Does the formula add value? Constituent-matched evaluation of composite metabolic indices for incident diabetes: a two-cohort comparative prognostic study

Abstract Background Composite lipid-glycaemic indices compress several routine measurements into a single scalar, yet are usually judged by adding them to reference models that omit the very measurements they contain. Treated as prespecified compression functions rather than new information, their value depends on whether the compression preserves the predictive information being compressed. We tested whether observed incremental prediction of incident diabetes persists when each transformation is compared with direct modelling of its own formula inputs. Methods We analysed two public longitudinal cohorts: NAGALA (Japan; 15464 participants, 373 events; eight transformations) and Rich Healthcare (China; 112483–199050 participants, 1428–2190 events; six transformations). Within each index-specific paired sample, five-fold cross-fitted Cox models compared a common reference model (age, sex, fasting plasma glucose), reference plus composite, and reference plus nonduplicated formula inputs. The primary estimand was the out-of-sample Harrell C difference (ΔC) between composite and constituent-matched models with paired bootstrap 95% confidence intervals. Three-year inverse-probability-of-censoring-weighted time-dependent AUC and prespecified sensitivity analyses assessed robustness. Results Against the conventional reference model, ΔC was positive in all 8 NAGALA comparisons and 5 of 6 Rich comparisons. After constituent matching, 9 of 14 ΔC estimates were numerically within ± 0.002. TG/HDL-C performed worse than its inputs in both cohorts (NAGALA ΔC − 0.0069, 95% CI − 0.0126 to − 0.0010; Rich − 0.0013, − 0.0021 to − 0.0006); VAI was worse in NAGALA (− 0.0208, − 0.0305 to − 0.0123) and METS-IR in Rich (− 0.0048, − 0.0070 to − 0.0026). The only statistically positive constituent-matched estimate was Rich TyG (+ 0.0037, + 0.0021 to + 0.0055), but this became − 0.0009 when all continuous predictors were modelled symmetrically with splines. No transformation showed a consistently positive advantage over its inputs in both cohorts. Conclusions The observed incremental value of metabolic composites depended strongly on the comparator. Gains over a simple reference usually attenuated when the same measurements were modelled directly, and residual advantages were transformation- and cohort-dependent. Because AIP is a monotone transformation of TG/HDL-C, the two carry the same rank information yet performed differently once modelled, indicating that differences between mathematically equivalent indices can reflect imposed functional form rather than biomarker content. Evaluations of incremental value should consider constituent-matched comparison.