发帖
雷达卡
目录：Introduction: Towards less casual causal inferences vii
I Causal inference without models 1
1 Adefinition 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 . . . . . . . . . . . . . . . . . . . . . 17
2.3 Standardization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Inverse probability weighting . . . . . . . . . . . . . . . . . . . . 20
3 Observational studies 25
3.1 Identifiability conditions . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Exchangeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 Positivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4 Consistency: First, define the counterfactual outcome . . . . . . 31
3.5 Consistency: Second, link counterfactuals to the observed data . 35
3.6 The target trial . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4 Effect modification 41
4.1 Definition of effect modification . . . . . . . . . . . . . . . . . . . 41
4.2 Stratification to identify effect modification . . . . . . . . . . . . 43
4.3 Why care about effect modification . . . . . . . . . . . . . . . . . 45
4.4 Stratification as a formof adjustment . . . . . . . . . . . . . . . 47
4.5Matching as another formof adjustment . . . . . . . . . . . . . . 49
4.6 Effect modification and adjustmentmethods . . . . . . . . . . . 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 andmarginal independence . . . . . . . . . . . 71
6.3 Causal diagrams and conditional independence . . . . . . . . . . 73
6.4 Positivity and consistency in causal diagrams . . . . . . . . . . . 75
6.5 A structural classification of bias . . . . . . . . . . . . . . . . . . 78
6.6 The structure of effect modification . . . . . . . . . . . . . . . . . 80
7 Confounding 83
7.1 The structure of confounding . . . . . . . . . . . . . . . . . . . . 83
7.2 Confounding and exchangeability . . . . . . . . . . . . . . . . . . 85
7.3 Confounding and the backdoor criterion . . . . . . . . . . . . . . 87
7.4 Confounding and confounders . . . . . . . . . . . . . . . . . . . . 90
7.5 Single-world intervention graphs . . . . . . . . . . . . . . . . . . 93
7.6 Confounding adjustment . . . . . . . . . . . . . . . . . . . . . . . 94
8 Selection bias 99
8.1 The structure of selection bias . . . . . . . . . . . . . . . . . . . 99
8.2 Examples of selection bias . . . . . . . . . . . . . . . . . . . . . . 101
8.3 Selection bias and confounding . . . . . . . . . . . . . . . . . . . 103
8.4 Selection bias and censoring . . . . . . . . . . . . . . . . . . . . . 105
8.5 How to adjust for selection bias . . . . . . . . . . . . . . . . . . . 107
8.6 Selection without bias . . . . . . . . . . . . . . . . . . . . . . . . 110
9 Measurement bias 113
9.1Measurement error . . . . . . . . . . . . . . . . . . . . . . . . . . 113
9.2 The structure ofmeasurement error . . . . . . . . . . . . . . . . 114
9.3 Mismeasured confounders . . . . . . . . . . . . . . . . . . . . . . 116
9.4 Intention-to-treat effect: the effect of a misclassified treatment . 117
9.5 Per-protocol effect . . . . . . . . . . . . . . . . . . . . . . . . . . 119
10 Random variability 123
10.1 Identification versus estimation . . . . . . . . . . . . . . . . . . 123
10.2 Estimation of causal effects . . . . . . . . . . . . . . . . . . . . 126
10.3 Themyth of the super-population . . . . . . . . . . . . . . . . . 128
10.4 The conditionality “principle” . . . . . . . . . . . . . . . . . . . 129
10.5 The curse of dimensionality . . . . . . . . . . . . . . . . . . . . 133
II Causal inference with models 137
11 Why model? 139
11.1 Data cannot speak for themselves . . . . . . . . . . . . . . . . . 139
11.2 Parametric estimators of the conditionalmean . . . . . . . . . . 141
11.3 Nonparametric estimators of the conditionalmean . . . . . . . 142
11.4 Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
11.5 The bias-variance trade-off . . . . . . . . . . . . . . . . . . . . . 145
12 IP weighting and marginal structural models 149
12.1 The causal question . . . . . . . . . . . . . . . . . . . . . . . . . 149
12.2 Estimating IP weights viamodeling . . . . . . . . . . . . . . . . 150
12.3 Stabilized IP weights . . . . . . . . . . . . . . . . . . . . . . . . 153
12.4Marginal structuralmodels . . . . . . . . . . . . . . . . . . . . . 155
12.5 Effect modification andmarginal structural models . . . . . . . 157
13 Standardization and the parametric g-formula 161
13.1 Standardization as an alternative to IP weighting . . . . . . . . 161
13.2 Estimating themean outcome viamodeling . . . . . . . . . . . 163
13.3 Standardizing the mean outcome to the confounder distribution 164
13.4 IP weighting or standardization? . . . . . . . . . . . . . . . . . 165
13.5 How seriously do we take our estimates? . . . . . . . . . . . . . 167
14 G-estimation of structural nested models 171
14.1 The causal question revisited . . . . . . . . . . . . . . . . . . . 171
14.2 Exchangeability revisited . . . . . . . . . . . . . . . . . . . . . . 172
14.3 Structural nestedmeanmodels . . . . . . . . . . . . . . . . . . 173
14.4 Rank preservation . . . . . . . . . . . . . . . . . . . . . . . . . . 175
14.5 G-estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
14.6 Structural nestedmodels with two ormore parameters . . . . . 179
15 Outcome regression and propensity scores 183
15.1 Outcome regression . . . . . . . . . . . . . . . . . . . . . . . . . 183
15.2 Propensity scores . . . . . . . . . . . . . . . . . . . . . . . . . . 185
15.3 Propensity stratification and standardization . . . . . . . . . . . 186
15.4 Propensitymatching . . . . . . . . . . . . . . . . . . . . . . . . 188
15.5 Propensitymodels, structural models, predictivemodels . . . . 189
16 Instrumental variable estimation 193
16.1 The three instrumental conditions . . . . . . . . . . . . . . . . . 193
16.2 The usual IV estimand . . . . . . . . . . . . . . . . . . . . . . . 196
16.3 A fourth identifying condition: homogeneity . . . . . . . . . . . 198
16.4 An alternative fourth condition: monotonicity . . . . . . . . . . 200
16.5 The three instrumental conditions revisited . . . . . . . . . . . 204
16.6 Instrumental variable estimation versus other methods . . . . . 206
17 Causal survival analysis 209
17.1 Hazards and risks . . . . . . . . . . . . . . . . . . . . . . . . . . 209
17.2 Fromhazards to risks . . . . . . . . . . . . . . . . . . . . . . . . 211
17.3Why censoringmatters . . . . . . . . . . . . . . . . . . . . . . . 214
17.4 IP weighting ofmarginal structural models . . . . . . . . . . . . 216
17.5 The parametric g-formula . . . . . . . . . . . . . . . . . . . . . 217
17.6 G-estimation of structural nestedmodels . . . . . . . . . . . . . 219
18 Variable selection for causal inference 223
18.1 The different goals of variable selection . . . . . . . . . . . . . . 223
18.2 Variables that induce or amplify bias . . . . . . . . . . . . . . . 225
18.3 Causal inference andmachine learning . . . . . . . . . . . . . . 228
18.4 Doubly robustmachine learning estimators . . . . . . . . . . . . 229
18.5 Variable selection is a difficult problem . . . . . . . . . . . . . . 230
III Causal inference from complex longitudinal data 233
19 Time-varying treatments 235
19.1 The causal effect of time-varying treatments . . . . . . . . . . . 235
19.2 Treatment strategies . . . . . . . . . . . . . . . . . . . . . . . . 236
19.3 Sequentially randomized experiments . . . . . . . . . . . . . . . 237
19.4 Sequential exchangeability . . . . . . . . . . . . . . . . . . . . . 240
19.5 Identifiability under some but not all treatment strategies . . . 241
19.6 Time-varying confounding and time-varying confounders . . . . 245
20 Treatment-confounder feedback 247
20.1 The elements of treatment-confounder feedback . . . . . . . . . 247
20.2 The bias of traditional methods . . . . . . . . . . . . . . . . . . 249
20.3Why traditionalmethods fail . . . . . . . . . . . . . . . . . . . 251
20.4 Why traditional methods cannot be fixed . . . . . . . . . . . . . 253
20.5 Adjusting for past treatment . . . . . . . . . . . . . . . . . . . . 254
21 G-methods for time-varying treatments 257
21.1 The g-formula for time-varying treatments . . . . . . . . . . . . 257
21.2 IP weighting for time-varying treatments . . . . . . . . . . . . . 260
21.3 A doubly robust estimator for time-varying treatments . . . . . 265
21.4 G-estimation for time-varying treatments . . . . . . . . . . . . . 267
21.5 Censoring is a time-varying treatment . . . . . . . . . . . . . . 273
22 Target trial emulation 277
22.1 The target trial (revisited) . . . . . . . . . . . . . . . . . . . . . 277
22.2 Causal effects in randomized trials . . . . . . . . . . . . . . . . 278
22.3 Causal effects in observational analyses that emulate a target trial281
22.4 Time zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
22.5 A unified analysis for causal inference . . . . . . . . . . . . . . . 284
前言：
Causal Inference is an admittedly pretentious title for a book. Causal inference
is a complex scientific task that relies on triangulating evidence from multiple
sources and on the application of a variety of methodological approaches. No
book can possibly provide a comprehensive description of methodologies for
causal inference across the sciences. The authors of any Causal Inference book
will have to choose which aspects of causal inference methodology they want
to emphasize.
The title of this introduction reflects our own choices: a book that helps
scientists–especially health and social scientists–generate and analyze data
to make causal inferences that are explicit about both the causal question and
the assumptions underlying the data analysis. Unfortunately, the scientific
literature is plagued by studies in which the causal question is not explicitly
stated and the investigators’ unverifiable assumptions are not declared. This
casual attitude towards causal inference has led to a great deal of confusion.
For example, it is not uncommon to find studies in which the effect estimates
are hard to interpret because the data analysis methods cannot appropriately
answer the causal question (were it explicitly stated) under the investigators’
assumptions (were they declared).
In this book, we stress the need to take the causal question seriously enough
to articulate it, and to delineate the separate roles of data and assumptions for
causal inference. Once these foundations are in place, causal inferences become
necessarily less casual, which helps prevent confusion. The book describes
various data analysis approaches that can be used to estimate the causal effect
of interest under a particular set of assumptions when data are collected on
each individual in a population. A key message of the book is that causal
inference cannot be reduced to a collection of recipes for data analysis.
The book is divided in three parts of increasing difficulty: Part I is about
causal inference without models (i.e., nonparametric identification of causal effects),
Part II is about causal inference with models (i.e., estimation of causal
effects with parametric models), and Part III is about causal inference from
complex longitudinal data (i.e., estimation of causal effects of time-varying
treatments). Throughout the text, we have interspersed Fine Points and Technical
points that elaborate on certain topics mentioned in the main text. Fine
Points are designed to be accessible to all readers while Technical Points are
designed for readers with intermediate training in statistics. The book provides
a cohesive presentation of concepts of, and methods for, causal inference
that are currently scattered across journals in several disciplines. We expect
that the book will be of interest to anyone interested in causal inference, e.g.,
epidemiologists, statisticians, psychologists, economists, sociologists, political
scientists, computer scientists. . .
Importantly, this is not a philosophy book. We remain agnostic about
metaphysical concepts like causality and cause. Rather, we focus on the identification
and estimation of causal effects in populations, that is, numerical
quantities that measure changes in the distribution of an outcome under different
interventions. For example, we discuss how to estimate the risk of death
in patients with serious heart failure if they received a heart transplant versus
if they did not receive a heart transplant. Our main goal is to help decision
makers make better decisions–actionable causal inference.
We are grateful to many people who have made this book possible. Stephen
Cole, Sander Greenland, Jay Kaufman, Eleanor Murray, Sonja Swanson, Tyler
VanderWeele, and Jan Vandenbroucke provided detailed comments. Goodarz
Danaei, Kosuke Kawai, Martin Lajous, and Kathleen Wirth helped create
the NHEFS dataset. The sample code in Part II was developed by Roger
Logan in SAS, Eleanor Murray and Roger Murray in Stata, and Joy Shi and
Sean McGrath in R. Roger Logan has also been our LaTeX wizard. Randall
Chaput helped create the figures in Chapters 1 and 2. Rob Calver, our patient
publisher, encouraged us to write the book and supported our decision.
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