and marginal structural models 11

12.1 The causal question . . . . . . . . . . . . . . . . . . . . . . . . . 11
12.2 Estimating IP weights via modeling . . . . . . . . . . . . . . . . 12
12.3 Stabilized IP weights . . . . . . . . . . . . . . . . . . . . . . . . 14
12.4 Marginal structural models . . . . . . . . . . . . . . . . . . . . . 17
12.5 Effect modification and marginal structural models . . . . . . . 19
12.6 Censoring and missing data . . . . . . . . . . . . . . . . . . . . 20

13 Standardization and the parametric g-formula 23

13.1 Standardization as an alternative to IP weighting . . . . . . . . 23
13.2 Estimating the mean outcome via modeling . . . . . . . . . . . 24
13.3 Standardizing the mean outcome to the confounder distribution 26
13.4 IP weighting or standardization? . . . . . . . . . . . . . . . . . 27
13.5 How seriously do we take our estimates? . . . . . . . . . . . . . 29

14 G-estimation of structural nested models 31

14.1 The causal question revisited . . . . . . . . . . . . . . . . . . . 31
14.2 Exchangeability revisited . . . . . . . . . . . . . . . . . . . . . . 32
14.3 Structural nested mean models . . . . . . . . . . . . . . . . . . 33
14.4 Rank preservation . . . . . . . . . . . . . . . . . . . . . . . . . . 35
14.5 G-estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
14.6 Structural nested models with two or more parameters . . . . . 39

15 Outcome regression and propensity scores 43

15.1 Outcome regression . . . . . . . . . . . . . . . . . . . . . . . . . 43
15.2 Propensity scores . . . . . . . . . . . . . . . . . . . . . . . . . . 45
15.3 Propensity stratification and standardization . . . . . . . . . . . 46
15.4 Propensity matching . . . . . . . . . . . . . . . . . . . . . . . . 47
15.5 Propensity models, structural models, predictive models . . . . 49

16 Instrumental variable methods 53

16.1 The three instrumental conditions . . . . . . . . . . . . . . . . . 53
16.2 A fourth identifiying condition: homogeneity . . . . . . . . . . . 55
16.3 An alternative fourth condition: monotonicity . . . . . . . . . . 57
16.4 Instrumental variable estimation with covariates . . . . . . . . . 60
16.5 Instrumental variable estimation versus other causal inference methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

17 Survival analysis 67

Hazards and risks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
The g-formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
IP weighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
G-estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

18 The bias-variance tradeoff 69

18.1 Mean square error . . . . . . . . . . . . . . . . . . . . . . . . . . 69
18.2 Selection of confounders . . . . . . . . . . . . . . . . . . . . . . 69
18.3 Weight truncation . . . . . . . . . . . . . . . . . . . . . . . . . . 70
18.4 Doubly-robust methods . . . . . . . . . . . . . . . . . . . . . . . 70