X M Y. What is mediation? Mediation analysis an introduction. Definition

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1 What is mediation? an introduction Ulla Hvidtfeldt Section of Social Medicine - Investigate underlying mechanisms of an association Opening the black box - Strengthen/support the main effect hypothesis - Test pathway specific hypotheses - Evaluate and improve interventions Mediation: how much of the effect of X on Y passes through M? ulah@sund.ku.dk X M Y Slide 1 Slide 2 Definition The totality of processes that explain an observed relationship between exposure and outcome Slide 3 Slide 4

2 Differentiation from confounding Terminology Parity Alcohol Estrogen Breast cancer Parity Alcohol Estrogen Breast cancer Both variables explain the association between alcohol and breast cancer in the statistical model but Estrogen, M, is part of the causal path Parity, C, is an underlying (non-causal) factor Indirect effect: Passes through an intermediate Direct effect: Total effect: through other pathways Direct + indirect effects (adjusted for confounding) Slide 5 Slide 6 Change-in-estimate - example Effect of SES on risk of lung cancer RR (crude) RR (adj. ) Low SES High SES 1 (reference) 1 (reference) % explained by smoking: ( ) (2.3 1) 100 = 85% Chocolate Blood Pressure CVD Slide 7 Slide 8

3 Change-in-estimate Potential problems 1. Regression analysis of Y on X 2. Regression analysis of Y on X, M How much does the estimate change from 1 to 2? Incorrect statistical analysis Linear, Cox og logistic regression Mathematically correct in linear models* Epidemiological challenges Main sources of bias: 1. Mediator-outcome confounding 2. Mediator-outcome confounding affected by the exposure 3. Interaction between exposure and mediator Slide 9 Slide 10 Enhedens navn 1. Mediator-outcome confounding Medicine Chocolate BP CVD 2. Mediator-outcome confounding affected by the exposure (AKA intermediate confounding / exposure-dependent confounding ) Physical activity SEP Obesity Breast cancer Asthma SES Smoking Lung cancer The risk of intermediate confounding is low the closer in time your exposure and mediators are measured If the intermediate confounder is measured you can include it in the model but this will not provide you with an isolated estimate of the mediating effect of your mediator of interest! Slide 11 Sted og dato Slide 12

4 Findings Alkohol Østrogen Brystkræft Slide 13 Slide 14 Findings Livsstil SEP Højt BMI Brystkræft Reproduktion Slide 15 Slide 16

5 UNIVERSITY OF COPENHAGEN DEPARTMENT OF BIOSTATISTICS Faculty of Health Sciences Department of Biostatistics University of Copenhagen 4. marts 2015 Slide 1/11 Analyze weight "Treatment"groups Several other variables used as "confounders", e.g. food consumption.

6 > Mediation - DAG Simplest version of the mediation problem: X / Y M In the application Y is weight (at end of study= X is treatment group M is food consumption (summed up over study period). The causal effect of X on Y is also called the total effect. Can this be decomposed into what we will call the direct effect of X on Y indirect effect of X on Y that is mediated through the mediator M Baron and Kenny Baron and Kenny This is a very active research area and there is a lot about this in the literature. Can easily be complicated, I return briefly to that :-) But in one situation, it is not so hard. Known as the Baron and Kenny approach. We shall assume that Y is quantitative as in the example (weight). We shall also assume that the mediator is quantitative (food intake). And we shall assume that we can apply linear models. We assume the following models Y = X + 2 M + Y (1) M = X + M (2) If we plug (2) into (1), we get Y =[ ]+[ ]X + Y (3) We call the total effect of X on Y We call 1 the direct effect of X on Y We call 2 1 the indirect effect of X on Y mediated via M.

7 `? Data example Data example lm(formula = M ~ X) lm(formula = Y ~ X + M) Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) <2e-16 *** X M <2e-16 *** The estimate of the direct effect is Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) <2e-16 *** X <2e-16 *** Estimate of total effect is Estimate of indirect effect is lm(formula = Y ~ X) Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) <2e-16 *** X <2e-16 *** Mediation The Baron and Kenny approach has a lot shortcomings, see for example Richiardi et al. (IJE, 2013). With binary outcome (disease: yes/no), we need another approach. If there is mediator outcome confounding there is a problem, why?: X / M / Y Good references on more involved analyses are VanderWeele and Vansteelandt (2009) and Lange et al. (2012) If you have data where this could be of interest you may have/wish to consult a statistician/epidemiologist. U