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Causal Diagrams for Interference Elizabeth L STATISTICAL SCIENCE Volume 29, Number 4 November 2014 Special Issue on Semiparametrics and Causal Inference Causal Etiology of the Research of James M. Robins ..............................................Thomas S. Richardson and Andrea Rotnitzky 459 Doubly Robust Policy Evaluation and Optimization ..........................Miroslav Dudík, Dumitru Erhan, John Langford and Lihong Li 485 Statistics,CausalityandBell’sTheorem.....................................Richard D. Gill 512 Standardization and Control for Confounding in Observational Studies: A Historical Perspective..............................................Niels Keiding and David Clayton 529 CausalDiagramsforInterference............Elizabeth L. Ogburn and Tyler J. VanderWeele 559 External Validity: From do-calculus to Transportability Across Populations .........................................................Judea Pearl and Elias Bareinboim 579 Nonparametric Bounds and Sensitivity Analysis of Treatment Effects .................Amy Richardson, Michael G. Hudgens, Peter B. Gilbert and Jason P. Fine 596 The Bayesian Analysis of Complex, High-Dimensional Models: Can It Be CODA? .......................................Y.Ritov,P.J.Bickel,A.C.GamstandB.J.K.Kleijn 619 Q-andA-learning Methods for Estimating Optimal Dynamic Treatment Regimes .............. Phillip J. Schulte, Anastasios A. Tsiatis, Eric B. Laber and Marie Davidian 640 A Uniformly Consistent Estimator of Causal Effects under the k-Triangle-Faithfulness Assumption...................................................Peter Spirtes and Jiji Zhang 662 Higher Order Tangent Spaces and Influence Functions...................Aad van der Vaart 679 Interference and Sensitivity Analysis .............. Tyler J. VanderWeele, Eric J. Tchetgen Tchetgen and M. Elizabeth Halloran 687 Structural Nested Models and G-estimation: The Partially Realized Promise .....................................................Stijn Vansteelandt and Marshall Joffe 707 ContentsofVolume29.......................................................................... 732 Statistical Science [ISSN 0883-4237 (print); ISSN 2168-8745 (online)], Volume 29, Number 4, November 2014. Published quarterly by the Institute of Mathematical Statistics, 3163 Somerset Drive, Cleveland, OH 44122, USA. Periodicals postage paid at Cleveland, Ohio and at additional mailing offices. POSTMASTER: Send address changes to Statistical Science, Institute of Mathematical Statistics, Dues and Subscriptions Office, 9650 Rockville Pike—Suite L2310, Bethesda, MD 20814-3998, USA. Copyright © 2014 by the Institute of Mathematical Statistics Printed in the United States of America EDITOR Peter Green University of Bristol and University of Technology, Sydney ASSOCIATE EDITORS Vincent Carey Samuel Kou Glenn Shafer Harvard University Harvard University Rutgers Business Jiahua Chen David Madigan School–Newark and University of British Columbia Columbia University New Brunswick Rong Chen Kerrie Mengersen Royal Holloway College, Rutgers University Queensland University University of London Dianne Cook of Technology Michael Stein Iowa State University Peter Müller University of Chicago Rainer Dahlhaus TheUniversityofTexas Eric Tchetgen Tchetgen University of Heidelberg Sonia Petrone Harvard School of Public Peter J. Diggle Bocconi University Health Lancaster University Annie Qu Yee Whye Teh Robin Evans University of Illinois, University of Oxford University of Oxford Urbana-Champaign Jon Wakefield Michael Friendly Nancy Reid University of Washington York University University of Toronto Guenther Walther Edward I. George Thomas Richardson Stanford University University of Pennsylvania University of Washington Jon Wellner Peter Green Christian Robert University of Washington University of Bristol University of Paris, Dauphine Martin Wells Peter Hoff Andrea Rotnitzky Cornell University University of Washington Universidad Torcuato Di Tella Tong Zhang Sylvie Huet and Harvard University Rutgers University INRA Thomas Severini Northwestern University MANAGING EDITOR T. N. Sriram University of Georgia PRODUCTION EDITOR Patrick Kelly EDITORIAL COORDINATOR Kristina Mattson PAST EXECUTIVE EDITORS Morris H. DeGroot, 1986–1988 Morris Eaton, 2001 Carl N. Morris, 1989–1991 George Casella, 2002–2004 Robert E. Kass, 1992–1994 Edward I. George, 2005–2007 Paul Switzer, 1995–1997 David Madigan, 2008–2010 Leon J. Gleser, 1998–2000 Jon A. Wellner, 2011–2013 Richard Tweedie, 2001 Statistical Science 2014, Vol. 29, No. 4, 459–484 DOI: 10.1214/14-STS505 © Institute of Mathematical Statistics, 2014 Causal Etiology of the Research of James M. Robins Thomas S. Richardson and Andrea Rotnitzky Abstract. This issue of Statistical Science draws its inspiration from the work of James M. Robins. Jon Wellner, the Editor at the time, asked the two of us to edit a special issue that would highlight the research topics studied by Robins and the breadth and depth of Robins’ contributions. Between the two of us, we have collaborated closely with Jamie for nearly 40 years. We agreed to edit this issue because we recognized that we were among the few in a position to relate the trajectory of his research career to date.1 REFERENCES CATOR, E. A. (2004). On the testability of the car assumption. Ann. Statist. 32 1957–1980. MR2102499 AALEN, O. (1978). Nonparametric inference for a family of count- COLOMBO,D.,MAATHUIS,M.H.,KALISCH,M.andRICHARD- ing processes. Ann. Statist. 6 701–726. MR0491547 SON, T. S. (2012). Learning high-dimensional directed acyclic ANDERSEN,P.K.,BORGAN,Ø.,GILL,R.D.andKEID- graphs with latent and selection variables. Ann. Statist. 40 294– ING, N. (1993). Statistical Models Based on Counting Pro- 321. MR3014308 cesses. Springer, New York. MR1198884 COX, D. R. (1958). Planning of Experiments. Wiley, New York. ARONOW,P.M.,GREEN,D.P.andLEE, D. K. K. (2014). Sharp MR0095561 bounds on the variance in randomized experiments. Ann. Statist. COX, D. R. (1972). Regression models and life-tables. J. R. Stat. 42 850–871. MR3210989 Soc. Ser. BStat. Methodol. 34 187–220. MR0341758 BALKE,A.andPEARL, J. (1994). Probabilistic evaluation of COX,D.R.andWERMUTH, N. (1999). Likelihood factorizations counterfactual queries. In Proceedings of the 12th Conference for mixed discrete and continuous variables. Scand. J. Stat. 26 on Artificial Intelligence 1 230–237. MIT Press, Menlo Park, 209–220. MR1707595 CA. DUDIK,M.,ERHAN,D.,LANGFORD,J.andLI, L. (2014). Dou- BANG,H.andROBINS, J. M. (2005). Doubly robust estimation in bly robust policy evaluation and learning. Statist. Sci. 29 485– missing data and causal inference models. Biometrics 61 962– 511. 972. MR2216189 EFRON,B.andHINKLEY, D. V. (1978). Assessing the accuracy of BAYARRI,M.J.andBERGER, J. O. (2000). p values for compos- the maximum likelihood estimator: Observed versus expected ite null models. J. Amer. Statist. Assoc. 95 1127–1142, 1157– Fisher information. Biometrika 65 457–487. MR0521817 1170. MR1804239 EVANS,R.J.andRICHARDSON, T. S. (2014). Markovian acyclic BELLMAN, R. (1957). Dynamic Programming. Princeton Univ. directed mixed graphs for discrete data. Ann. Statist. 42 1452– Press, Princeton, NJ. MR0090477 1482. MR3262457 BICKEL,P.J.,KLAASSEN,C.A.J.,RITOV,Y.andWELL- FIRTH,D.andBENNETT, K. E. (1998). Robust models in proba- NER, J. A. (1993). Efficient and Adaptive Estimation for Semi- bility sampling. J. R. Stat. Soc. Ser. BStat. Methodol. 60 3–21. parametric Models. Johns Hopkins Univ. Press, Baltimore, MD. MR1625672 MR1245941 FLEMING,T.R.andHARRINGTON, D. P. (1991). Counting Pro- BLALOCK, H. M., ed. (1971). Causal Models in the Social Sci- cesses and Survival Analysis. Wiley, New York. MR1100924 ences. Aldine Publishing, Chicago, IL. FRANGAKIS,C.E.andRUBIN, D. B. (1999). Addressing compli- CAI,T.T.,LEVINE,M.andWANG, L. (2009). Variance function cations of intention-to-treat analysis in the combined presence estimation in multivariate nonparametric regression with fixed of all-or-none treatment-noncompliance and subsequent miss- design. J. Multivariate Anal. 100 126–136. MR2460482 ing outcomes. Biometrika 86 365–379. MR1705410 CASSEL,C.M.,SÄRNDAL,C.E.andWRETMAN, J. H. (1976). FRANGAKIS,C.E.andRUBIN, D. B. (2002). Principal stratifica- Some results on generalized difference estimation and general- tion in causal inference. Biometrics 58 21–29. MR1891039 ized regression estimation for finite populations. Biometrika 63 FREEDMAN, D. A. (2006). Statistical models for causation: What 615–620. MR0445666 inferential leverage do they provide? Eval. Rev. 30 691–713. Thomas S. Richardson is Professor and Chair, Department of Statistics, University of Washington, Box 354322, Seattle, Washington 98195, USA (e-mail: [email protected]). Andrea Rotnitzky is Professor, Department of Economics, Universidad Torcuato Di Tella & CONICET, Av. Figueroa Alcorta 7350, Sáenz Valiente 1010, Buenos Aires, Argentina (e-mail: [email protected]). GILBERT, E. S. (1982). Some confounding factors in the study of NEYMAN, J. (1923). Sur les applications de la théorie des proba- mortality and occupational exposures. American J. Epidemiol- bilités aux experiences agricoles: Essai des principes. Roczniki ogy 116 177–188. Nauk Rolniczych X 1–51. In Polish. English translation by GILBERT,P.B.,BOSCH,R.J.andHUDGENS, M. G. (2003). D. Dabrowska and T. Speed in Statist. Sci. 5 (1990) 463–472. Sensitivity analysis for the assessment of causal vaccine effects OGBURN,E.L.andVANDERWEELE, T. J. (2014). Causal dia- on viral load in HIV vaccine trials. Biometrics 59 531–541. grams for interference. Statist. Sci. 29 559–578. MR2004258 ORELLANA,L.,ROTNITZKY,A.andROBINS,
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