Fig. 1

Rationale and stepwise design of the study. In step 1, a time course analysis to investigate any impact of late-PN versus early-PN on daily plasma concentrations of 3HB. Therefore, all patients with a PICU stay of at least 5 days and plasma samples available from admission until day 5 in the PICU were selected and matched for center, demographics, and type and severity of illness. In the resulting matched cohort of 96 children, daily plasma 3HB, insulin, glucagon, and glucose concentrations were determined and the time point of “maximal 3HB effect” was identified. In step 2, in the total study population, the concentration of plasma 3HB and in step 1 affected ketogenic regulators were determined on the average time point of “maximal 3HB effect” identified in step 1. For patients with a shorter PICU stay, the sample on the last day in PICU was used as surrogate (1142 patients with available plasma, of which 580 randomized to late-PN and 562 randomized to early-PN). In step 3, a multivariable statistical analysis was performed to assess whether any impact of late-PN as compared with early-PN on 3HB could explain its beneficial effects on outcome. “a” represents the effect of the intervention (late-PN versus early-PN) on the outcome of interest (time to live weaning from mechanical ventilatory support, time to live PICU discharge, and acquisition of new infection), “b” represents the effect of the intervention (late-PN versus early-PN) on the hypothesized mediator—plasma 3HB concentration, and “c” represents the association of the potential mediator with the outcome of interest (time to live weaning from mechanical ventilatory support, time to live PICU discharge, and acquisition of new infection)