Fig. 1
Estimating treatment benefit for children with sepsis and septic shock treated with extracorporeal life support (ECMO) versus controls. The marginal mean for estimated mortality is shown (y-scale) versus the baseline mortality score (x-scale) for children treated with ECMO (dark blue line) versus controls (light blue line). Full lines indicate the effect estimate, and dashed lines indicate 95% confidence intervals. The benefit threshold, defined as the baseline risk for which ECMO became beneficial, reflects the intersection of both lines at 47.1% predicted risk of mortality. The predicted mortality risk is adjusted for covariates on respiratory failure (PaO2/FiO2 ratio, intubation, treatment with HFOV); cardiovascular (arterial hypotension, shock on presentation, cardiac arrest pre ICU admission), metabolic (high lactate), central nervous system (dilated pupils), and renal (need for renal replacement) dysfunction; and underlying immunosuppression. The naïve baseline risk model is given by F1, where pB is the baseline probability of mortality estimated among non-treated patients, BRS is the Baseline Risk Score, B0 is the intercept, and Bn and X represent a matrix of coefficients and risk factors. F1: Logit(pB) = BRS = B0 + BnX. The treatment model is given by F2, where pD is the estimated mortality rate, BRS is the Baseline Risk Score (from F1), B0 is the intercept, and ECMO is a binary treatment variable (1 = yes). The final term is an interaction term between treatment and the baseline risk score. F2: Logit(pD) = B0 + B1 × BRS + B2 × ECMO + B3 × (ECMO ∗ BRS)