{"id":8137,"date":"2026-04-03T11:48:42","date_gmt":"2026-04-03T11:48:42","guid":{"rendered":"https:\/\/www.proefschriftmaken.nl\/portfolio\/judith-rijnhart\/"},"modified":"2026-04-23T09:01:29","modified_gmt":"2026-04-23T09:01:29","slug":"judith-rijnhart","status":"publish","type":"us_portfolio","link":"https:\/\/www.proefschriftmaken.nl\/en\/portfolio\/judith-rijnhart\/","title":{"rendered":"Judith Rijnhart"},"content":{"rendered":"","protected":false},"excerpt":{"rendered":"","protected":false},"author":8,"featured_media":14100,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"us_portfolio_category":[45],"class_list":["post-8137","us_portfolio","type-us_portfolio","status-publish","has-post-thumbnail","hentry","us_portfolio_category-new-template"],"acf":{"naam_van_het_proefschift":"Comparison of methods for statistical mediation analysis within epidemiological research","samenvatting":"Er is geen Nederlandse samenvatting beschikbaar. De Engelse samenvatting vind je <a href=\"https:\/\/www.proefschriftmaken.nl\/en\/portfolio\/judith-rijnhart\/\">hier<\/a>.","summary":"Background\nFor many years, epidemiologists were mainly focused on the estimation of exposure-outcome effects. Nowadays, epidemiologists are also interested in assessing the causal mechanisms underlying exposure-outcome effects. Mediation analysis can be used to gain insight in these causal mechanisms, as it decomposes the total exposure-outcome effect into a direct effect and an indirect effect through a mediator. A mediator is a variable that represents the causal mechanism underlying the exposure-outcome effect. Traditionally, mediation analysis is performed based on a sequence of three linear regression equations. The first equation is used to estimate the total exposure-outcome effect. The second equation is used to estimate the exposure-mediator effect. The third equation is used to estimate the mediator-outcome effect adjusted for the exposure, and the direct exposure-outcome effect adjusted for the mediator. The indirect effect is estimated as either the product of the exposure-mediator effect estimate and the mediator-outcome effect estimate, i.e., the product-of-coefficients estimator, or as the difference between the total effect estimate and the direct effect estimate, i.e., the difference-in-coefficients estimator. These traditional effect estimators are also commonly used to estimate effects for mediation models with a binary mediator or outcome variable, using logistic regression to estimate the regression equations.\n\nIn recent years, causal mediation analysis gained in popularity. Causal mediation analysis is based on the potential outcomes framework and counterfactual framework and defines the direct, indirect, and total effect as the difference between two potential outcomes. A potential outcome is the outcome value that would be observed had a subject been exposed to a certain exposure level. The exposure levels of interest are typically denoted by x* and x. Two potential outcomes can be observed based on these exposure levels, one under exposure level x* and one under exposure level x. The difference between these two potential outcomes is the causal effect. To ensure that the difference between two potential outcomes is only due to the difference in the exposure, the two potential outcomes need to be measured simultaneously. However, in practice we cannot simultaneously observe multiple potential outcomes for one subject. Instead, under certain no unmeasured confounding assumptions, we can estimate potential outcomes and causal effects at the population-average level based on a group of subjects.\n\nThe potential outcomes in mediation analysis are not only dependent on exposure levels, but also on mediator values. The mediator can either be set to a predetermined value, or to a value that would naturally be observed under exposure level x* or x. Six potential outcomes are defined based on all possible combinations of exposure and mediator values. Based on the differences between these potential outcomes, six causal effects are defined: the controlled direct effect (CDE), pure natural direct effect (PNDE), total natural direct effect (TNDE), pure natural indirect effect (PNIE), total natural indirect effect (TNIE), and total effect (TE).\n\nThe CDE is the direct effect of changing the exposure level from x to x*, while holding all subjects\u2019 mediator values constant at a predetermined value. The PNDE is the natural direct effect of changing the exposure level from x to x*, while holding each subject\u2019s mediator value constant at the value that would naturally be observed under exposure level x*. The TNDE is the natural direct effect of changing the exposure level from x to x*, while holding each subject\u2019s mediator value constant at the value that would naturally be observed under exposure level x. The PNIE is the natural indirect effect of changing the exposure level under which each subject\u2019s mediator value is observed from x to x*, while holding the exposure level constant at x*. The TNIE is the natural indirect effect of changing the exposure level under which each subject\u2019s mediator value is observed from x to x*, while holding the exposure level constant at x. The TE is the total effect of changing the exposure level from x to x* on the outcome. These definitions are not based on a specific estimation method. Various nonparametric and parametric methods can be used to estimate the causal effects, including simulations, numerical integration, and multiple regression analysis.\n\nCausal mediation analysis naturally incorporates exposure-mediator interaction, which means that the natural direct effect estimates may differ in magnitude across mediator values, and the natural indirect effect estimates may differ in magnitude across exposure values. In the absence of exposure-mediator interaction, the PNDE and TNDE estimates will be the same, and the PNIE and TNIE estimates will be the same.\n\nThere are some important differences between traditional and causal mediation analysis. Traditional mediation analysis does not incorporate exposure-mediator interaction in its effect definitions while causal mediation analysis does incorporate exposure-mediator interaction in its effect definitions. Another important difference between traditional and causal mediation analysis is that the causal effect definitions are not dependent on a specific estimation method, while the traditional effects are defined and estimated based on (linear) regression coefficients. The causal effect definitions can therefore be applied to any mediation model, and do not necessarily depend on parametric assumptions, such as normality of the residuals and linearity of the effect estimates. Based on these differences between traditional and causal mediation analysis, the question arises when and why the effect estimates from these two methods are the same or different.\n\nAim\nThe aim of this thesis is to assess the similarities and differences in the effect estimates yielded by traditional mediation analysis and causal mediation analysis for mediation models frequently encountered in epidemiological research. Simulation studies and empirical data examples were used to compare the traditional and causal effect estimates for mediation models with 1) a continuous mediator and a continuous outcome, 2) a continuous mediator and a binary outcome, and 3) a binary mediator and a binary outcome.\n\nModels with a continuous mediator and a continuous outcome\n\nChapter two shows that the traditional and causal effect estimates based on linear regression analysis are the same for models without exposure-mediator interaction. In other words, the traditional direct effect estimate is the same as the natural direct effect (NDE) estimate, the traditional indirect effect estimate is the same as the natural indirect effect (NIE) estimate, and the traditional total effect estimate is the same as the TE estimate. These findings also hold when the effect estimates are adjusted for confounding. To allow for exposure-mediator interaction, the third regression equation in traditional mediation analysis can be expanded by adding an exposure-mediator interaction term. In the presence of an exposure-mediator interaction, the PNDE and TNDE can be estimated by multiplying the estimated interaction coefficient with the mean mediator value observed under exposure levels x* and x, respectively, and adding this quantity to the direct exposure-outcome effect estimate. The PNIE and TNIE can be estimated by multiplying the estimated interaction coefficient with the values representing the exposure levels x* and x, respectively, and adding this quantity to the mediator-outcome effect estimate before applying the product-of-coefficients estimator.\n\nModels with a continuous mediator and a binary outcome\n\nChapter three shows that the traditional and causal direct effect estimates based on logistic regression analysis are the same for mediation models without exposure-mediator interaction. However, the traditional product-of-coefficients estimator and difference-in-coefficients estimator yield different indirect effect estimates. Standardization of the underlying regression coefficients minimizes the difference between these two indirect effect estimates, but does not fully dissolve the difference. In this situation, the unstandardized traditional product-of-coefficients estimate is the same as the NIE estimate.\n\nChapter four shows that the difference-in-coefficients estimate of the indirect effect can be decomposed into a non-collapsibility effect estimate and the NIE estimate. The non-collapsibility effect is estimated as the difference between the traditional total effect estimate and TE estimate, and the NIE is estimated as the difference between the TE estimate and the NDE estimate. The magnitude of the non-collapsibility effect was shown to be dependent on the magnitude of the mediator-outcome effect. In line with the strict collapsibility condition, the non-collapsibility effect reduces to zero when the mediator-outcome effect equals zero.\n\nChapter five shows that the traditional and causal estimates of the direct and total effect differ in the presence of an exposure-mediator interaction. In this situation, the traditional direct effect estimates conditional on the average mediator value under exposure levels x* and x are similar to CDE estimates rather than the PNDE and TNDE estimates, respectively. In other words, the traditional direct effects are estimated conditional on mediator values, while the PNDE and TNDE are estimated as the conditional direct effect estimate for each mediator value averaged across all mediator values observed under exposure levels x* and x. The traditional indirect effects estimated conditional on exposure levels x* and x are equal to the PNIE and TNIE estimates, respectively.\n\nModels with a binary mediator and a binary outcome\n\nChapter three shows that the traditional and causal direct effect estimates are the same for mediation models without exposure-mediator interaction. However, when the exposure-mediator effect is estimated based on logistic regression analysis, the two traditional indirect effect estimators yield effect estimates that are different from the NIE estimate. Chapter six shows that the indirect effect estimate based on the traditional product-of-coefficients estimator approximates the NIE estimate when the exposure-mediator effect is estimated using a linear probability model. A linear probability model is a linear regression model estimated with a binary dependent variable. Chapter six also shows that, in the presence of exposure-mediator interaction, the traditional direct effects estimated conditional on the average mediator value under exposure level x* and x are similar to CDE estimates rather than the PNDE and TNDE estimates, respectively. In the presence of exposure-mediator interaction, the traditional indirect effect estimates conditional on exposure levels x* and x approximate the PNIE and TNIE estimates, respectively, when the exposure-mediator effect is estimated using a linear probability model.\n\nConclusion\nCausal mediation analysis is the preferred method for mediation analysis, as this method provides general definitions of causal effects that can be applied to any mediation model. In some situations, traditional mediation analysis can be used to estimate causal effects, for example when the mediator and outcome are both continuous, while in other situations the causal estimators are needed to ensure a causal interpretation of the effect estimates. Epidemiologists use mediation analysis to unravel the causal mechanisms underlying exposure-outcome effects. Causal mediation analysis provides general definitions of the causal effect that constitute these causal mechanisms. These causal effect definitions can be applied to derive the causal effect estimators for any type of mediation model. Therefore, causal mediation analysis should become the default method for mediation analysis in epidemiological research.","auteur":"Judith Rijnhart","auteur_slug":"judith-rijnhart","publicatiedatum":"25 maart 2021","taal":"EN","url_flipbook":"https:\/\/ebook.proefschriftmaken.nl\/ebook\/judithrijnhart?iframe=true","url_download_pdf":"","url_epub":"","ordernummer":"FTP-202604031145","isbn":"978-94-6423-135-9","doi_nummer":"","naam_universiteit":"Vrije Universiteit Amsterdam","afbeeldingen":14100,"naam_student:":"","binnenwerk":"","universiteit":"Vrije Universiteit Amsterdam","cover":"","afwerking":"","cover_afwerking":"","design":""},"_links":{"self":[{"href":"https:\/\/www.proefschriftmaken.nl\/en\/wp-json\/wp\/v2\/us_portfolio\/8137","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.proefschriftmaken.nl\/en\/wp-json\/wp\/v2\/us_portfolio"}],"about":[{"href":"https:\/\/www.proefschriftmaken.nl\/en\/wp-json\/wp\/v2\/types\/us_portfolio"}],"author":[{"embeddable":true,"href":"https:\/\/www.proefschriftmaken.nl\/en\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/www.proefschriftmaken.nl\/en\/wp-json\/wp\/v2\/comments?post=8137"}],"version-history":[{"count":1,"href":"https:\/\/www.proefschriftmaken.nl\/en\/wp-json\/wp\/v2\/us_portfolio\/8137\/revisions"}],"predecessor-version":[{"id":8138,"href":"https:\/\/www.proefschriftmaken.nl\/en\/wp-json\/wp\/v2\/us_portfolio\/8137\/revisions\/8138"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.proefschriftmaken.nl\/en\/wp-json\/wp\/v2\/media\/14100"}],"wp:attachment":[{"href":"https:\/\/www.proefschriftmaken.nl\/en\/wp-json\/wp\/v2\/media?parent=8137"}],"wp:term":[{"taxonomy":"us_portfolio_category","embeddable":true,"href":"https:\/\/www.proefschriftmaken.nl\/en\/wp-json\/wp\/v2\/us_portfolio_category?post=8137"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}