Fig. 3: Dose–response relationships between clinical frailty, frailty-related metabolic signatures, and all-cause mortality.

Restricted cubic spline (RCS) functions were used to model the dose–response associations of physical frailty (A), its metabolomic signature (B), frailty index (C), and its metabolomic signature (D) with all-cause mortality. Hazard ratios (HRs) and 95% confidence intervals (CIs) were estimated using Cox proportional hazards models adjusted for age, sex, body mass index, Townsend Deprivation Index, ethnicity, educational attainment, physical activity, smoking status, alcohol consumption frequency, and dietary factors including total fruit and vegetable intake, oily and non-oily fish, red meat (beef, lamb, or pork), poultry, and processed meat consumption. Curves represent adjusted HRs shown as solid red lines, with light pink shaded areas indicating the corresponding 95% CIs. Knots were placed at the 10th, 50th, and 90th percentiles of each exposure distribution. Horizontal black dashed lines represent the reference value (HR = 1.0). P-values for overall and non-linear associations were derived from likelihood ratio tests and are shown in each panel. MS metabolic signature, HR hazard ratio, CI confidence interval.