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E-raamat: Causality: Statistical Perspectives and Applications

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"This book looks at a broad collection of contributions from experts in their fields"--

A state of the art volume on statistical causality

Causality: Statistical Perspectives and Applications presents a wide-ranging collection of seminal contributions by renowned experts in the field, providing a thorough treatment of all aspects of statistical causality. It covers the various formalisms in current use, methods for applying them to specific problems, and the special requirements of a range of examples from medicine, biology and economics to political science.

This book:

  • Provides a clear account and comparison of formal languages, concepts and models for statistical causality.
  • Addresses examples from medicine, biology, economics and political science to aid the reader's understanding.
  • Is authored by leading experts in their field.
  • Is written in an accessible style.

Postgraduates, professional statisticians and researchers in academia and industry will benefit from this book.

List of contributors
xv
An overview of statistical causality xvii
Carlo Berzuini
Philip Dawid
Luisa Bernardinelli
1 Statistical causality: Some historical remarks
1(5)
D.R. Cox
1.1 Introduction
1(1)
1.2 Key issues
2(1)
1.3 Rothamsted view
2(1)
1.4 An earlier controversy and its implications
3(1)
1.5 Three versions of causality
4(1)
1.6 Conclusion
4(2)
References
4(2)
2 The language of potential outcomes
6(9)
Arvid Sjolander
2.1 Introduction
6(1)
2.2 Definition of causal effects through potential outcomes
7(2)
2.2.1 Subject-specific causal effects
7(1)
2.2.2 Population causal effects
8(1)
2.2.3 Association versus causation
9(1)
2.3 Identification of population causal effects
9(2)
2.3.1 Randomized experiments
9(2)
2.3.2 Observational studies
11(1)
2.4 Discussion
11(4)
References
13(2)
3 Structural equations, graphs and interventions
15(10)
Ilya Shpitser
3.1 Introduction
15(1)
3.2 Structural equations, graphs, and interventions
16(9)
3.2.1 Graph terminology
16(1)
3.2.2 Markovian models
17(2)
3.2.3 Latent projections and semi-Markovian models
19(1)
3.2.4 Interventions in semi-Markovian models
19(1)
3.2.5 Counterfactual distributions in NPSEMs
20(2)
3.2.6 Causal diagrams and counterfactual independence
22(1)
3.2.7 Relation to potential outcomes
22(1)
References
23(2)
4 The decision-theoretic approach to causal inference
25(18)
Philip Dawid
4.1 Introduction
25(1)
4.2 Decision theory and causality
26(2)
4.2.1 A simple decision problem
26(1)
4.2.2 Causal inference
27(1)
4.3 No confounding
28(1)
4.4 Confounding
29(4)
4.4.1 Unconfounding
29(1)
4.4.2 Nonconfounding
30(1)
4.4.3 Back-door formula
31(2)
4.5 Propensity analysis
33(1)
4.6 Instrumental variable
34(3)
4.6.1 Linear model
36(1)
4.6.2 Binary variables
36(1)
4.7 Effect of treatment of the treated
37(1)
4.8 Connections and contrasts
37(3)
4.8.1 Potential responses
37(2)
4.8.2 Causal graphs
39(1)
4.9 Postscript
40(3)
Acknowledgements
40(1)
References
40(3)
5 Causal inference as a prediction problem: Assumptions, identification and evidence synthesis
43(16)
Sander Greenland
5.1 Introduction
43(1)
5.2 A brief commentary on developments since 1970
44(2)
5.2.1 Potential outcomes and missing data
45(1)
5.2.2 The prognostic view
45(1)
5.3 Ambiguities of observational extensions
46(1)
5.4 Causal diagrams and structural equations
47(1)
5.5 Compelling versus plausible assumptions, models and inferences
47(3)
5.6 Nonidentification and the curse of dimensionality
50(1)
5.7 Identification in practice
51(2)
5.8 Identification and bounded rationality
53(1)
5.9 Conclusion
54(5)
Acknowledgments
55(1)
References
55(4)
6 Graph-based criteria of identifiability of causal questions
59(12)
Ilya Shpitser
6.1 Introduction
59(1)
6.2 Interventions from observations
59(2)
6.3 The back-door criterion, conditional ignorability, and covariate adjustment
61(2)
6.4 The front-door criterion
63(1)
6.5 Do-calculus
64(1)
6.6 General identification
65(3)
6.7 Dormant independences and post-truncation constraints
68(3)
References
69(2)
7 Causal inference from observational data: A Bayesian predictive approach
71(14)
Elja Arjas
7.1 Background
71(1)
7.2 A model prototype
72(4)
7.3 Extension to sequential regimes
76(4)
7.4 Providing a causal interpretation: Predictive inference from data
80(2)
7.5 Discussion
82(3)
Acknowledgement
83(1)
References
83(2)
8 Assessing dynamic treatment strategies
85(16)
Carlo Berzuini
Philip Dawid
Vanessa Didelez
8.1 Introduction
85(1)
8.2 Motivating example
86(1)
8.3 Descriptive versus causal inference
87(1)
8.4 Notation and problem definition
88(1)
8.5 HIV example continued
89(1)
8.6 Latent variables
89(1)
8.7 Conditions for sequential plan identifiability
90(2)
8.7.1 Stability
90(1)
8.7.2 Positivity
91(1)
8.8 Graphical representations of dynamic plans
92(2)
8.9 Abdominal aortic aneurysm surveillance
94(1)
8.10 Statistical inference and computation
95(2)
8.11 Transparent actions
97(1)
8.12 Refinements
98(1)
8.13 Discussion
99(2)
Acknowledgements
99(1)
References
99(2)
9 Causal effects and natural laws: Towards a conceptualization of causal counterfactuals for nonmanipulable exposures, with application to the effects of race and sex
101(13)
Tyler J. VanderWeele
Miguel A. Hernan
9.1 Introduction
101(1)
9.2 Laws of nature and contrary to fact statements
102(1)
9.3 Association and causation in the social and biomedical sciences
103(1)
9.4 Manipulation and counterfactuals
103(1)
9.5 Natural laws and causal effects
104(3)
9.6 Consequences of randomization
107(1)
9.7 On the causal effects of sex and race
108(3)
9.8 Discussion
111(3)
Acknowledgements
112(1)
References
112(2)
10 Cross-classifications by joint potential outcomes
114(12)
Arvid Sjolander
10.1 Introduction
114(1)
10.2 Bounds for the causal treatment effect in randomized trials with imperfect compliance
115(4)
10.3 Identifying the compiler causal effect in randomized trials with imperfect compliance
119(2)
10.4 Defining the appropriate causal effect in studies suffering from truncation by death
121(2)
10.5 Discussion
123(3)
References
124(2)
11 Estimation of direct and indirect effects
126(25)
Stijn Vansteelandt
11.1 Introduction
126(1)
11.2 Identification of the direct and indirect effect
127(5)
11.2.1 Definitions
127(2)
11.2.2 Identification
129(3)
11.3 Estimation of controlled direct effects
132(14)
11.3.1 G-computation
132(1)
11.3.2 Inverse probability of treatment weighting
133(4)
11.3.3 G-estimation for additive and multiplicative models
137(4)
11.3.4 G-estimation for logistic models
141(1)
11.3.5 Case-control studies
142(1)
11.3.6 G-estimation for additive hazard models
143(3)
11.4 Estimation of natural direct and indirect effects
146(1)
11.5 Discussion
147(4)
Acknowledgements
147(1)
References
148(3)
12 The mediation formula: A guide to the assessment of causal pathways in nonlinear models
151(29)
Judea Pearl
12.1 Mediation: Direct and indirect effects
151(6)
12.1.1 Direct versus total effects
151(1)
12.1.2 Controlled direct effects
152(2)
12.1.3 Natural direct effects
154(2)
12.1.4 Indirect effects
156(1)
12.1.5 Effect decomposition
157(1)
12.2 The mediation formula: A simple solution to a thorny problem
157(13)
12.2.1 Mediation in nonparametric models
157(2)
12.2.2 Mediation effects in linear, logistic, and probit models
159(5)
12.2.3 Special cases of mediation models
164(5)
12.2.4 Numerical example
169(1)
12.3 Relation to other methods
170(3)
12.3.1 Methods based on differences and products
170(1)
12.3.2 Relation to the principal-strata direct effect
171(2)
12.4 Conclusions
173(7)
Acknowledgments
174(1)
References
175(5)
13 The sufficient cause framework in statistics, philosophy and the biomedical and social sciences
180(12)
Tyler J. VanderWeele
13.1 Introduction
180(1)
13.2 The sufficient cause framework in philosophy
181(1)
13.3 The sufficient cause framework in epidemiology and biomedicine
181(4)
13.4 The sufficient cause framework in statistics
185(1)
13.5 The sufficient cause framework in the social sciences
185(2)
13.6 Other notions of sufficiency and necessity in causal inference
187(1)
13.7 Conclusion
188(4)
Acknowledgements
189(1)
References
189(3)
14 Analysis of interaction for identifying causal mechanisms
192(16)
Carlo Berzuini
Philip Dawid
Hu Zhang
Miles Parkes
14.1 Introduction
192(1)
14.2 What is a mechanism?
193(1)
14.3 Statistical versus mechanistic interaction
193(1)
14.4 Illustrative example
194(2)
14.5 Mechanistic interaction defined
196(1)
14.6 Epistasis
197(1)
14.7 Excess risk and superadditivity
197(3)
14.8 Conditions under which excess risk and superadditivity indicate the presence of mechanistic interaction
200(1)
14.9 Collapsibility
201(1)
14.10 Back to the illustrative study
202(2)
14.11 Alternative approaches
204(1)
14.12 Discussion
204(4)
Ethics statement
205(1)
Financial disclosure
205(1)
References
206(2)
15 Ion channels as a possible mechanism of neurodegeneration in multiple sclerosis
208(10)
Luisa Bernardinelli
Carlo Berzuini
Luisa Foco
Roberta Pastorino
15.1 Introduction
208(1)
15.2 Background
209(1)
15.3 The scientific hypothesis
209(1)
15.4 Data
210(1)
15.5 A simple preliminary analysis
211(2)
15.6 Testing for qualitative interaction
213(1)
15.7 Discussion
214(4)
Acknowledgments
216(1)
References
216(2)
16 Supplementary variables for causal estimation
218(16)
Roland R. Ramsahai
16.1 Introduction
218(2)
16.2 Multiple expressions for causal effect
220(2)
16.3 Asymptotic variance of causal estimators
222(1)
16.4 Comparison of causal estimators
222(4)
16.4.1 Supplement C with L or not
223(1)
16.4.2 Supplement L with C or not
224(1)
16.4.3 Replace C with L or not
225(1)
16.5 Discussion
226(8)
Acknowledgements
226(1)
Appendices
227(1)
16.A Estimator given all X's recorded
227(1)
16.B Derivations of asymptotic variances
227(2)
16.C Expressions with correlation coefficients
229(1)
16.D Derivation of ΔII's
230(1)
16.E Relation between ρ2rl/t and ρ2rl/c
231(1)
References
232(2)
17 Time-varying confounding: Some practical considerations in a likelihood framework
234(19)
Rhian Daniel
Bianca De Stavola
Simon Cousens
17.1 Introduction
234(1)
17.2 General setting
235(3)
17.2.1 Notation
235(1)
17.2.2 Observed data structure
235(1)
17.2.3 Intervention strategies
236(1)
17.2.4 Potential outcomes
237(1)
17.2.5 Time-to-event outcomes
237(1)
17.2.6 Causal estimands
238(1)
17.3 Identifying assumptions
238(1)
17.4 G-computation formula
239(3)
17.4.1 The formula
239(1)
17.4.2 Plug-in regression estimation
240(2)
17.5 Implementation by Monte Carlo simulation
242(1)
17.5.1 Simulating an end-of-study outcome
242(1)
17.5.2 Simulating a time-to-event outcome
242(1)
17.5.3 Inference
242(1)
17.5.4 Losses to follow-up
243(1)
17.5.5 Software
243(1)
17.6 Analyses of simulated data
243(6)
17.6.1 The data
243(1)
17.6.2 Regimes to be compared
244(1)
17.6.3 Parametric modelling choices
245(1)
17.6.4 Results
246(3)
17.7 Further considerations
249(2)
17.7.1 Parametric model misspecification
249(1)
17.7.2 Competing events
249(1)
17.7.3 Unbalanced measurement times
250(1)
17.8 Summary
251(2)
References
251(2)
18 `Natural experiments' as a means of testing causal inferences
253(20)
Michael Rutter
18.1 Introduction
253(1)
18.2 Noncausal interpretations of an association
253(2)
18.3 Dealing with confounders
255(1)
18.4 `Natural experiments'
256(10)
18.4.1 Genetically sensitive designs
257(2)
18.4.2 Children of twins (CoT) design
259(2)
18.4.3 Strategies to identify the key environmental risk feature
261(2)
18.4.4 Designs for dealing with selection bias
263(1)
18.4.5 Instrumental variables to rule out reverse causation
264(1)
18.4.6 Regression discontinuity (RD) designs to deal with unmeasured confounders
265(1)
18.5 Overall conclusion on `natural experiments'
266(7)
18.5.1 Supported causes
266(1)
18.5.2 Disconfirmed causes
267(1)
Acknowledgement
267(1)
References
268(5)
19 Nonreactive and purely reactive doses in observational studies
273(17)
Paul R. Rosenbaum
19.1 Introduction: Background, example
273(4)
19.1.1 Does a dose-response relationship provide information that distinguishes treatment effects from biases due to unmeasured covariates?
273(1)
19.1.2 Is more chemotherapy for ovarian cancer more effective or more toxic?
274(3)
19.2 Various concepts of dose
277(7)
19.2.1 Some notation: Covariates, outcomes, and treatment assignment in matched pairs
277(1)
19.2.2 Reactive and nonreactive doses of treatment
278(1)
19.2.3 Three test statistics that use doses in different ways
279(1)
19.2.4 Randomization inference in randomized experiments
280(1)
19.2.5 Sensitivity analysis
281(2)
19.2.6 Sensitivity analysis in the example
283(1)
19.3 Design sensitivity
284(3)
19.3.1 What is design sensitivity?
284(2)
19.3.2 Comparison of design sensitivity with purely reactive doses
286(1)
19.4 Summary
287(3)
References
287(3)
20 Evaluation of potential mediators in randomised trials of complex interventions (psychotherapies)
290(20)
Richard Emsley
Graham Dunn
20.1 Introduction
290(1)
20.2 Potential mediators in psychological treatment trials
291(2)
20.3 Methods for mediation in psychological treatment trials
293(4)
20.4 Causal mediation analysis using instrumental variables estimation
297(4)
20.5 Causal mediation analysis using principal stratification
301(1)
20.6 Our motivating example: The SoCRATES trial
302(3)
20.6.1 What are the joint effects of sessions attended and therapeutic alliance on the PANSS score at 18 months?
303(1)
20.6.2 What is the direct effect of random allocation on the PANSS score at 18 months and how is this influenced by the therapeutic alliance?
304(1)
20.6.3 Is the direct effect of the number of sessions attended on the PANSS score at 18 months influenced by therapeutic alliance?
305(1)
20.7 Conclusions
305(5)
Acknowledgements
306(1)
References
307(3)
21 Causal inference in clinical trials
310(17)
Krista Fischer
Ian R. White
21.1 Introduction
310(2)
21.2 Causal effect of treatment in randomized trials
312(4)
21.2.1 Observed data and notation
312(1)
21.2.2 Defining the effects of interest via potential outcomes
312(2)
21.2.3 Adherence-adjusted ITT analysis
314(2)
21.3 Estimation for a linear structural mean model
316(5)
21.3.1 A general estimation procedure
316(1)
21.3.2 Identifiability and closed-form estimation of the parameters in a linear SMM
317(2)
21.3.3 Analysis of the EPHT trial
319(2)
21.4 Alternative approaches for causal inference in randomized trials comparing experimental treatment with a control
321(3)
21.4.1 Principal stratification
321(1)
21.4.2 SMM for the average treatment effect on the treated (ATT)
322(2)
21.5 Discussion
324(3)
References
325(2)
22 Causal inference in time series analysis
327(28)
Michael Eichler
22.1 Introduction
327(1)
22.2 Causality for time series
328(7)
22.2.1 Intervention causality
328(3)
22.2.2 Structural causality
331(1)
22.2.3 Granger causality
332(2)
22.2.4 Sims causality
334(1)
22.3 Graphical representations for time series
335(4)
22.3.1 Conditional distributions and chain graphs
336(1)
22.3.2 Path diagrams and Granger causality graphs
337(1)
22.3.3 Markov properties for Granger causality graphs
338(1)
22.4 Representation of systems with latent variables
339(4)
22.4.1 Marginalization
341(1)
22.4.2 Ancestral graphs
342(1)
22.5 Identification of causal effects
343(3)
22.6 Learning causal structures
346(3)
22.7 A new parametric model
349(2)
22.8 Concluding remarks
351(4)
References
352(3)
23 Dynamic molecular networks and mechanisms in the biosciences: A statistical framework
355(16)
Clive G. Bowsher
23.1 Introduction
355(1)
23.2 SKMs and biochemical reaction networks
356(2)
23.3 Local independence properties of SKMs
358(4)
23.3.1 Local independence and kinetic independence graphs
358(3)
23.3.2 Local independence and causal influence
361(1)
23.4 Modularisation of SKMs
362(3)
23.4.1 Modularisations and dynamic independence
362(1)
23.4.2 MIDIA Algorithm
363(2)
23.5 Illustrative example - MAPK cell signalling
365(4)
23.6 Conclusion
369(1)
23.7 Appendix: SKM regularity conditions
369(2)
Acknowledgements
370(1)
References
370(1)
Index 371
Carlo Berzuini and Philip Dawid, Statistical Labority, centre for Mathematical Sciences, University of Cambridge, UK. Luisa Bernardinelli, MRC Biostatistics Unit, Institute of Public Health, Cambridge, UK.
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