Age-range–matched external validation of standard liver volume equations: Methodological re-evaluation of 13 regression models

Abstract

Background and aim Accurate estimation of standard liver volume (SLV) is essential in hepatobiliary surgery, particularly in living donor liver transplantation and hepatic resection. Numerous and substantially divergent SLV equations have been proposed, yet it remains unclear which are methodologically valid. Although several comparative and validation studies have been reported, these have typically evaluated equations beyond their original derivation ranges, thereby conflating external validity with extrapolation and ignoring physiologically distinct processes across the lifespan. As a result, a proper external validation of existing SLV equations has not been systematically performed. Methods Thirteen previously proposed SLV formulae were selected for methodologically constrained external validation in individuals without known liver disease (n = 1152). Each equation was evaluated strictly within its original derivation age range using age-range–matched cohorts. Agreement between estimated SLV and computed tomography–measured total liver volume (TLV) was assessed using Bland–Altman analysis and intraclass correlation coefficients (ICC). Model performance was further examined in older adults and across subgroups defined by sex, obesity, and emaciation. Results Urata’s (proportional function of body surface area) and Noda’s (power function of body weight) formulae showed the highest agreement within their derivation age ranges. When extrapolated beyond these ranges, systematic age-dependent bias emerged, consistent with age-related hepatic involution rather than model structure. TLV remained stable between 20 and 49 years of age but declined linearly after 50 years at a rate of 2.7–2.8% per five years. Obesity was associated with increased TLV due to steatosis, whereas sex and emaciation had minimal effects. Conclusions This study demonstrates that failure to respect derivation age ranges leads to misleading assessments of SLV equation performance. Age-range–matched external validation clarifies prior inconsistencies and provides a generalizable framework for evaluating regression-based prediction models, with implications for both clinical epidemiology and quantitative medical research.