A Residual Approach to Estimate Biological Age from Gompertz Modeling

Abstract Biological age (BA) and its residual relative to chronological age are popularly used to quantify individual aging. Although these residuals independently predict age-related health outcomes, conventional BA measures often lack robustness in heterogeneous populations, and their residuals are not directly derivable in clinical practice. To address these limitations, we introduce the Gompertz law-based residual (GOLD-R) framework, a method designed to directly estimate BA residuals and optimized for cross-sectional data. We demonstrated the applicability and robustness of GOLD-R across multiple data types and populations. First, training on DNA methylation data from the EWAS Data Hub, the framework outperformed established epigenetic clocks in predicting mortality in a pan-cancer dataset. Then, applied to UK Biobank proteomics data, GOLD-R generated organismal and organ-specific aging measures that proved more robust than conventional age-prediction approaches in forecasting incident diseases and mortality. Finally, extending the analysis to clinical biomarkers using the NHANES and HRS, we found that GOLD-R residuals, derived from clinical biomarkers, surpassed those from both epigenetic and phenotypic clocks in performance. In summary, our findings establish GOLD-R as a robust algorithm for biological age estimation, providing a practical tool for both research and clinical applications. Competing Interest Statement The authors have declared no competing interest. Funding Statement This work was supported by the National Natural Science Foundation of China (32300533, 82301768, 32100510), the Shanghai Sailing Program (23YF1430500). Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes Data Availability Human DNA methylation data was downloaded from EWAS Data Hub (https://ngdc.cncb.ac.cn/ewas/datahub). The data from the NHANES are publicly available at https://www.cdc.gov/nchs/nhanes/index.htm. The data from the HRS are available upon application at https://hrs.isr.umich.edu/. The data from the UK Biobank are available upon application at www.ukbiobank.ac.uk/register-apply. This research was conducted using UK Biobank Resource under Application Number 103791.