Mediation analysis for logistic regression with interactions: Application of a surrogate marker in ophthalmology

Abstract

Mediation analysis is often based on fitting two models, one including and another excluding a potential mediator, and subsequently quantify the mediated effects by combining parameter estimates from these two models. Standard errors of such derived parameters may be approximated using the delta method. For a study evaluating a treatment effect on visual acuity, a binary outcome, we demonstrate how mediation analysis may conveniently be carried out by means of marginally fitted logistic regression models in combination with the delta method. Several metrics of mediation are estimated and results are compared to findings using existing methods.

Regulatory problems and developmental psychopathology within the first 2 years of living—a nested in cohort population-based study

“…Mediation analysis for binary outcomes was carried out following the general methodology by MacKinnon et al (40). Specifically, proportions mediated for early maternal mental health problems and relationship problems were estimated by means of the ratio between the direct mediated effect and the total effect using estimates on the log odds scale (41). Accompanying approximate 95% confidence intervals were also estimated using the corresponding standard errors on the log odds scale.…”

“…Due to the small sample size statistical tests were not applied as power was low as is the case for many mediation analyses (42). However, a tentative cutoff for claiming substantial mediation around 30%-40% may be used (41). Statistical analyses were performed with the statistical program SAS, version 9.4 (SAS Institute Inc., Cary, NC, USA).…”