In a cross-sectional . eCollection 2022. The causal inference literature has made a considerable contribution to mediation analysis by providing definitions for direct and indirect effects that allow for the effect decomposition of a total effect into a direct and an indirect effect even in settings involving nonlinearities and interactions (1, 2), thereby circumventing an important limitation to the concepts and methods for mediation that have been used in the social sciences (2). In this paper, we consider the use of the odds ratio scale for mediation analysis. Though, have the same question as Dina- how to read he non significant values? We consider a setting in which the mediator M is continuous and the outcome Y is dichotomous. Finally, this standard approach in the social science literature applies only if there are no interactions between A and M in regression model 5; the approach described in the text, however, can still be employed when such interactions are present. All rights reserved. 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. This website uses cookies to improve your experience while you navigate through the website. trailer VanderWeele TJ. Cerebrovasc Dis. Blog/News Performance of Existing and Novel Symptom- and Antigen TestingBased COVID-19 Case Definitions in a Community Setting, Peripheral Neuropathy and Vision and Hearing Impairment in US Adults With and Without Diabetes, Physical Activity Trends Among Adults in a National mHealth Program: A Population-Based Cohort Study of 411,528 Adults, Estimating the Long-Term Causal Effects of Attending Historically Black Colleges or Universities on Depressive Symptoms, Are We Undercounting the True Burden of Mortality Related to Suicide, Alcohol-Related, or Drug Use? The odds ratio is the ratio of the odds of an event occurring in one group to the odds of it occurring in another group. 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. So the odds ratio for condition 1 is a ratio of the odds of answering correctly in condition 1 compared to the odds of answering correctly in condition 6. How do i do to interprate that condition? Second, the methods described above require a rare outcome; this was necessary in the derivations and also circumvents collapsibility issues with odds ratios (39); some existing work considers or could be adapted for non-rare outcomes (16, 40); future work will consider settings in which the outcome is not rare and compare power, bias, and efficiency properties of the estimators. On the risk difference scale, the conditional natural indirect effect can be defined as, On the risk difference scale, natural direct and indirect effects have the property that the total effect. (36) were generated by using the data-generating models obtained in the previous analysis. We will denote this prevalence by . Example of mediation with exposure A, mediator M, outcome Y, covariates C, and a mediator-outcome confounder L that is itself affected by the exposure. For the standard mediation analysis techniques used in the epidemiologic and social science literatures to be valid, an assumption of no interaction between the effects of the exposure and the mediator on the outcome is needed. (2009) who provides formulas to convert log odds ratio to d and d to r. For the last step (d to r), you are supposed to use a correction factor . 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. Odds ratios for mediation analysis for a dichotomous outcome. where ij is the covariance between and in model 6, and ij is the covariance between and in model 7; these covariances are given in the regression output of standard statistical software. Proportion explained: a causal interpretation for standard measures of indirect effect? government site. 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. At the very least, epidemiologists, before applying the standard approach, should test whether 3 = 0 in the regression model 7 and should consider whether the no-unmeasured-confounding assumptions described above are satisfied. Estimation based on case-control designs with known prevalence probability. Nondifferential misclassification of such a variable can introduce bias in the odds ratios within the strata of the confounding variable. For example, lets say you have an experiment with six conditions and a binary outcome: did the subject answer correctly or not. Dummy coding, interactions, quadratic termsthey all work the same way. Search for other works by this author on: We extend the definitions of direct and indirect effects (, As with the total causal effect, we can also define direct and indirect effects on either the risk difference or the odds ratio scale. For simplicity in the example, we suppose treatment is binary and let A = 1 denote estrogen therapy and A = 0 otherwise. Specifically, I have several Likert itens regarding motivations which are measured in 5 points (strongly disagree to strongly agree). Group: select a variable with codes that identify 2 groups (e.g. When data are used from a case-control study design, the estimators of (1, 2, 3, 4) obtained from logistic regression 7 using case-control data will consistently estimate the same parameters of a logistic regression using cohort data. Kaufman JS, MacLehose RF, Kaufman S. A further critique of the analytic strategy of adjusting for covariates to identify biologic mediation [electronic article]. Expressions 8 and 9 generalize mediation analysis with a dichotomous outcome to settings in which there may be interactions on the odds ratio scale between the exposure and mediator of interest. Several further comments merit attention. We will follow the exposition of VanderWeele (12) and VanderWeele and Vansteelandt (9) on the identification assumptions proposed by Pearl (2). 0000001153 00000 n Privacy Policy According to the logistic model, the log odds function, , is given by The odds ratio is defined as the ratio of the odds for those with the risk factor () to the . Tagged With: dummy coding, logistic regression, odds ratio. Multivariable analysis in cerebrovascular research: practical notes for the clinician. The site is secure. Robins JM, Greenland S. Identifiability and exchangeability for direct and indirect effects. 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. The 2 most common pitfalls with mediation analysis in the epidemiologic literature are 1) ignoring possible mediator-outcome confounding and 2) ignoring possible interactions between the effects of exposure and mediator on the outcome. The first uses 12 as a measure of the mediated effect, and the second uses 1 1 as a measure of the mediated effect. If there is evidence that 3 0, then this standard approach of merely including the mediator in a regression for the outcome Y to obtain direct and indirect effects should not be used. We assume it is known by design so that sampling variability for is neglible. Fallibility in estimating direct effects. 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]. S. V. was supported by Interuniversity Attraction Poles (IAP) research network grant P06/03 from the Belgian government (Belgian Science Policy). Simulation Results for Natural Direct Effects for Bias, Empirical and Estimated Standard Errors, and Coverage Probabilities of 95% Confidence Intervals, With Varying Outcome Prevalence and Exposure-Mediator Interactions. Log in Table 1 shows (on the log odds scale) the bias, empirical standard error (ESE), average of the estimated standard errors (SSEs), and coverage of 95% confidence intervals for the natural indirect effects log odds ratios with a = 1 and a* = 0, as based on 1,000 simulated data sets. The term is also used to refer to sample-based estimates of this ratio. COVID-19 vaccine uptake among people who inject drugs in Tijuana Mexico. Simulation Results for Natural Direct Effects for Bias, Empirical and Estimated Standard Errors, and Coverage Probabilities of 95% Confidence Intervals, With Varying Outcome Prevalence and Exposure-Mediator Interactions. If this assumption holds, then the odds ratio for the total causal effect, ORa,a*|cTE, is identified and can be estimated from the data using. 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. moser004@mc.duke.edu; . Second, the methods described above require a rare outcome; this was necessary in the derivations and also circumvents collapsibility issues with odds ratios (39); some existing work considers or could be adapted for non-rare outcomes (16, 40); future work will consider settings in which the outcome is not rare and compare power, bias, and efficiency properties of the estimators. Oxford University Press is a department of the University of Oxford. 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