The estimation technique for natural direct and indirect effect odds ratios will require assumptions 14 above and will combine the results of a linear and logistic regression to obtain the effects of interest; the estimation technique for natural direct and indirect effects will also require that the outcome Y is rare so that odds ratios approximate risk ratios, which allows one to obtain particularly simple formulae. The Analysis Factor uses cookies to ensure that we give you the best experience of our website. American Journal of Epidemiology The Author 2010. HWKn8=4/X-OCUtBv:CY{$lfv,o) "h#fOTj{k"z}g4|_. Harvey-Vera A, Munoz S, Artamonova I, Abramovitz D, Mittal ML, Rosales C, Strathdee SA, Rangel MG. Front Public Health. It is important to use the appropriate effect measure based on the study design. Editor's note: Invited commentaries on this article appear on pages 1349 and 1352, and the authors response is published on page 1355. We will let Yam denote the value of the outcome that would have been observed had the exposure, A, and the mediator, M, been set, possibly contrary to fact, to levels a and m, respectively. These identification assumptions were presented to identify direct and indirect effects on the risk difference scale but they apply also to the odds ratio scale. Following this logic, skipping ahead more than one point at a time, you use the following equation: (Odds Ratio^number of intervals difference) = difference in odds. Unable to load your collection due to an error, Unable to load your delegates due to an error. A question of interest may then be the extent to which the effect of estrogen therapy A on cardiovascular disease Y is mediated through serum lipid concentrations M and the extent to which it is through other pathways (3, 4). Defining and estimating intervention effects for groups that will develop an auxiliary outcome. We will let A denote an exposure of interest, Y a dichotomous outcome, and M a potential mediator. On the odds ratio scale, the conditional natural indirect effect can be interpreted as comparing the odds, conditional on C = c, of the outcome Y if exposure had been a but if the mediator had been fixed to Ma (i.e., to what it would have been if exposure had been a) to the odds, conditional on C = c, of the outcome Y if exposure had been a but if the mediator had been fixed to Ma* (i.e., to what it would have been if exposure had been a*). If, however, there is a variable . Because this holds for all a, we must have that 1 (1 + 21) and thus 1 1 21. Standard analyses, ignoring such interactions, gave corresponding natural indirect effect odds ratios of 1.04 (95% CI: 0.99, 1.10), 1.04 (95% CI: 0.99, 1.09), and 1.04 (95% CI: 0.99, 1.19), respectively. Tyler J. VanderWeele, Stijn Vansteelandt, Odds Ratios for Mediation Analysis for a Dichotomous Outcome, American Journal of Epidemiology, Volume 172, Issue 12, 15 December 2010, Pages 13391348, https://doi.org/10.1093/aje/kwq332. However, when fitting the linear regression model 6 for the mediator M using case-control data, the case-control study design cannot be ignored. Barry Kurt Moser, Barry Kurt Moser. If assumptions 1 and 2 hold, then the controlled direct effect on the risk difference scale and on the odds ratio scale is identified, and ORa,a*|cCDE(m) is then given by. endstream endobj 80 0 obj<> endobj 82 0 obj<> endobj 83 0 obj<>/XObject<>/ProcSet[/PDF/Text/ImageB]>> endobj 84 0 obj<> endobj 85 0 obj<> endobj 86 0 obj<>stream 2022 Sep 6;10:931306. doi: 10.3389/fpubh.2022.931306. Accessibility It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. About You need one variable for each category except one. sY4W&JR?\!fl^k(D1l_ u2 On the odds ratio scale, the odds ratio for the total effect decomposes into a product of odds ratios for the natural direct and indirect effect: To identify total effects, it is generally assumed that, conditional on some set of measured covariates, Controlled direct effects on the risk difference or risk ratio scale are identified if conditioning on the set of covariates, Unfortunately, in many studies using mediation analysis, little attention is given to data collection for variables confounding the mediator-outcome relation. Direct effect models. Author affiliations: Departments of Epidemiology and Biostatistics, Harvard School of Public Health, Boston, Massachusetts (Tyler J. VanderWeele); and Department of Applied Mathematics and Computer Sciences, Ghent University, Ghent, Belgium (Stijn Vansteelandt). Efficacy and Safety of Tacrolimus Therapy for a Single Chinese Cohort With Very-Late-Onset Myasthenia Gravis. All dummy coding means is recoding the original categorical variable into a set of binary variables that have values of one and zero. Very informative and rather easy to understand. Occup Environ Med. government site. For example, A may denote estrogen therapy, M serum lipid concentrations, and Y cardiovascular disease. Nutr Metab Insights. An estimator can also be given for the natural direct effect odds ratio (refer to the Web Appendix material) but is more complicated because, when there is interaction between A and M in the logistic model for Y, the natural direct effect will be different for subjects with different covariate values C. Model 7 and expressions 8 and 9 essentially generalize the Baron-Kenny approach to allow for exposure-mediator interactions. Because there are six conditions, youll need 5 dummy variables. The formula for the controlled direct effect odds ratio requires that assumptions 1 and 2 hold and that model 7 is correctly specified; no rare outcome assumption is required. (36) were generated by using the data-generating models obtained in the previous analysis. Alternatively, standard errors for expressions 8 and 9 could be obtained by bootstrapping. As noted above, when there are mediator-outcome confounding variables that are unmeasured or for which control has not been made, estimates of direct and indirect effects will generally be biased. 2022 Sep 27;15:11786388221125107. doi: 10.1177/11786388221125107. If, however, the outcome is not rare or if the error term in regression model 6 is heteroscedastic or not normally distributed, then the 2 quantities 12 and 1 1 need not be approximately equal. Tagged With: dummy coding, logistic regression, odds ratio. Results from simulations of case-control data with prevalence-weighted regressions for the mediator followed a similar pattern as for the estimator of the natural indirect effect: bias if one ignores a substantial exposure-mediator interaction when present and bias when the rare-outcome assumption is violated. If assumption 1 is satisfied but assumption 2 fails (i.e., if there is mediator-outcome confounding), then estimators for the direct and indirect effect will in general be biased (1, 2, 13, 14). Koh YS, Koh GC, Matchar DB, Hong SI, Tai BC. In the cardiovascular example, OR1,0|cCDE(m) would denote the odds ratio for cardiovascular disease comparing therapy and no therapy with serum lipid concentrations fixed at level m. The so-called natural direct effect (2) or pure direct effect (1) differs from the controlled direct effect in that the intermediate M is set to the level Ma*, the level it would have naturally been under some reference condition for the exposure, A =a*; the natural direct effect, conditional on C = c, on the risk difference scale thus takes the form E[YaMa*Ya*Ma*|c]. Concerning the consistency assumption in causal inference. In this section, we describe how the above approach can be adapted when using case-control data. Bethesda, MD 20894, Web Policies The estimation technique for controlled direct effect odds ratios will require only assumptions 1 and 2 and will make use of a single logistic regression. Ninety-five percent confidence intervals for the controlled direct effect odds ratio in expression 8 and the natural indirect effect odds ratio in expression 9 can be computed by using standard regression output and are given, respectively, by. Nondifferential misclassification of such a variable can introduce bias in the odds ratios within the strata of the confounding variable. thank you for those explanations. On the risk difference scale, the total effect, conditional on C = c, comparing exposure level a with a*, is defined by E[YaYa*|c] and compares the average outcome in stratum C = c if A had been set to a with the average outcome in stratum C = c if A had been set to a*. Standard analyses, ignoring such interactions, gave corresponding natural indirect effect odds ratios of 1.04 (95% CI: 0.99, 1.10), 1.04 (95% CI: 0.99, 1.09), and 1.04 (95% CI: 0.99, 1.19), respectively. 8600 Rockville Pike The case-control setting is of particular importance in mediation analysis with a dichotomous outcome because often, if the outcome is rare, it will be infeasible to conduct a cohort study with a sufficient number of individuals with the outcome. If, however, there is a variable L that is an effect of A and affects both M and Y, then assumption 4 is violated and natural direct and indirect effects will not in general be identified (17), irrespective of whether data are available on L. In such settings, it may still be possible to identify controlled direct effect odds ratios, but alternative statistical approaches such as marginal structural models (12, 18, 19) or structural nested models (2024) will generally be needed. Ten Have TR, Joffe MM, Lynch KG, et al. VanderWeele TJ, Vansteelandt S. Conceptual issues concerning mediation, interventions and composition. The odds ratio for condition 2 is the ratio of the odds of answering correctly in condition 2 compared to condition 6. One great thing about logistic regression, at least for those of us who are trying to learn how to use it, is that the predictor variables work exactly the same way as they do in linear regression. Considering that no significant evidence of an interaction between dampness or mold exposure and perception of control was found (P = 0.91, 0.89, and 0.22 for minimal, moderate, and extensive dampness or mold exposure, respectively, relative to no exposure), the fact that these results are very similar is not surprising. 2022 Mar 30;13:843523. doi: 10.3389/fneur.2022.843523. The left-hand side is the odds ratio for the total causal effect, ORa,a*|cTE; the right-hand side is an expression that can be estimated from the data. The term is also used to refer to sample-based estimates of this ratio. As another example of mediation and to illustrate the approach we have described, we reanalyzed a previously reported study (36) with residence in a damp and moldy dwelling as the exposure, depression as the outcome, and perception of control over one's home as the mediator. If you continue we assume that you consent to receive cookies on all websites from The Analysis Factor. For two strata, the effect on the odds ratios is dependent on separate measur Berkeley, CA: Berkeley Electronic Press; 2008, Dampness and mold in the home and depression: an examination of mold-related illness and perceived control of one's home as possible depression pathways, Modelling treatment-effect heterogeneity in randomized controlled trials of complex interventions (psychological treatments), Confounding and collapsibility in causal inference, Statistical assessment of mediational effects for logistic mediational models, Intermediacy and gene-environment interaction: the example of CHRNA5-A3 region, smoking, nicotine dependence, and lung cancer, On the adjustment for covariates in genetic association analysis: a novel, simple principle to infer direct causal effects. Huang B, Sivaganesan S, Succop P, et al. The objective of this paper is to develop a new estimator of the same odds ratio parameters through regression analysis on the original continuous outcome without the inherent loss of information caused by dichotomizing. Proportion explained: a causal interpretation for standard measures of indirect effect? An Analysis Using Veteran Colorado Death Certificate Data, About the Johns Hopkins Bloomberg School of Public Health, REGRESSION ANALYSIS FOR DIRECT AND INDIRECT EFFECT ODDS RATIOS, ODDS RATIOS FOR MEDIATION ANALYSIS IN CASE-CONTROL STUDIES, Receive exclusive offers and updates from Oxford Academic, Assistant or Associate Professors in Orthodontics, Open Rank Informatics Research Faculty Position, Postdoctoral Fellowship Infections and Immunoepidemiology Branch, Assistant Professor in the Department of Psychiatry and Human Behavior, Copyright 2022 Johns Hopkins Bloomberg School of Public Health. When the mediator M is dichotomous, rather than continuous, a somewhat similar approach to the one described here could potentially be used, but the analytic formulas for mediated effects no longer take quite as simple a form. The use of this scale has the advantage that, when the outcome is rare and the mediator continuous, direct and indirect effects can be estimated through very simple regressions, even with data arising from a case-control study design. Odds Ratio = 1: The ratio equals one when the numerator and denominator are equal. The https:// ensures that you are connecting to the The standard approach of omitting the 3am product term in assessing mediation is highly problematic when correct specification of a logistic regression model for Y requires the product term. A question of interest may then be the extent to which the effect of estrogen therapy A on cardiovascular disease Y is mediated through serum lipid concentrations M and the extent to which it is through other pathways (3, 4). COVID-19 vaccine uptake among people who inject drugs in Tijuana Mexico. When the mediator M is dichotomous, rather than continuous, a somewhat similar approach to the one described here could potentially be used, but the analytic formulas for mediated effects no longer take quite as simple a form. First, we have seen that, although mediation analysis is more difficult when there is interaction between the exposure and the mediator (1, 33, 37), this interaction can in fact be accommodated. Of a dichotomous outcome and a control group, or any other dichotomous classification holds when case-control. And the output from the us National Institutes of Health website of the odds ratio scale, first! 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