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Do Causal Concentration-Response Functions Exist?

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Quantitative Risk Analysis of Air Pollution Health Effects

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 299))

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Abstract

Concentration-response (C-R) functions relating concentrations of pollutants in ambient air to mortality risks or other adverse health effects provide the basis for many public health risk assessments, benefits estimates for clean air regulations, and recommendations for revisions to existing air quality standards (Schwartz et al. 2002). The assumption that C-R functions relating levels of exposure and levels of response estimated from historical data usefully predict how future changes in concentrations would change risks has seldom been carefully tested. This chapter critically reviews literature on C-R functions for fine particulate matter (PM2.5) and mortality risks, building on the ideas and methods from Chaps. 2, 7 and 8 (especially that regression coefficients do not necessarily have valid causal interpretations) and Chaps. 9, 10, 11, 12, and 13 (especially that Bayesian networks and partial dependence plots can provide useful additional information about dependence relationships that help to identify, constrain, and quantify potential direct and total causal relationships, modelled via invariant causal conditional probability tables). We find that most of the historically influentialpapers in the literature on PM2.5 and mortality risks only describe historical statistical associations rather than valid causal models for predicting effects of interventions that change concentrations. The few papers that explicitly attempt to model causality rely on unverified statistical modeling assumptions, casting doubt on their predictions about effects of interventions. Modern causal inference algorithms for observational data (Chap. 9) have been little used in C-R modeling to date. Applying these methods to publicly available data from Boston and the South Coast Air Quality Management District around Los Angeles shows that C-R functions estimated for one do not hold for the other. Changes in month-specific PM2.5 concentrations from one year to the next do not help to predict corresponding changes in average elderly mortality rates in either location. Thus, the assumption that estimated statistical C-R relations predict effects of pollution-reducing interventions may not be true. Better causal modeling methods are needed to better predict how reducing air pollution would affect public health.

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References

  • Aliferis CE, Statnikov A, Tsamardinos I, Mani S, Koutsoukos XS. Local causal and markov blanket induction for causal discovery and feature selection for classification part I: algorithms and empirical evaluation. J Mach Learn Res. 2010;11:171–234.

    Google Scholar 

  • Angrist JD, Imbens GW, Rubin DB. Identification of causal effects using instrumental variables. J Am Stat Assoc. 1996;91(434):444–55.

    Article  Google Scholar 

  • Apte JS, Marshall JD, Cohen AJ, Brauer M. Addressing global mortality from ambient PM2.5. Environ Sci Technol. 2015;49(13):8057–66.

    Article  Google Scholar 

  • Baiocchi M, Cheng J, Small DS. Instrumental variable methods for causal inference. Stat Med. 2014;33(13):2297–340.

    Article  Google Scholar 

  • Bareinboim E, Pearl J (2013) Meta-transportability of causal effects: a formal approach. In: Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics

    Google Scholar 

  • Blalock HM. Causal inferences in nonexperimental research. Chapel Hill: UNC Press; 1967.

    Google Scholar 

  • Bontempi G, Flauder M. From dependency to causality: a machine learning approach. J Mach Learn Res. 2015;16:2437–57.

    Google Scholar 

  • Breiman L, Friedman J, Olshen R, Stone C. Classification and regression trees. Belmont: Wadsworth; 1984.

    Google Scholar 

  • Campbell DT, Stanley JC. Experimental and quasi-experimental designs for research. Boston: Houghton Mifflin Company; 1963.

    Google Scholar 

  • Chay K, Dobkin C, Greenstone M. The clean air act of 1970 and adult mortality. J Risk Uncertain. 2003;27:279–300.

    Article  Google Scholar 

  • Chen Y, Ebenstein A, Greenstone M, Li H. Evidence on the impact of sustained exposure to air pollution on life expectancy from China’s Huai River policy. Proc Natl Acad Sci U S A. 2013;110(32):12936–41. https://doi.org/10.1073/pnas.1300018110.

    Article  Google Scholar 

  • Chipman H, McCulloch R (2016) Package ‘BayesTree’. https://cran.r-project.org/web/packages/BayesTree/BayesTree.pdf

  • Clancy L, Goodman P, Sinclair H, Dockery DW. Effect of air-pollution control on death rates in Dublin, Ireland: an intervention study. Lancet. 2002;360(9341):1210–4.

    Article  Google Scholar 

  • Cooper GF, Bahar I, Becich MJ, Benos PV, Berg J, Espino JU, Glymour C, Jacobson RC, Kienholz M, Lee AV, Lu X, Scheines R, Center for Causal Discovery Team. The center for causal discovery of biomedical knowledge from big data. J Am Med Inform Assoc. 2015;22(6):1132–6.

    Article  Google Scholar 

  • Cox LA Jr, Popken DA. Has reducing PM2.5 and ozone caused reduced mortality rates in the United States? Ann Epidemiol. 2015;25(3):162–73.

    Article  Google Scholar 

  • Cox LA Jr. A causal model of chronic obstructive pulmonary disease (COPD) risk. Risk Anal. 2011;31(1):38–62.

    Article  Google Scholar 

  • Cox LA Jr. Rethinking the meaning of concentration–response functions and the estimated burden of adverse health effects attributed to exposure concentrations. Risk Anal. 2016;36(9):1770–9.

    Article  Google Scholar 

  • Cromar KR, Gladson LA, Perlmutt LD, Ghazipura M, Ewart GW. American Thoracic Society and Marron Institute Report. Estimated excess morbidity and mortality caused by air pollution above American Thoracic Society-Recommended Standards, 2011-2013. Ann Am Thorac Soc. 2016;13(8):1195–201.

    Article  Google Scholar 

  • Dash D, Voortman M, de Jongh M. Sequences of mechanisms for causal reasoning in artificial intelligence. In: Proceeding IJCAI ‘13 Proceedings of the twenty-third international joint conference on artificial intelligence. New York: AAAI Press; 2013. p. 839–45.

    Google Scholar 

  • Dell LD, Mundt KA, Luippold RS, Nunes AP, Cohen L, Burch MT, Heidenreich MJ, Bachand AM, International Carbon Black Association. A cohort mortality study of employees in the U.S. carbon black industry. J Occup Environ Med. 2006;48(12):1219–29.

    Article  Google Scholar 

  • Di Q, Wang Y, Zanobetti A, Koutrakis P, Dominici F, Schwartz JD. Association of short-term exposure to air pollution with mortality in older adults. J Am Med Assoc. 2017;318(24):2446–56.

    Article  Google Scholar 

  • Dockery D, Pope C, Xu X, et al. An association between air pollution and mortality in six US cities. N Engl J Med. 1993;329:1753–9.

    Article  Google Scholar 

  • Dockery DW, Rich DQ, Goodman PG, Clancy L, Ohman-Strickland P, George P, Kotlov T, HEI Health Review Committee. Effect of air pollution control on mortality and hospital admissions in Ireland. Res Rep Health Eff Inst. 2013;176:3–109.

    Google Scholar 

  • Dominici F, Greenstone M, Sunstein CR. Science and regulation. Particulate matter matters. Science. 2014;344(6181):257–9.

    Article  Google Scholar 

  • Faes L, Porta A, Nollo G. Algorithms for the inference of causality in dynamic processes: application to cardiovascular and cerebrovascular variability. Conf Proc IEEE Eng Med Biol Soc. 2015;2015:1789–92.

    Google Scholar 

  • Fann N, Lamson AD, Anenberg SC, Wesson K, Risley D, Hubbell BJ. Estimating the national public health burden associated with exposure to ambient PM2.5 and ozone. Risk Anal. 2012;32(1):81–95.

    Article  Google Scholar 

  • Fedak KM, Bernal A, Capshaw ZA, Gross S. Applying the Bradford Hill criteria in the 21st century: how data integration has changed causal inference in molecular epidemiology. Emerg Themes Epidemiol. 2015;12:14.

    Article  Google Scholar 

  • Frangakis CE, Rubin DB. Principal stratification in causal inference. Biometrics. 2002;58:21–9.

    Article  Google Scholar 

  • Franklin M, Zeka A, Schwartz J. Association between PM2. 5 and all-cause and specific-cause mortality in 27 US communities. J Expo Sci Environ Epidemiol. 2006;17:279–87.

    Article  Google Scholar 

  • Frey HC. Dose-response models are conditional on determination of causality. Risk Anal. 2016;36(9):1751–4.

    Article  Google Scholar 

  • Frey L, Fisher D, Tsamardinos I, Aliferis CF, Statnikov A, (2003). Identifying Markov blankets with decision tree induction. In: Proceedings of the third IEEE international conference on data mining, Melbourne, FL Nov 19–22 2003. pp 59–66

    Google Scholar 

  • Friston K, Moran R, Seth AK. Analysing connectivity with Granger causality and dynamic causal modelling. Curr Opin Neurobiol. 2013;23(2):172–8.

    Article  Google Scholar 

  • Furqan MS, Siyal MY. Random forest Granger causality for detection of effective brain connectivity using high-dimensional data. J Integr Neurosci. 2016;15(1):55–66.

    Article  Google Scholar 

  • Giannadaki D, Lelieveld J, Pozzer A. Implementing the US air quality standard for PM2.5 worldwide can prevent millions of premature deaths per year. Environ Health. 2016;15(1):88.

    Article  Google Scholar 

  • Glaeser EL(2006) Researcher incentives and empirical methods. NBER Technical Working Paper No. 329 October

    Google Scholar 

  • Goto D, Ueda K, Ng CFS, Takami A, Ariga T, Matsuhashi K, Nakajima T. Estimation of excess mortality due to long-term exposure to PM2.5 in Japan using a high-resolution model for present and future scenarios. Atmos Environ. 2016;140:320–32.

    Article  Google Scholar 

  • Green LC, Crouch EA, Ames MR, Lash TL. What’s wrong with the National Ambient Air Quality Standard (NAAQS) for fine particulate matter (PM(2.5))? Regul Toxicol Pharmacol. 2002;35(3):327–37.

    Article  Google Scholar 

  • Greenland S. Multiple-bias modelling for analysis of observational data. J R Stat Soc A. 2005;168(2):267–306.

    Article  Google Scholar 

  • Greven S, Dominici F, Zeger S. An approach to the estimation of chronic air pollution effects using spatio-temporal information. J Am Stat Assoc. 2011;106:396–406.

    Article  Google Scholar 

  • Halliday DM, Senik MH, Stevenson CW, Mason R. Non-parametric directionality analysis - extension for removal of a single common predictor and application to time series. J Neurosci Methods. 2016;268:87–97.

    Article  Google Scholar 

  • Hart J, Garshick E, Dockery D, Smith T, Ryan L, Laden F. Long-term ambient multi-pollutant exposures and mortality. Am J Respir Crit Care Med. 2011;183:73–8.

    Article  Google Scholar 

  • Hernan M, Vanderweele T. On compound treatments and transportability of causal inference. Epidemiology. 2011;22:368.

    Article  Google Scholar 

  • Hernandez B, Raftery AE, Pennington SR, Parnell AC (2015) Bayesian additive regression trees using Bayesian model averaging. https://arxiv.org/pdf/1507.00181.pdf

  • Hill AB. The environment and disease: association or causation? Proc R Soc Med. 1965;58:295–300.

    Google Scholar 

  • Hill J (2016) Atlantic causal inference conference competition: is your SATT where it’s at? http://jenniferhill7.wixsite.com/acic-2016/competition

  • Höfler M. The Bradford Hill considerations on causality: a counterfactual perspective. Emerg Themes Epidemiol. 2005;2:11.

    Article  Google Scholar 

  • Höfler M, Lieb R, Wittchen HU. Estimating causal effects from observational data with a model for multiple bias. Int J Methods Psychiatr Res. 2007;16(2):77–87.

    Article  Google Scholar 

  • Imai K, Keele L, Tingley D, Yamamoto T. Unpacking the black box of causality: learning about causal mechanisms from experimental and observational studies. Am Polit Sci Rev. 2011;105:4.

    Article  Google Scholar 

  • Keele L, Tingley D, Yamamoto T. Identifying mechanisms behind policy interventions via causal mediation analysis. J Policy Anal Manage. 2015;34(4):937–63.

    Article  Google Scholar 

  • Kenny DA. Correlation and causality. New York: Wiley; 1979.

    Google Scholar 

  • Kim J, Yoon K, Choi JC, Kim H, Song JK. The association between wind-related variables and stroke symptom onset: a case-crossover study on Jeju Island. Environ Res. 2016;150:97–105.

    Article  Google Scholar 

  • Kleinberg S, Hripcsak G. A review of causal inference for biomedical informatics. J Biomed Inform. 2011;44(6):1102–12.

    Article  Google Scholar 

  • Koller D, Friedman N. (2009). Probabilistic Graphical Models: Principles and Techniques. The MIT Press. Cambridge, MA USA.

    Google Scholar 

  • Krstić G. A reanalysis of fine particulate matter air pollution versus life expectancy in the United States. J Air Waste Manag Assoc. 2013;63(2):133–5.

    Article  Google Scholar 

  • Krstić G, Krstić NS, Mauricio Z-B. The br2—weighting Method for Estimating the Effects of Air Pollution on Population Health. J Mod Appl Stat Methods. 2016;15(2):42. https://doi.org/10.22237/jmasm/1478004000.

    Article  Google Scholar 

  • Laden F, Schwartz J, Speizer FE, Dockery DW. Reduction in fine particulate air pollution and mortality: extended follow-up of the Harvard Six Cities study. Am J Respir Crit Care Med. 2006;173:667–72.

    Article  Google Scholar 

  • Lagani V, Triantafillou S, Ball G, Tegnér J, Tsamardinos I. Probabilistic computational causal discovery for systems biology. In: Geris L, Gomez-Cabrero D, editors. Uncertainty in biology: a computational modeling approach, vol. 17. Cham: Springer; 2016.

    Chapter  Google Scholar 

  • Lee S, Honavar V (2013) m-Transportability: transportability of a causal effect from multiple environments. In: Proceedings of the twenty-seventh AAAI conference on artificial intelligence. www.aaai.org/ocs/index.php/AAAI/AAAI13/paper/viewFile/6303/7210

  • Lepeule J, Laden F, Dockery D, Schwartz J. Chronic exposure to fine particles and mortality: an extended follow-up of the Harvard Six Cities study from 1974 to 2009. Environ Health Perspect. 2012;120:965–70.

    Article  Google Scholar 

  • Lewis-Beck MS, Bryman A, Liao TF. Encyclopedia of social science research methods. Thousand Oaks: Sage Publications; 2003.

    Google Scholar 

  • Lin H, Liu T, Fang F, Xiao J, Zeng W, Li X, Guo L, Tian L, Schootman M, Stamatakis KA, Qian Z, Ma W. Mortality benefits of vigorous air quality improvement interventions during the periods of APEC blue and parade blue in Beijing. Environ Pollut. 2016;220:222–7.

    Article  Google Scholar 

  • Lo WC, Shie RH, Chan CC, Lin HH. Burden of disease attributable to ambient fine particulate matter exposure in Taiwan. J Formos Med Assoc. 2016;116(1):32–40.

    Article  Google Scholar 

  • Lopiano KK, Smith RL, Young SS (2015) Air quality and acute deaths in California, 2000–2012. https://arxiv.org/abs/1502.03062

  • Maldonado G. Toward a clearer understanding of causal concepts in epidemiology. Ann Epidemiol. 2013;23(12):743–9.

    Article  Google Scholar 

  • Marra G, Radice R, Missiroli S. Testing the hypothesis of absence of unobserved confounding in semiparametric bivariate probit models. Comput Stat. 2014;29:715.

    Article  Google Scholar 

  • McClellan RO. Providing context for ambient particulate matter and estimates of attributable mortality. Risk Anal. 2016;36(9):1755–65.

    Article  Google Scholar 

  • Mohammad Y, Nishida T. Discovering causal change relationships between processes in complex system. Los Alamitos: Institute of Electrical & Electronics Engineers (IEEE); 2011.

    Book  Google Scholar 

  • Moolgavkar SH. Fine particulate matter pollution and mortality. Risk Anal. 2016;36(9):1766–9.

    Article  Google Scholar 

  • Morabito M, Crisci A, Messeri A, Capecchi V, Modesti PA, Gensini GF, Orlandini S. Environmental temperature and thermal indices: what is the most effective predictor of heat-related mortality in different geographical contexts? Sci World J. 2014;2014:961750.

    Article  Google Scholar 

  • North DW. Introduction to special issue on air pollution health risks. Risk Anal. 2016;36(9):1688–92. https://doi.org/10.1111/risa.12707.

    Article  Google Scholar 

  • North DW. Book reviews mega-review: causality books. Risk Anal. 2019;39(7):1647–54.

    Google Scholar 

  • Obenchain RL, Young SS. Local control strategy: simple analyses of air pollution data can reveal heterogeneity in longevity outcomes. Risk Anal. 2016;37(9):1742–53.

    Article  Google Scholar 

  • O’Malley AJ. Instrumental variable specifications and assumptions for longitudinal analysis of mental health cost offsets. Health Serv Outcome Res Methodol. 2012;12(4):254–72.

    Article  Google Scholar 

  • Pearl J. Comment: graphical models, causality, and intervention. Stat Sci. 1993;8:266–9.

    Article  Google Scholar 

  • Pearl J. Causality: models, reasoning, and inference. 1st ed. New York: Cambridge University Press; 2000.

    Google Scholar 

  • Pearl J. Causal inference in statistics: an overview. Stat Surveys. 2009a;3:96–146. https://doi.org/10.1214/09-SS057.

    Article  Google Scholar 

  • Pearl J. Causality: models, reasoning and inference. 2nd ed. New York: Cambridge University Press; 2009b.

    Book  Google Scholar 

  • Pearl J. An introduction to causal inference. Int J Biostat. 2010;6(2):7.

    Article  Google Scholar 

  • Pearl J. Reply to commentary by Imai, Keele, Tingley, and Yamamoto concerning causal mediation analysis. Psychol Methods. 2014;19(4):488–92.

    Article  Google Scholar 

  • Petersen ML, van der Laan MJ. Causal models and learning from data: integrating causal modeling and statistical estimation. Epidemiology. 2014;25(3):418–26.

    Article  Google Scholar 

  • Pope CA, Burnett RT, Thun MJ, et al. Lung cancer, cardiopulmonary mortality, and long-term exposure to fine particulate air pollution. JAMA. 2002;287:1132–41.

    Article  Google Scholar 

  • Pope CA, Cropper M, Coggins J, Cohen A. Health benefits of air pollution abatement policy: role of the shape of the concentration-response function. J Air Waste Manag Assoc. 2015;65(5):516–22.

    Article  Google Scholar 

  • Robins JM, Blevins D, Ritter G, Wulfsohn M. G-estimation of the effect of prophylaxis therapy for Pneumocystis carinii pneumonia on the survival of AIDS patients. Epidemiology. 1992;3:319–36.

    Article  Google Scholar 

  • Rosenbaum PR, Rubin DB. The central role of the propensity score in observational studies for causal effects. Biometrika. 1983;70(1):41–55. https://doi.org/10.1093/biomet/70.1.41.

    Article  Google Scholar 

  • Rottman BM, Hastie R. Reasoning about causal relationships: inferences on causal networks. Psychol Bull. 2014;140(1):109–39. https://doi.org/10.1037/a0031903.

    Article  Google Scholar 

  • Rubin DB. Estimating causal effects of treatments in randomized and nonrandomized studies. J Educ Psychol. 1974;66(5):688–701. https://doi.org/10.1037/h0037350.

    Article  Google Scholar 

  • Rubin DB. Bayesian inference for causal effects: the role of randomization. Ann Stat. 1978;6:34–58.

    Article  Google Scholar 

  • Rubin DB. Direct and indirect causal effects via potential outcomes (with discussion). Scand J Stat. 2004;31:161–70.

    Article  Google Scholar 

  • Schiatti L, Nollo G, Rossato G, Faes L. Extended Granger causality: a new tool to identify the structure of physiological networks. Physiol Meas. 2015;36(4):827–43.

    Article  Google Scholar 

  • Schreiber T. Measuring information transfer. Phys Rev Lett. 2000;85(2):461–4. https://doi.org/10.1103/PhysRevLett.85.461.

    Article  Google Scholar 

  • Schwartz J. The effects of particulate air pollution on daily deaths: a multicity case crossover analysis. Occup Environ Med. 2004;61:956–61.

    Article  Google Scholar 

  • Schwartz J, Laden F, Zanobetti A. The concentration-response relation between PM(2.5) and daily deaths. Environ Health Perspect. 2002;110(10):1025–9.

    Article  Google Scholar 

  • Schwartz S, Gatto NM, Campbell UB. Transportabilty and causal generalization. Epidemiology. 2011;22(5):745–6.

    Article  Google Scholar 

  • Schwartz J, Austin E, Bind MA, Zanobetti A, Koutrakis P. Estimating causal associations of fine particles with daily deaths in Boston. Am J Epidemiol. 2015;182(7):644–50.

    Article  Google Scholar 

  • Schwartz J, Bind MA, Koutrakis P. Estimating causal effects of local air pollution on daily deaths: effect of low levels. Environ Health Perspect. 2016;125(1):23–9.

    Article  Google Scholar 

  • Shadish W, Cook T, Campbell D. Experimental and quasi-experimental designs for generalized causal inference. Boston: Houghton Mifflin; 2002.

    Google Scholar 

  • Shpitser I, Pearl J. Complete identification methods for the causal hierarchy. J Mach Learn Res. 2008;9:1941–79.

    Google Scholar 

  • Simon HA. Causal ordering and identifiability. In: Hood WC, Koopmans TC, editors. Studies in econometric method. Cowles commission forresearch in economics monograph No. 14. New York: Wiley; 1953. p. 49–74.

    Google Scholar 

  • Simon HA. Spurious correlation: a causal interpretation. J Am Stat Assoc. 1954;49(267):467–79.

    Google Scholar 

  • Slack MK, Draugalis JR. Establishing the internal and external validity of experimental studies. Am J Health Syst Pharm. 2001;58(22):2173–81.

    Article  Google Scholar 

  • Smith AE. Inconsistencies in risk analyses for ambient air pollutant regulations. Risk Anal. 2016;36(9):1737–44.

    Article  Google Scholar 

  • Spirtes P. Introduction to causal inference. J Mach Learn Res. 2010;11:1643–62.

    Google Scholar 

  • Spirtes P, Zhang K. Causal discovery and inference: concepts and recent methodological advances. Appl Inform. 2016;3:3.

    Article  Google Scholar 

  • Spirtes P, Meek C, Richardson T. Causal inference in the presence of latent variables and selection bias. In: UAI’95 proceedings of the eleventh conference on uncertainty in artificial intelligence. San Francisco: Morgan Kaufmann Publishers Inc.; 1995. p. 499–506.

    Google Scholar 

  • Sun J, Taylor D, Boll EM. Causal network inference by optimal causation entropy. SIAM J Appl Dyn Syst. 2015;14(1):73–106.

    Article  Google Scholar 

  • Textor J (2015) Drawing and analyzing causal DAGS with DAGitty. http://www.dagitty.net/manual-2.x.pdf

  • Textor J, Hardt J, Knüppel S. DA Gitty: a graphical tool for analyzing causal diagrams. Epidemiology. 2011;22(5):745. https://doi.org/10.1097/EDE.0b013e318225c2be.

    Article  Google Scholar 

  • United States Environmental Protection Agency (2015) BenMAP environmental benefits mapping and analysis program – community edition. User’s manual appendices. www.epa.gov/sites/production/files/2015-04/documents/benmap-ce_user_manual_appendices_march_2015.pdf

  • Urban A, Kyselý J. Comparison of UTCI with other thermal indices in the assessment of heat and cold effects on cardiovascular mortality in the Czech Republic. Int J Environ Res Public Health. 2014;11(1):952–67.

    Article  Google Scholar 

  • Valberg PA. Possible noncausal bases for correlations between low concentrations of ambient particulate matter and daily mortality. Nonlinearity Biol Toxicol Med. 2003;1(4):521–30. https://doi.org/10.1080/15401420390271137.

    Article  Google Scholar 

  • Vanderweele TJ. Principal stratification--uses and limitations. Int J Biostat. 2011;7(1):28.

    Article  Google Scholar 

  • Wang Y, Kloog I, Coull BA, Kosheleva A, Zanobetti A, Schwartz JD. Estimating causal effects of long-term PM2.5 exposure on mortality in New Jersey. Environ Health Perspect. 2016;124(8):1182–8.

    Article  Google Scholar 

  • Wibral M, Pampu N, Priesemann V, Siebenhühner F, Seiwert H, Lindner M, Lizier JT, Vicente R. Measuring information-transfer delays. PLoS One. 2013;8(2):e55809. https://doi.org/10.1371/journal.pone.0055809.

    Article  Google Scholar 

  • Wiener N. The theory of prediction. In: Beckenbach EF, editor. Modern mathematics for engineers. New York: McGraw-Hill; 1956.

    Google Scholar 

  • Woodward J (2013) Causation and manipulability. In: Edward N. Zalta (ed) The Stanford encyclopedia of philosophy. http://plato.stanford.edu/archives/win2013/entries/causation-mani/

  • Wright S. Correlation and causation. J Agric Res. 1921;20:557–85.

    Google Scholar 

  • Wu MH, Frye RE, Zouridakis G. A comparison of multivariate causality based measures of effective connectivity. Comput Biol Med. 2011;41(12):1132–41.

    Article  Google Scholar 

  • Yang H, Testa JR, Carbone M. Mesothelioma epidemiology, carcinogenesis and pathogenesis. Curr Treat Options in Oncol. 2008;9(2-3):147–57.

    Article  Google Scholar 

  • Young SS, Xia JQ. Assessing geographic heterogeneity and variable importance in an air pollution data set. Sta Anal Data Mining. 2013;6(4):375–86.

    Article  Google Scholar 

  • Yule A, Udny G. Why do we sometimes get nonsense-correlations between time-series? -- A study in sampling and the nature of time-series. J R Stat Soc. 1926;89(1):1–63.

    Article  Google Scholar 

  • Zhang JL, Rubin DB. Estimation of causal effects via principal stratification when some outcomes are truncated by “death”. J Educ Behav Stat. 2003;28:353–68. https://doi.org/10.3102/10769986028004353.

    Article  Google Scholar 

  • Zigler CM, Dominici F, Wang Y. Estimating causal effects of air quality regulations using principal stratification for spatially correlated multivariate intermediate outcomes. Biostatistics. 2012;13(2):289–302.

    Article  Google Scholar 

  • Zigler CM, Kim C, Choirat C, Hansen JB, Wang Y, Hund L, Samet J, King G, Dominici F, HEI Health Review Committee. Causal inference methods for estimating long-term health effects of air quality regulations. Res Rep Health Eff Inst. 2016;187:5–49.

    Google Scholar 

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    Louis Anthony Cox Jr.

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Cox Jr., L.A. (2021). Do Causal Concentration-Response Functions Exist?. In: Quantitative Risk Analysis of Air Pollution Health Effects. International Series in Operations Research & Management Science, vol 299. Springer, Cham. https://doi.org/10.1007/978-3-030-57358-4_15

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