Statistical analysis
To quantitatively investigate direct and indirect effects, we used the concepts of the “natural direct” effect and the “indirect effect” [Some strong assumptions are required to identify natural direct and indirect effects: (i) no unmeasured confounding of the exposure-outcome relationship; (ii) no unmeasured confounding of the outcome-mediator relationship; (iii) no unmeasured confounding of the exposure-mediator relationship; and (iv) no mediator-outcome confounder that is itself affected by the exposure. In randomized studies such as the ESAX-DN study, assumptions (i) and (iii) would hold because of the randomization of the treatment, but (ii) and (iv) would not necessarily hold and cannot be confirmed by the data.To overcome this problem with the assumptions, a methodology with multiple mediators was considered in this analysis. The confounder for the mediator-outcome relationship was considered the mediator, and the joint indirect effect of all mediators was estimated [To estimate the natural direct and indirect effects, we used the regression-based approach for single mediator and multiple mediator settings (details are shown in Supplementary Text In addition to the direct and indirect effects, the proportion of the mediated effect was calculated as (indirect effect/total effect) × 100 (%), which expresses how much of the total effect is mediated through mediators. The CIs for estimates were constructed based on the bootstrap method with 1000 replications.As in the ESAX-DN study, the log-transformed UACR was used in the analyses and back-transformed and expressed in the original scale in the results (i.e., the effect on UACR reduction was expressed as the geometric mean ratio to baseline, compared with placebo). All statistical analyses were performed using SAS System Release 9.4 (SAS Institute Japan Ltd., Tokyo, Japan).