Estimating the Bayesian posterior distribution of indirect effects in causal longitudinal mediation analysis

Many research studies aim to unveil the causal mechanism underlying a particular phenomenon; mediation analysis is increasingly used for this scope, and longitudinal data are particularly suited for mediation since they ensure the correct temporal order among variables and the time spanning allows the causal effects to unfold. This explains the rise of interest in the topic of longitudinal mediation analysis. Many approaches have been proposed to cope with longitudinal mediation (Fosen et al., 2005; Lin et al., 2017), among which mixed-effect modelling. In a recent paper, Bind et al. (Biostatistics, 2016) made use of generalised mixed effect models and provided conditions for the identifiability of mediational effects in a causal longitudinal mediation setting. One of the thorniest problems of mediation analysis is the estimation of confidence intervals for the mediated effect, since its distribution has been proved to be generally asymmetric and difficult to derive (Lockwood and Mackinnon, 1998; MacKinnon et al., 2002). Recently, a Bayesian approach has been proposed to overcome this issue, since MCMC algorithms allow to obtain the entire distribution of the effect and hence to estimate a credibility interval. We combine Bind et al. approach with the Bayesian one, by imposing prior distributions on the coefficients of the generalized mixed models for the mediator and the outcome, estimating a posteriori distribution for the mediated effect and obtaining the correspondent credibility interval. A simulation study to compare the performance of the Bayesian method versus the traditional ML and an application to real epidemiological data are provided.