Mediational E-values

Abstract

Background: Mediation analysis is a powerful tool for understanding mechanisms, but conclusions about direct and indirect effects will be invalid if there is unmeasured confounding of the mediator–outcome relationship. Sensitivity analysis methods allow researchers to assess the extent of this bias but are not always used. One particularly straightforward technique that requires minimal assumptions is nonetheless difficult to interpret, and so would benefit from a more intuitive parameterization. Methods: We conducted an exhaustive numerical search over simulated mediation effects, calculating the proportion of scenarios in which a bound for unmeasured mediator–outcome confounding held under an alternative parameterization. Results: In over 99% of cases, the bound for the bias held when we described the strength of confounding directly via the confounder–mediator relationship instead of via the conditional exposure–confounder relationship. Conclusions: Researchers can conduct sensitivity analysis using a method that describes the strength of the confounder–outcome relationship and the approximate strength of the confounder–mediator relationship that, together, would be required to explain away a direct or indirect effect.

Prenatal and prepubertal exposures to tobacco smoke in men may cause lower lung function in future offspring: a three-generation study using a causal modelling approach

“…Unmeasured genetic confounding unlikely explains away the direct effect of paternal early smoking on offspring's FEV 1 and FVC, as the few risk loci for both nicotine dependence and lung function identified in genetic studies (such as rs16969968 in the cholinergic receptor nicotinic α5 subunit CHRNA5 gene) [ 43 , 44 ] have weaker associations than the computed mediational E-values [ 39 ]. Therefore, we speculate that our findings could reflect epigenetic alterations (such as DNA methylation, histone modification and microRNAs) in developing germ cells [ 45 – 47 ], leading to reduced lung volumes in offspring.…”

“…We speculate that the negative indirect effect of grandmothers’ smoking during pregnancy (through biological mechanisms for which fathers’ lung function in adulthood is an indicator) on grandchildren's FEV 1 /FVC could be explained by epigenetic changes [ 59 , 60 ], resulting in airflow obstruction in offspring [ 60 ], and this effect is unlikely fully explained away by unmeasured risk loci, as suggested by the computed mediational E-value [ 39 ]. Tobacco smoking may cause heritable changes of the germ cell epigenome, particularly in the prenatal period [ 60 , 61 ].…”

“…Sensitivity analyses were performed in order to assess: 1) whether the estimated effects changed after the inclusion of up to two unmeasured confounders (U 1 and U 2 ) in model 1 and model 2, by using probabilistic (Monte Carlo) simulations in the Umediation package [ 38 ] ( https://github.com/SharonLutz/Umediation ; see supplementary material ); 2) which is the minimum strength of association that an unmeasured confounder would need to have with both the mediator and outcome, conditional on the measured confounders, to fully explain away the observed direct or indirect effects (mediational E-values) [ 39 ], by using the Evalue package [ 40 ] ( https://github.com/mayamathur/evalue_package ). The mediational E-values were returned on the risk ratio scale through an approximate conversion [ 41 , 42 ]; 3) whether the estimated effects of fathers’ smoking in prepuberty changed when the analyses were repeated by excluding the 182 offspring whose father had smoked after their birth; and 4) whether the estimated effects changed when using offspring's post-bronchodilator lung function measurements (available from 369 offspring).…”

Cardiovascular risk factor mediation of the effects of education and Genetic Risk Score on cardiovascular disease: a prospective observational cohort study of the Framingham Heart Study

“…Sensitivity analyses evaluating how much unmeasured mediator outcome confounding would explain away the observed NDEs and NIEs were also undertaken. 20 …”

Investigating the Mechanisms of Graded Sensorimotor Precision Training in Adults With Chronic Nonspecific Low Back Pain: Protocol for a Causal Mediation Analysis of the RESOLVE Trial

“…We will conduct a sensitivity analysis to determine the robustness of the estimated NIE and NDE to possible unmeasured confounding in the joint mediated effect model [ 85 ]. The mediational E-value [ 86 ] will be used to assess the minimum strength of the relationship between an unmeasured confounder and the mediator, conditional on measured confounders, that would reduce the NIE and NDE to 0. A comparatively large E-value in relation to known confounders implies that considerable unmeasured confounding would be required to reduce the NIE and NDE to 0.…”