Text and Causal Inference: a Review of Using Text to Remove Confounding from Causal Estimates
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The Practice of Causal Inference in Cancer Epidemiology
Vol. 5. 303-31 1, April 1996 Cancer Epidemiology, Biomarkers & Prevention 303 Review The Practice of Causal Inference in Cancer Epidemiology Douglas L. Weedt and Lester S. Gorelic causes lung cancer (3) and to guide causal inference for occu- Preventive Oncology Branch ID. L. W.l and Comprehensive Minority pational and environmental diseases (4). From 1965 to 1995, Biomedical Program IL. S. 0.1. National Cancer Institute, Bethesda, Maryland many associations have been examined in terms of the central 20892 questions of causal inference. Causal inference is often practiced in review articles and editorials. There, epidemiologists (and others) summarize evi- Abstract dence and consider the issues of causality and public health Causal inference is an important link between the recommendations for specific exposure-cancer associations. practice of cancer epidemiology and effective cancer The purpose of this paper is to take a first step toward system- prevention. Although many papers and epidemiology atically reviewing the practice of causal inference in cancer textbooks have vigorously debated theoretical issues in epidemiology. Techniques used to assess causation and to make causal inference, almost no attention has been paid to the public health recommendations are summarized for two asso- issue of how causal inference is practiced. In this paper, ciations: alcohol and breast cancer, and vasectomy and prostate we review two series of review papers published between cancer. The alcohol and breast cancer association is timely, 1985 and 1994 to find answers to the following questions: controversial, and in the public eye (5). It involves a common which studies and prior review papers were cited, which exposure and a common cancer and has a large body of em- causal criteria were used, and what causal conclusions pirical evidence; over 50 studies and over a dozen reviews have and public health recommendations ensued. -
Statistics and Causal Inference (With Discussion)
Applied Statistics Lecture Notes Kosuke Imai Department of Politics Princeton University February 2, 2008 Making statistical inferences means to learn about what you do not observe, which is called parameters, from what you do observe, which is called data. We learn the basic principles of statistical inference from a perspective of causal inference, which is a popular goal of political science research. Namely, we study statistics by learning how to make causal inferences with statistical methods. 1 Statistical Framework of Causal Inference What do we exactly mean when we say “An event A causes another event B”? Whether explicitly or implicitly, this question is asked and answered all the time in political science research. The most commonly used statistical framework of causality is based on the notion of counterfactuals (see Holland, 1986). That is, we ask the question “What would have happened if an event A were absent (or existent)?” The following example illustrates the fact that some causal questions are more difficult to answer than others. Example 1 (Counterfactual and Causality) Interpret each of the following statements as a causal statement. 1. A politician voted for the education bill because she is a democrat. 2. A politician voted for the education bill because she is liberal. 3. A politician voted for the education bill because she is a woman. In this framework, therefore, the fundamental problem of causal inference is that the coun- terfactual outcomes cannot be observed, and yet any causal inference requires both factual and counterfactual outcomes. This idea is formalized below using the potential outcomes notation. -
Bayesian Causal Inference
Bayesian Causal Inference Maximilian Kurthen Master’s Thesis Max Planck Institute for Astrophysics Within the Elite Master Program Theoretical and Mathematical Physics Ludwig Maximilian University of Munich Technical University of Munich Supervisor: PD Dr. Torsten Enßlin Munich, September 12, 2018 Abstract In this thesis we address the problem of two-variable causal inference. This task refers to inferring an existing causal relation between two random variables (i.e. X → Y or Y → X ) from purely observational data. We begin by outlining a few basic definitions in the context of causal discovery, following the widely used do-Calculus [Pea00]. We continue by briefly reviewing a number of state-of-the-art methods, including very recent ones such as CGNN [Gou+17] and KCDC [MST18]. The main contribution is the introduction of a novel inference model where we assume a Bayesian hierarchical model, pursuing the strategy of Bayesian model selection. In our model the distribution of the cause variable is given by a Poisson lognormal distribution, which allows to explicitly regard discretization effects. We assume Fourier diagonal covariance operators, where the values on the diagonal are given by power spectra. In the most shallow model these power spectra and the noise variance are fixed hyperparameters. In a deeper inference model we replace the noise variance as a given prior by expanding the inference over the noise variance itself, assuming only a smooth spatial structure of the noise variance. Finally, we make a similar expansion for the power spectra, replacing fixed power spectra as hyperparameters by an inference over those, where again smoothness enforcing priors are assumed. -
Causal Effects of Monetary Shocks: Semiparametric
Causal effects of monetary shocks: Semiparametric conditional independence tests with a multinomial propensity score1 Joshua D. Angrist Guido M. Kuersteiner MIT Georgetown University This Revision: April 2010 1This paper is a revised version of NBER working paper 10975, December 2004. We thank the Romers’for sharing their data, Alberto Abadie, Xiaohong Chen, Jordi Gali, Simon Gilchrist, Yanqin Fan, Stefan Hoderlein, Bernard Salanié and James Stock for helpful discussions and seminar and conference participants at ASSA 2006, Auckland, Berkeley, BU, Columbia, Harvard-MIT, Georgetown, Indiana, Illinois, Konstanz, LAMES 2006, the 2004 NSF/NBER Time Series Conference, CIREQ Monteral, Rochester, Rutgers, Stanford, St. Gallen, the Triangle Econometrics Workshop, UCLA, Wisconsin, Zurich and the 2nd conference on evaluation research in Mannheim for helpful comments. Thanks also go to the editor and referees for helpful suggestions and comments. Kuersteiner gratefully acknowledges support from NSF grants SES-0095132 and SES-0523186. Abstract We develop semiparametric tests for conditional independence in time series models of causal effects. Our approach is motivated by empirical studies of monetary policy effects. Our approach is semiparametric in the sense that we model the process determining the distribution of treatment —the policy propensity score — but leave the model for outcomes unspecified. A conceptual innovation is that we adapt the cross-sectional potential outcomes framework to a time series setting. We also develop root-T consistent distribution-free inference methods for full conditional independence testing, appropriate for dependent data and allowing for first-step estimation of the (multinomial) propensity score. Keywords: Potential outcomes, monetary policy, causality, conditional independence, functional martingale difference sequences, Khmaladze transform, empirical Rosenblatt transform 1 Introduction The causal connection between monetary policy and real economic variables is one of the most important and widely studied questions in macroeconomics. -
Articles Causal Inference in Civil Rights Litigation
VOLUME 122 DECEMBER 2008 NUMBER 2 © 2008 by The Harvard Law Review Association ARTICLES CAUSAL INFERENCE IN CIVIL RIGHTS LITIGATION D. James Greiner TABLE OF CONTENTS I. REGRESSION’S DIFFICULTIES AND THE ABSENCE OF A CAUSAL INFERENCE FRAMEWORK ...................................................540 A. What Is Regression? .........................................................................................................540 B. Problems with Regression: Bias, Ill-Posed Questions, and Specification Issues .....543 1. Bias of the Analyst......................................................................................................544 2. Ill-Posed Questions......................................................................................................544 3. Nature of the Model ...................................................................................................545 4. One Regression, or Two?............................................................................................555 C. The Fundamental Problem: Absence of a Causal Framework ....................................556 II. POTENTIAL OUTCOMES: DEFINING CAUSAL EFFECTS AND BEYOND .................557 A. Primitive Concepts: Treatment, Units, and the Fundamental Problem.....................558 B. Additional Units and the Non-Interference Assumption.............................................560 C. Donating Values: Filling in the Missing Counterfactuals ...........................................562 D. Randomization: Balance in Background Variables ......................................................563 -
Causation and Causal Inference in Epidemiology
PUBLIC HEALTH MAnERS Causation and Causal Inference in Epidemiology Kenneth J. Rothman. DrPH. Sander Greenland. MA, MS, DrPH. C Stat fixed. In other words, a cause of a disease Concepts of cause and causal inference are largely self-taught from early learn- ing experiences. A model of causation that describes causes in terms of suffi- event is an event, condition, or characteristic cient causes and their component causes illuminates important principles such that preceded the disease event and without as multicausality, the dependence of the strength of component causes on the which the disease event either would not prevalence of complementary component causes, and interaction between com- have occun-ed at all or would not have oc- ponent causes. curred until some later time. Under this defi- Philosophers agree that causal propositions cannot be proved, and find flaws or nition it may be that no specific event, condi- practical limitations in all philosophies of causal inference. Hence, the role of logic, tion, or characteristic is sufiicient by itself to belief, and observation in evaluating causal propositions is not settled. Causal produce disease. This is not a definition, then, inference in epidemiology is better viewed as an exercise in measurement of an of a complete causal mechanism, but only a effect rather than as a criterion-guided process for deciding whether an effect is pres- component of it. A "sufficient cause," which ent or not. (4m JPub//cHea/f/i. 2005;95:S144-S150. doi:10.2105/AJPH.2004.059204) means a complete causal mechanism, can be defined as a set of minimal conditions and What do we mean by causation? Even among eral. -
Experiments & Observational Studies: Causal Inference in Statistics
Experiments & Observational Studies: Causal Inference in Statistics Paul R. Rosenbaum Department of Statistics University of Pennsylvania Philadelphia, PA 19104-6340 1 My Concept of a ‘Tutorial’ In the computer era, we often receive compressed • files, .zip. Minimize redundancy, minimize storage, at the expense of intelligibility. Sometimes scientific journals seemed to have been • compressed. Tutorial goal is: ‘uncompress’. Make it possible to • read a current article or use current software without going back to dozens of earlier articles. 2 A Causal Question At age 45, Ms. Smith is diagnosed with stage II • breast cancer. Her oncologist discusses with her two possible treat- • ments: (i) lumpectomy alone, or (ii) lumpectomy plus irradiation. They decide on (ii). Ten years later, Ms. Smith is alive and the tumor • has not recurred. Her surgeon, Steve, and her radiologist, Rachael de- • bate. Rachael says: “The irradiation prevented the recur- • rence – without it, the tumor would have recurred.” Steve says: “You can’t know that. It’s a fantasy – • you’re making it up. We’ll never know.” 3 Many Causal Questions Steve and Rachael have this debate all the time. • About Ms. Jones, who had lumpectomy alone. About Ms. Davis, whose tumor recurred after a year. Whenever a patient treated with irradiation remains • disease free, Rachael says: “It was the irradiation.” Steve says: “You can’t know that. It’s a fantasy. We’ll never know.” Rachael says: “Let’s keep score, add ’em up.” Steve • says: “You don’t know what would have happened to Ms. Smith, or Ms. Jones, or Ms Davis – you just made it all up, it’s all fantasy. -
Causation and Experimentation
CHAPTER 6 Causation and Experimentation LEARNING OBJECTIVES 1. List the three criteria for establishing a causal relationship and the two cautions that can improve under- standing of a causal connection. 2. Contrast the strengths and weaknesses of dealing with nonspuriousness through statistical control and through randomization. 3. Explain the meaning of the expression “correlation does not prove causation.” 4. Name two challenges to using experimental designs and two difficulties with identifying idiographic causal explanations. 5. Name and illustrate the three different quasi-experimental designs. 6. Define the individual and group units of analysis and explain the role they play in the ecological and reduc- tionist fallacies. 22 DoWhat Donot We Mean copy, by Causation? post, or distribute At the end of 2013, almost 2.5 million people in the United States were incarcerated in prisons or local jails (Glaze & Kaeble, 2014). The large prison population coupled with lawsuits has prompted most correctional institutions to begin classifying inmates into different security levels (e.g., minimum and maximum) based on objective criteria such as the severity of their offenses, previous records, and so forth. Obviously, the security level of an institution in which an inmate is classified will affect his or her incarceration experience. For example, someone who is assigned to a maxi- mum security prison instead of one with a lower level of security will also have differential access to things such as 119 Copyright ©2018 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. -
Elements of Causal Inference
Elements of Causal Inference Foundations and Learning Algorithms Adaptive Computation and Machine Learning Francis Bach, Editor Christopher Bishop, David Heckerman, Michael Jordan, and Michael Kearns, As- sociate Editors A complete list of books published in The Adaptive Computation and Machine Learning series appears at the back of this book. Elements of Causal Inference Foundations and Learning Algorithms Jonas Peters, Dominik Janzing, and Bernhard Scholkopf¨ The MIT Press Cambridge, Massachusetts London, England c 2017 Massachusetts Institute of Technology This work is licensed to the public under a Creative Commons Attribution- Non- Commercial-NoDerivatives 4.0 license (international): http://creativecommons.org/licenses/by-nc-nd/4.0/ All rights reserved except as licensed pursuant to the Creative Commons license identified above. Any reproduction or other use not licensed as above, by any electronic or mechanical means (including but not limited to photocopying, public distribution, online display, and digital information storage and retrieval) requires permission in writing from the publisher. This book was set in LaTeX by the authors. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Names: Peters, Jonas. j Janzing, Dominik. j Scholkopf,¨ Bernhard. Title: Elements of causal inference : foundations and learning algorithms / Jonas Peters, Dominik Janzing, and Bernhard Scholkopf.¨ Description: Cambridge, MA : MIT Press, 2017. j Series: Adaptive computation and machine learning series -
Causation in Mixed Methods Research
Methodological/Theoretical Discussion Journal of Mixed Methods Research 1–20 Causation in Mixed Methods Ó The Author(s) 2017 Reprints and permissions: Research: The Meeting of sagepub.com/journalsPermissions.nav DOI: 10.1177/1558689817719610 Philosophy, Science, and journals.sagepub.com/home/mmr Practice R. Burke Johnson1, Federica Russo2, and Judith Schoonenboom3 Abstract This article provides a systematic and pluralistic theory of causation that fits the kind of reason- ing commonly found in mixed methods research. It encompasses a variety of causal concepts, notions, approaches, and methods. Each instantiation of the theory is like a mosaic, where the image appears when the tiles are appropriately displayed. This means that researchers should carefully construct a causal mosaic for each research study, articulating what is causally relevant given their particular research questions, purposes, contexts, methods, methodologies, para- digms, and resources. Our theory includes 11 propositions that can guide researchers addres- sing causation. Keywords causal pluralism, mixed methods, theory of causation The purpose of this article is to articulate how mixed methods research (MMR) can address the timeless issue of cause-and-effect or causation. Although the issue of causation has been exten- sively articulated for quantitative research (e.g., Shadish, Cook, & Campbell, 2002) and qualita- tive research (Maxwell, 2004a, 2004b, 2012a), causation has not been systematically articulated yet for MMR, except with regard to the relevance of critical -
A Logic for Causal Inference in Time Series with Discrete and Continuous Variables
A Logic for Causal Inference in Time Series with Discrete and Continuous Variables Samantha Kleinberg Columbia University New York, NY [email protected] Abstract windows of time. Similarly, Granger causality [1969] allows for only discrete lags between cause and effect and assumes Many applications of causal inference, such as find- that the relationships are between individual variables. Fi- ing the relationship between stock prices and news nally, prior work on inferring complex causal relationships reports, involve both discrete and continuous vari- represented as logical formulas identified factors that substan- ables observed over time. Inference with these tially impact the probability of the effect, but required that all complex sets of temporal data, though, has re- variables be discretized [Kleinberg and Mishra, 2009]. mained difficult and required a number of simplifi- In this work we address the problem of inference when we cations. We show that recent approaches for infer- are interested primarily in the level of the effect. We will ring temporal relationships (represented as logical show that instead of a difference in probability, a cause’s sig- formulas) can be adapted for inference with contin- nificance for an effect can be assessed using an average dif- uous valued effects. Building on advances in logic, ference in conditional expectation. By extending the under- PCTLc (an extension of PCTL with numerical con- lying logic used to represent the relationships, this approach straints) is introduced here to allow representation allows for structured representation and automated inference and inference of relationships with a mixture of of complex temporal relationships with discrete and contin- discrete and continuous components. -
Week 10: Causality with Measured Confounding
Week 10: Causality with Measured Confounding Brandon Stewart1 Princeton November 28 and 30, 2016 1These slides are heavily influenced by Matt Blackwell, Jens Hainmueller, Erin Hartman, Kosuke Imai and Gary King. Stewart (Princeton) Week 10: Measured Confounding November 28 and 30, 2016 1 / 176 Where We've Been and Where We're Going... Last Week I regression diagnostics This Week I Monday: F experimental Ideal F identification with measured confounding I Wednesday: F regression estimation Next Week I identification with unmeasured confounding I instrumental variables Long Run I causality with measured confounding ! unmeasured confounding ! repeated data Questions? Stewart (Princeton) Week 10: Measured Confounding November 28 and 30, 2016 2 / 176 1 The Experimental Ideal 2 Assumption of No Unmeasured Confounding 3 Fun With Censorship 4 Regression Estimators 5 Agnostic Regression 6 Regression and Causality 7 Regression Under Heterogeneous Effects 8 Fun with Visualization, Replication and the NYT 9 Appendix Subclassification Identification under Random Assignment Estimation Under Random Assignment Blocking Stewart (Princeton) Week 10: Measured Confounding November 28 and 30, 2016 3 / 176 1 The Experimental Ideal 2 Assumption of No Unmeasured Confounding 3 Fun With Censorship 4 Regression Estimators 5 Agnostic Regression 6 Regression and Causality 7 Regression Under Heterogeneous Effects 8 Fun with Visualization, Replication and the NYT 9 Appendix Subclassification Identification under Random Assignment Estimation Under Random Assignment Blocking Stewart