Table 3.

Examination of Identifiability Assumptions for Causal Mediation Analysis

References	No unmeasured exposure-outcome confounders		No unmeasured mediator-outcome confounders		No unmeasured exposure-mediator confounders		No mediator-outcome confounder affected by the exposure
	Acknowledged assumption	Empirical analyses or sensitivity analyses	Acknowledged assumption	Empirical analyses or sensitivity analyses	Acknowledged assumption	Empirical analyses or sensitivity analyses	Acknowledged assumption	Empirical analyses or sensitivity analyses
Studies estimating controlled direct effects only
Banack et al. [26]	✓	Not reported	✓	Unmeasured confounder cardiorespiratory-fitness Estimates of the direct effect of cardiorespiratory fitness on mortality from well-established literature. No literature on estimates of prevalence differences of unmeasured confounder—so a range of 10–90 % was considered	Not applicable
Mendola et al. [33]	✓	Not reported	✓	Unmeasured confounder maternal infection Estimates of the direct effect of maternal infection on neonatal outcome ranged from 2 to 10. Prevalence differences of unmeasured confounder—so a range of 1–99 % was considered. Whether this was done because no literature was available on which to base the sensitivity analyses was not reported	Not applicable
Messerlian et al. [34]	✓	It is unclear if they were addressing this concern although additional pre-specified stratum- specific with different reference categories and exposure groups were used for sensitivity analyses	✓	Stratified analyses “triangulated” those derived from marginal structural models. It is unclear if they were addressing this concern	Not applicable
Rao et al. [36]	✓	Unmeasured confounder situation that unmeasured confounders could be correlated with exposure, mediator, and outcome were considered. Using parameters, such as γ (conditional increase in risk for oral cancer), P1 (prevalence in smokers/chewers/drinkers), and P2 (prevalence among non-smokers/non-chewers/non-drinkers) were specified. The bias introduced by unmeasured confounders that may entirely invalidate the controlled direct effect was calculated	✓	Unmeasured confounder considered with the exposure-outcome relationship	Not applicable
Studies estimating natural direct and indirect effects
D’Amelio et al. [27]	Randomized controlled trial-not applicable		✓a	Not reported	Randomized controlled trial-not applicable		✓a	No sensitivity analyses, but adjusted for biomarkers that were unbalanced between the two treatment groups at baseline
Freeman et al. [28]	Randomized controlled trial-not applicable		✓	No sensitivity analyses, but adjusted for baseline confounders; can’t rule out	Randomized controlled trial-not applicable		✓	Not reported
Jackson et al. [29]	✓	Showed risk factors by antipsychotic group	✓	No sensitivity analyses, but adjusted for many risk factors; cannot rule out residual confounding	✓	No sensitivity analysis, but residual confounding (i.e. delirium) at baseline that could bias the total and indirect effects upwards was acknowledged	✓	No sensitivity analyses, but conducted stratified analyses by mediators to provide qualitative evidence for whether or not the association between mediator and mortality is modified by antipsychotic type
Louwies et al. [31]	X	No sensitivity analyses, but adjusted for confounders in Table 1, except day of the week	X	Not reported	X	Not reported	X	Not reported
Lu et al. [32]	✓	Excluded first 3 years of follow-up to reduce the influence of baseline confounders Restricted the analysis to never-smokers to better control for confounding by smoking	✓	Unmeasured confounder Common cause of metabolic mediators and coronary heart disease (e.g. family history, genetic factors, residual confounding due to measurement error in diet and physical activity). Sensitivity analyses done with two scenarios: (1) mild confounding (increased hazard ratio by factor of 1.1 and prevalence 20 % for normal weight/25 % for overweight/obese); and (2) strong confounding (increased hazard ratio by factor of 1.8 and prevalence of 45 % for normal weight and 40 % for overweight/obese)	✓	Restricted the analysis to never-smokers to better control for confounding by smoking	✓	Not reported
Raghavan et al. [35]	X	Not reported	X	No sensitivity analyses, but mediation analysis was conducted with all three metabolic mediators (CIR, HOMA-IR and MSS) together	X	No sensitivity analyses, but mediation analysis was conducted with all three metabolic mediators (CIR, HOMA-IR and MSS) together	X	Not reported
Song et al. [37]	✓	No sensitivity analysis, but included all the covariates that may confound the relationship	✓	No sensitivity analysis, but included all the covariates that may confound the relationship	✓	No sensitivity analysis, but included all the covariates that may confound the relationship	✓	Sensitivity analysis was conducted through excluding BMI, a mediator-outcome confounder that is possibly affected by the exposure (low birth weight)
Xie et al. [38]	X	Not reported	X	Not reported	X	Not reported	X	Not reported
Effects not identified
Kositsawat et al. [30]	X	Not reported	X	Not reported	X	Not reported	X	Not reported

CIR beta cell corrected insulin response; HOMA-IR homeostatic model assessment for insulin resistance; MSS metabolic syndrome score

^aIdentifiability assumptions were not specifically mentioned in the article but appeared to have appropriate references