Causality

List of contributors xv An overview of statistical causality xvii Carlo Berzuini, Philip Dawid and Luisa Bernardinelli 1 Statistical causality: Some historical remarks 1 D.R. Cox 1.1 Introduction 1 1.2 Key issues 2 1.3 Rothamsted view 2 1.4 An earlier controversy and its implications 3 1.5 Three versions of causality 4 1.6 Conclusion 4 References 4 2 The language of potential outcomes 6 Arvid Sjölander 2.1 Introduction 6 2.2 Definition of causal effects through potential outcomes 7 2.3 Identification of population causal effects 9 2.4 Discussion 11 References 13 3 Structural equations, graphs and interventions 15 Ilya Shpitser 3.1 Introduction 15 3.2 Structural equations, graphs, and interventions 16 References 23 4 The decision-theoretic approach to causal inference 25 Philip Dawid 4.1 Introduction 25 4.2 Decision theory and causality 26 4.3 No confounding 28 4.4 Confounding 29 4.5 Propensity analysis 33 4.6 Instrumental variable 34 4.7 Effect of treatment of the treated 37 4.8 Connections and contrasts 37 4.9 Postscript 40 Acknowledgements 40 References 40 5 Causal inference as a prediction problem: Assumptions, identification and evidence synthesis 43 Sander Greenland 5.1 Introduction 43 5.2 A brief commentary on developments since 1970 44 5.3 Ambiguities of observational extensions 46 5.4 Causal diagrams and structural equations 47 5.5 Compelling versus plausible assumptions, models and inferences 47 5.6 Nonidentification and the curse of dimensionality 50 5.7 Identification in practice 51 5.8 Identification and bounded rationality 53 5.9 Conclusion 54 Acknowledgments 55 References 55 6 Graph-based criteria of identifiability of causal questions 59 Ilya Shpitser 6.1 Introduction 59 6.2 Interventions from observations 59 6.3 The back-door criterion, conditional ignorability, and covariate adjustment 61 6.4 The front-door criterion 63 6.5 Do-calculus 64 6.6 General identification 65 6.7 Dormant independences and post-truncation constraints 68 References 69 7 Causal inference from observational data: A Bayesian predictive approach 71 Elja Arjas 7.1 Background 71 7.2 A model prototype 72 7.3 Extension to sequential regimes 76 7.4 Providing a causal interpretation: Predictive inference from data 80 7.5 Discussion 82 Acknowledgement 83 References 83 8 Assessing dynamic treatment strategies 85 Carlo Berzuini, Philip Dawid, and Vanessa Didelez 8.1 Introduction 85 8.2 Motivating example 86 8.3 Descriptive versus causal inference 87 8.4 Notation and problem definition 88 8.5 HIV example continued 89 8.6 Latent variables 89 8.7 Conditions for sequential plan identifiability 90 8.8 Graphical representations of dynamic plans 92 8.9 Abdominal aortic aneurysm surveillance 94 8.10 Statistical inference and computation 95 8.11 Transparent actions 97 8.12 Refinements 98 8.13 Discussion 99 Acknowledgements 99 References 99 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 Tyler J. VanderWeele and Miguel A. Hernán 9.1 Introduction 101 9.2 Laws of nature and contrary to fact statements 102 9.3 Association and causation in the social and biomedical sciences 103 9.4 Manipulation and counterfactuals 103 9.5 Natural laws and causal effects 104 9.6 Consequences of randomization 107 9.7 On the causal effects of sex and race 108 9.8 Discussion 111 Acknowledgements 112 References 112 10 Cross-classifications by joint potential outcomes 114 Arvid Sjölander 10.1 Introduction 114 10.2 Bounds for the causal treatment effect in randomized trials with imperfect compliance 115 10.3 Identifying the complier causal effect in randomized trials with imperfect compliance 119 10.4 Defining the appropriate causal effect in studies suffering from truncation by death 121 10.5 Discussion 123 References 124 11 Estimation of direct and indirect effects 126 Stijn Vansteelandt 11.1 Introduction 126 11.2 Identification of the direct and indirect effect 127 11.3 Estimation of controlled direct effects 132 11.4 Estimation of natural direct and indirect effects 146 11.5 Discussion 147 Acknowledgements 147 References 148 12 The mediation formula: A guide to the assessment of causal pathways in nonlinear models 151 Judea Pearl 12.1 Mediation: Direct and indirect effects 151 12.2 The mediation formula: A simple solution to a thorny problem 157 12.3 Relation to other methods 170 12.4 Conclusions 173 Acknowledgments 174 References 175 13 The sufficient cause framework in statistics, philosophy and the biomedical and social sciences 180 Tyler J. VanderWeele 13.1 Introduction 180 13.2 The sufficient cause framework in philosophy 181 13.3 The sufficient cause framework in epidemiology and biomedicine 181 13.4 The sufficient cause framework in statistics 185 13.5 The sufficient cause framework in the social sciences 185 13.6 Other notions of sufficiency and necessity in causal inference 187 13.7 Conclusion 188 Acknowledgements 189 References 189 14 Analysis of interaction for identifying causal mechanisms 192 Carlo Berzuini, Philip Dawid, Hu Zhang and Miles Parkes 14.1 Introduction 192 14.2 What is a mechanism? 193 14.3 Statistical versus mechanistic interaction 193 14.4 Illustrative example 194 14.5 Mechanistic interaction defined 196 14.6 Epistasis 197 14.7 Excess risk and superadditivity 197 14.8 Conditions under which excess risk and superadditivity indicate the presence of mechanistic interaction 200 14.9 Collapsibility 201 14.10 Back to the illustrative study 202 14.11 Alternative approaches 204 14.12 Discussion 204 Ethics statement 205 Financial disclosure 205 References 206 15 Ion channels as a possible mechanism of neurodegeneration in multiple sclerosis 208 Luisa Bernardinelli, Carlo Berzuini, Luisa Foco, and Roberta Pastorino 15.1 Introduction 208 15.2 Background 209 15.3 The scientific hypothesis 209 15.4 Data 210 15.5 A simple preliminary analysis 211 15.6 Testing for qualitative interaction 213 15.7 Discussion 214 Acknowledgments 216 References 216 16 Supplementary variables for causal estimation 218 Roland R. Ramsahai 16.1 Introduction 218 16.2 Multiple expressions for causal effect 220 16.3 Asymptotic variance of causal estimators 222 16.4 Comparison of causal estimators 222 16.5 Discussion 226 Acknowledgements 226 Appendices 227 16.A Estimator given all X's recorded 227 16.B Derivations of asymptotic variances 227 16.C Expressions with correlation coefficients 229 16.D Derivation of I's 230 16.E Relation between rho2 rl|t and rho2 rl|c 231 References 232 17 Time-varying confounding: Some practical considerations in a likelihood framework 234 Rhian Daniel, Bianca De Stavola and Simon Cousens 17.1 Introduction 234 17.2 General setting 235 17.3 Identifying assumptions 238 17.4 G-computation formula 239 17.5 Implementation by Monte Carlo simulation 242 17.6 Analyses of simulated data 243 17.7 Further considerations 249 17.8 Summary 251 References 251 18 'Natural experiments' as a means of testing causal inferences 253 Michael Rutter 18.1 Introduction 253 18.2 Noncausal interpretations of an association 253 18.3 Dealing with confounders 255 18.4 'Natural experiments' 256 18.5 Overall conclusion on 'natural experiments' 266 Acknowledgement 267 References 268 19 Nonreactive and purely reactive doses in observational studies 273 Paul R. Rosenbaum 19.1 Introduction: Background, example 273 19.2 Various concepts of dose 277 19.3 Design sensitivity 284 19.4 Summary 287 References 287 20 Evaluation of potential mediators in randomised trials of complex interventions (psychotherapies) 290 Richard Emsley and Graham Dunn 20.1 Introduction 290 20.2 Potential mediators in psychological treatment trials 291 20.3 Methods for mediation in psychological treatment trials 293 20.4 Causal mediation analysis using instrumental variables estimation 297 20.5 Causal mediation analysis using principal stratification 301 20.6 Our motivating example: The SoCRATES trial 302 20.7 Conclusions 305 Acknowledgements 306 References 307 21 Causal inference in clinical trials 310 Krista Fischer and Ian R. White 21.1 Introduction 310 21.2 Causal effect of treatment in randomized trials 312 21.3 Estimation for a linear structural mean model 316 21.4 Alternative approaches for causal inference in randomized trials comparing experimental treatment with a control 321 21.5 Discussion 324 References 325 22 Causal inference in time series analysis 327 Michael Eichler 22.1 Introduction 327 22.2 Causality for time series 328 22.3 Graphical representations for time series 335 22.4 Representation of systems with latent variables 339 22.5 Identification of causal effects 343 22.6 Learning causal structures 346 22.7 A new parametric model 349 22.8 Concluding remarks 351 References 352 23 Dynamic molecular networks and mechanisms in the biosciences: A statistical framework 355 Clive G. Bowsher 23.1 Introduction 355 23.2 SKMs and biochemical reaction networks 356 23.3 Local independence properties of SKMs 358 23.4 Modularisation of SKMs 362 23.5 Illustrative example - MAPK cell signalling 365 23.6 Conclusion 369 23.7 Appendix: SKM regularity conditions 369 Acknowledgements 370 References 370 Index 371