Bayesian joint modeling for causal mediation analysis with a binary outcome and a binary mediator: Exploring the role of obesity in the association between cranial radiation therapy for childhood acute lymphoblastic leukemia treatment and the long-term risk of insulin resistance

Abstract

Mediation analysis with a binary outcome is notoriously more challenging than with a continuous outcome. A new Bayesian approach for performing causal mediation with a binary outcome and a binary mediator, named the t-link approach, is introduced. This approach relies on the Bayesian multivariate logistic regression model introduced by O'Brien and Dunson (2004) and its Student-t approximation. By re-expressing the Mediation Formula, it is shown how to use this multivariate latent model for estimating the natural direct and indirect effects of an exposure on an outcome in any measure scale of interest (e.g., odds or risk ratio, risk difference). The t-link mediation approach has several valuable features which, to our knowledge, are not found together in existing binary-binary mediation analysis approaches. In particular, it allows for sensitivity analyses regarding the impact of unmeasured mediator-outcome confounders on the natural effects estimates. The proposed mediation approach was evaluated and compared with two other benchmark approaches using simulated data. Results revealed the usefulness of the t-link mediation approach when the sample size is small or moderate. Lastly, the t-link approach was applied for assessing the impact of cranial radiation therapy given to treat childhood acute lymphoblastic leukemia on the long-term risk of insulin resistance, where this effect is possibly mediated by obesity.