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Appendix 1. Description of the four-way decomposition approach in more detailThe four-way decomposition approach is a regression-based method that deconstructs the excess relative risk for the total effect of smoking on bladder cancer (ERRTE) into four components. The ERRTE is defined on the ratio scale as the relative risk for the total effect of smoking on bladder cancer minus one (ERRTE=RRTE-1), and its components are the excess relative risks for the controlled direct effect (ERRCDE), the reference interaction (ERRINTref), the mediated interaction (ERRINTmed), and the pure indirect effect (ERRPIE). ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"sGDkkmLl","properties":{"formattedCitation":"[1]","plainCitation":"[1]","noteIndex":0},"citationItems":[{"id":118,"uris":[""],"uri":[""],"itemData":{"id":118,"type":"book","title":"Explanation in Causal Inference: Methods for Mediation and Interaction","publisher":"Oxford University Press","publisher-place":"Oxford, New York","number-of-pages":"728","source":"Oxford University Press","event-place":"Oxford, New York","abstract":"The book provides an accessible but comprehensive overview of methods for mediation and interaction. There has been considerable and rapid methodological development on mediation and moderation/interaction analysis within the causal-inference literature over the last ten years. Much of this material appears in a variety of specialized journals, and some of the papers are quite technical. There has also been considerable interest in these developments from empirical researchers in the social and biomedical sciences. However, much of the material is not currently in a format that is accessible to them. The book closes these gaps by providing an accessible, comprehensive, book-length coverage of mediation. The book begins with a comprehensive introduction to mediation analysis, including chapters on concepts for mediation, regression-based methods, sensitivity analysis, time-to-event outcomes, methods for multiple mediators, methods for time-varying mediation and longitudinal data, and relations between mediation and other concepts involving intermediates such as surrogates, principal stratification, instrumental variables, and Mendelian randomization. The second part of the book concerns interaction or \"moderation,\" including concepts for interaction, statistical interaction, confounding and interaction, mechanistic interaction, bias analysis for interaction, interaction in genetic studies, and power and sample-size calculation for interaction. The final part of the book provides comprehensive discussion about the relationships between mediation and interaction and unites these concepts within a single framework. This final part also provides an introduction to spillover effects or social interaction, concluding with a discussion of social-network analyses.The book is written to be accessible to anyone with a basic knowledge of statistics. Comprehensive appendices provide more technical details for the interested reader. Applied empirical examples from a variety of fields are given throughout. Software implementation in SAS, Stata, SPSS, and R is provided. The book should be accessible to students and researchers who have completed a first-year graduate sequence in quantitative methods in one of the social- or biomedical-sciences disciplines. The book will only presuppose familiarity with linear and logistic regression, and could potentially be used as an advanced undergraduate book as well.","ISBN":"978-0-19-932587-0","shortTitle":"Explanation in Causal Inference","author":[{"family":"VanderWeele","given":"Tyler"}],"issued":{"date-parts":[["2015",3,13]]}}}],"schema":""} [1] These causal effects of smoking on bladder cancer risk capture all possible combinations of mediation and interaction, where mediation occurs when the exposure causes the mediator, and interaction occurs when the change in the mediator is necessary for the exposure to have an effect ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"ivKoN0eW","properties":{"formattedCitation":"[1]","plainCitation":"[1]","noteIndex":0},"citationItems":[{"id":118,"uris":[""],"uri":[""],"itemData":{"id":118,"type":"book","title":"Explanation in Causal Inference: Methods for Mediation and Interaction","publisher":"Oxford University Press","publisher-place":"Oxford, New York","number-of-pages":"728","source":"Oxford University Press","event-place":"Oxford, New York","abstract":"The book provides an accessible but comprehensive overview of methods for mediation and interaction. There has been considerable and rapid methodological development on mediation and moderation/interaction analysis within the causal-inference literature over the last ten years. Much of this material appears in a variety of specialized journals, and some of the papers are quite technical. There has also been considerable interest in these developments from empirical researchers in the social and biomedical sciences. However, much of the material is not currently in a format that is accessible to them. The book closes these gaps by providing an accessible, comprehensive, book-length coverage of mediation. The book begins with a comprehensive introduction to mediation analysis, including chapters on concepts for mediation, regression-based methods, sensitivity analysis, time-to-event outcomes, methods for multiple mediators, methods for time-varying mediation and longitudinal data, and relations between mediation and other concepts involving intermediates such as surrogates, principal stratification, instrumental variables, and Mendelian randomization. The second part of the book concerns interaction or \"moderation,\" including concepts for interaction, statistical interaction, confounding and interaction, mechanistic interaction, bias analysis for interaction, interaction in genetic studies, and power and sample-size calculation for interaction. The final part of the book provides comprehensive discussion about the relationships between mediation and interaction and unites these concepts within a single framework. This final part also provides an introduction to spillover effects or social interaction, concluding with a discussion of social-network analyses.The book is written to be accessible to anyone with a basic knowledge of statistics. Comprehensive appendices provide more technical details for the interested reader. Applied empirical examples from a variety of fields are given throughout. Software implementation in SAS, Stata, SPSS, and R is provided. The book should be accessible to students and researchers who have completed a first-year graduate sequence in quantitative methods in one of the social- or biomedical-sciences disciplines. The book will only presuppose familiarity with linear and logistic regression, and could potentially be used as an advanced undergraduate book as well.","ISBN":"978-0-19-932587-0","shortTitle":"Explanation in Causal Inference","author":[{"family":"VanderWeele","given":"Tyler"}],"issued":{"date-parts":[["2015",3,13]]}}}],"schema":""} [1].Component of the ERRMediationInteraction CDENoNo INTrefNoYes INTmedYesYes PIEYesNoFor a continuous mediator and binary outcome, the approach is based on the following logistic and linear regression models, where the linear regression model is fit only among controls to account for the case-control study design: (1) (2)Using the coefficients from the regression models in equations 1 and 2, VanderWeele derived equations 3, 4, 5, and 6 for estimating the relevant causal effects as components of the ERR. (3) (4) (5) (6)These four causal effects are calculated based on specific levels of the mediator and covariates. We set indicator variables for each category of race/ethnicity, education level, WHI study arm, and DNA extraction method equal to the proportions observed among controls. Similarly, we set age (65.46), follow-up time in days (5131.51), and year of enrollment (2.38) to their averages in controls. We restricted to non-smoking controls to calculate average M-values in the absence of smoking-related hypomethylation, and used an m* of 3.98 for cg05575921, 1.55 for cg03636183, and 3.84 for cg19859270. To calculate the proportion of ERR, each component of the ERR is divided by the total ERR (i.e. ERRTE). Confidence intervals and p-values were calculated for the component and proportion estimates based on the delta method. ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"OHDnNHlQ","properties":{"formattedCitation":"[1]","plainCitation":"[1]","noteIndex":0},"citationItems":[{"id":118,"uris":[""],"uri":[""],"itemData":{"id":118,"type":"book","title":"Explanation in Causal Inference: Methods for Mediation and Interaction","publisher":"Oxford University Press","publisher-place":"Oxford, New York","number-of-pages":"728","source":"Oxford University Press","event-place":"Oxford, New York","abstract":"The book provides an accessible but comprehensive overview of methods for mediation and interaction. There has been considerable and rapid methodological development on mediation and moderation/interaction analysis within the causal-inference literature over the last ten years. Much of this material appears in a variety of specialized journals, and some of the papers are quite technical. There has also been considerable interest in these developments from empirical researchers in the social and biomedical sciences. However, much of the material is not currently in a format that is accessible to them. The book closes these gaps by providing an accessible, comprehensive, book-length coverage of mediation. The book begins with a comprehensive introduction to mediation analysis, including chapters on concepts for mediation, regression-based methods, sensitivity analysis, time-to-event outcomes, methods for multiple mediators, methods for time-varying mediation and longitudinal data, and relations between mediation and other concepts involving intermediates such as surrogates, principal stratification, instrumental variables, and Mendelian randomization. The second part of the book concerns interaction or \"moderation,\" including concepts for interaction, statistical interaction, confounding and interaction, mechanistic interaction, bias analysis for interaction, interaction in genetic studies, and power and sample-size calculation for interaction. The final part of the book provides comprehensive discussion about the relationships between mediation and interaction and unites these concepts within a single framework. This final part also provides an introduction to spillover effects or social interaction, concluding with a discussion of social-network analyses.The book is written to be accessible to anyone with a basic knowledge of statistics. Comprehensive appendices provide more technical details for the interested reader. Applied empirical examples from a variety of fields are given throughout. Software implementation in SAS, Stata, SPSS, and R is provided. The book should be accessible to students and researchers who have completed a first-year graduate sequence in quantitative methods in one of the social- or biomedical-sciences disciplines. The book will only presuppose familiarity with linear and logistic regression, and could potentially be used as an advanced undergraduate book as well.","ISBN":"978-0-19-932587-0","shortTitle":"Explanation in Causal Inference","author":[{"family":"VanderWeele","given":"Tyler"}],"issued":{"date-parts":[["2015",3,13]]}}}],"schema":""} [1]Within this framework, the ERRCDE captures the excess relative risk of bladder cancer attributable to the direct effect of smoking if there were no smoking-mediator interaction and the mediator was fixed to m*. The ERRINTref captures the excess relative risk of bladder cancer attributable to the change in the effect of smoking that would be observed only if smoking and the mediator occurred together when the mediator is fixed to m*. The ERRINTmed captures the excess relative risk of bladder cancer attributable both to the change in the effect of smoking that would be observed only if smoking and the mediator occurred together and to the changes in the mediator caused by smoking. The ERRPIE captures the excess relative risk of bladder cancer that would be observed if the changes in the mediator caused by smoking occurred in never smokers.Appendix 1: References ADDIN ZOTERO_BIBL {"uncited":[],"omitted":[],"custom":[]} CSL_BIBLIOGRAPHY [1] VanderWeele T. Explanation in Causal Inference: Methods for Mediation and Interaction. Oxford, New York: Oxford University Press; 2015.Appendix 2: Short list of WHI investigatorsProgram Office: (National Heart, Lung, and Blood Institute, Bethesda, Maryland) Jacques Rossouw, Shari Ludlam, Joan McGowan, Leslie Ford, and Nancy GellerClinical Coordinating Center: (Fred Hutchinson Cancer Research Center, Seattle, WA) Garnet Anderson, Ross Prentice, Andrea LaCroix, and Charles KooperbergInvestigators and Academic Centers: (Brigham and Women's Hospital, Harvard Medical School, Boston, MA) JoAnn E. Manson; (MedStar Health Research Institute/Howard University, Washington, DC) Barbara V. Howard; (Stanford Prevention Research Center, Stanford, CA) Marcia L. Stefanick; (The Ohio State University, Columbus, OH) Rebecca Jackson; (University of Arizona, Tucson/Phoenix, AZ) Cynthia A. Thomson; (University at Buffalo, Buffalo, NY) Jean Wactawski-Wende; (University of Florida, Gainesville/Jacksonville, FL) Marian Limacher; (University of Iowa, Iowa City/Davenport, IA) Jennifer Robinson; (University of Pittsburgh, Pittsburgh, PA) Lewis Kuller; (Wake Forest University School of Medicine, Winston-Salem, NC) Sally Shumaker; (University of Nevada, Reno, NV) Robert BrunnerWomen’s Health Initiative Memory Study: (Wake Forest University School of Medicine, Winston-Salem, NC) Mark Espeland____________________________________________________________________________For a list of all the investigators who have contributed to WHI science, please visit: ................
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