Comparison of cNORM and LMS methods for estimating reference percentile curves from biometric data

Accurate reference curves for biometric measures are essential for population health monitoring and screening. The Lambda Mu Sigma Method (LMS), introduced by Cole and Green, is widely used in public health for generating age-specific reference percentiles. This study compares LMS with cNORM, a distribution-free approach based on Taylor polynomials, previously validated in psychometric applications. Using publicly accessible National Health and Nutrition Examination Survey (NHANES) datasets, we compared the performance of LMS and cNORM in modelling reference curves for body mass index (BMI) and maximum oxygen consumption (VO_2max). We repeatedly drew random samples of different size to compute the models and cross-validated these to examine accuracy and bias of both methods across different percentile ranges. Performance metrics included R², root mean square error and systematic deviation (Bias) from empirical percentiles. Both cNORM and LMS achieved high accuracy across the full distributions of BMI and VO₂_max, but cNORM showed superior precision in extreme percentiles (± 2 SD), critical for identifying at-risk individuals. Accuracy improved with larger sample sizes, with a stronger effect for LMS, while interactions between method and sample size were dataset-specific and inconsistent. The distribution free approach implemented in cNORM offers a viable alternative to LMS for generating reference curves in public health applications, particularly when accurate classification in extreme ranges is crucial for screening decisions.