From Nagelkerke's R2 to Liability-Scale Variance Explained for Polygenic Scores
- 1University of Oxford
Abstract
It is desirable to quantify the prediction accuracy of polygenic scores (PGS) for disease on the scale of liability and adjusted for case-control ascertainment in the test sample, because that allows comparison across prevalence and ascertainment. Previous expressions have focused in their derivation and implementation on linear regression on the observed 0-1 scale followed by a transformation of the coefficient of determination (R2) to the scale of liability, adjusted for ascertainment. Yet most statistical analyses with empirical data use logistic regression. The differences in scale have led to confusion and incorrect transformations in the literature. Here we provide a new derivation and simple equation, validated by simulation, that allows a direct transformation from the empirical results from logistic regression to the scale of liability.
Related
- From Monogenic Variants to Polygenic Risk Scores in Inherited Cardiomyopathies: Clinical Utility, Ancestry Gaps, and Future Implementation in Arab Populations
- BLocPRS: locus-aware ensembles of polygenic scores provide accurate linear prediction
- GeneSIS: enhancing transferability of polygenic scores with variant-level gene-by-sex interaction effects
- Education-related polygenic scores show different associations with youth mental health in parent-offspring trios
- Polygenic Risk Scores of Coronary Heart Disease in Chronic Kidney Disease Population: The CRIC Study
BibTeX
@misc{uffelmann2026from,
title = {{From Nagelkerke's R2 to Liability-Scale Variance Explained for Polygenic Scores}},
author = {E. Uffelmann and P. M. Visscher},
howpublished = {bioRxiv},
year = {2026},
month = sep,
doi = {10.64898/2026.09.12.751172},
url = {https://www.biorxiv.org/content/10.64898/2026.09.12.751172v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - From Nagelkerke's R2 to Liability-Scale Variance Explained for Polygenic Scores
AU - E. Uffelmann
AU - P. M. Visscher
PY - 2026
DA - 2026/09/12
PB - bioRxiv
DO - 10.64898/2026.09.12.751172
UR - https://www.biorxiv.org/content/10.64898/2026.09.12.751172v1
AB - It is desirable to quantify the prediction accuracy of polygenic scores (PGS) for disease on the scale of liability and adjusted for case-control ascertainment in the test sample, because that allows comparison across prevalence and ascertainment. Previous expressions have focused in their derivation and implementation on linear regression on the observed 0-1 scale followed by a transformation of the coefficient of determination (R2) to the scale of liability, adjusted for ascertainment. Yet most statistical analyses with empirical data use logistic regression. The differences in scale have led to confusion and incorrect transformations in the literature. Here we provide a new derivation and simple equation, validated by simulation, that allows a direct transformation from the empirical results from logistic regression to the scale of liability.
ER -