Fig. 1

Causal models of intervention mechanisms, effect decomposition, and sensitivity plots of the SARAH and EXACT trials. The causal models panel shows the hypothesised mechanisms of each intervention. The blue lines represent the effect of the intervention on the outcome through the mediator of interest (indirect effect); the green line represents the effect of the intervention on the outcome that is not exerted through the mediator (direct effect) which includes all other possible mechanisms; and the black lines represent possible confounding effects that were adjusted for in the analysis. Each model assumes that the intervention does not modify the mediator-outcome effect. The effect decomposition panel shows how the average total effect of the intervention on the outcome is decomposed into the indirect effect (blue lines in the causal models), and the direct effect (green lines). These effects are presented as unstandardised effects with their 95% confidence intervals. The sensitivity plots show how much the estimated indirect effect would change if there was residual confounding of the mediator-outcome effect. The sensitivity parameter (horizontal axis) represents hypothesised levels of residual confounding: 0 indicates no residual confounding, and − 1.0 and 1.0 are the maximum levels of residual confounding. The dashed horizontal line represents the estimated indirect effect when there is no residual confounding (sensitivity parameter = 0). The curved solid line represents the estimated indirect effect at varied levels of residual confounding. In the SARAH trial, the indirect effect estimate would become 0 if there was moderate residual confounding (sensitivity parameter = 0.30), whereas in the EXACT trial, the indirect effect is stable across levels of residual confounding. The grey zones represent 95% confidence intervals