dGAMLSS: An exact, distributed algorithm to fit Generalized Additive Models for Location, Scale, and Shape for privacy-preserving population reference charts

Abstract There is growing interest in estimating population reference ranges across age and sex to better identify atypical clinically-relevant measurements throughout the lifespan. For this task, the World Health Organization recommends using Generalized Additive Models for Location, Scale, and Shape (GAMLSS) which can model non-linear growth trajectories under complex distributions that address the heterogeneity in human populations. Fitting GAMLSS models requires large, generalizable sample sizes, especially for accurate estimation of extreme quantiles, but obtaining such multi-site data can be challenging due to privacy concerns and practical considerations. In settings where patient data cannot be shared, privacy-preserving distributed algorithms for federated learning can be used, but no such algorithm exists for GAMLSS. We propose distributed GAMLSS (dGAMLSS), a distributed algorithm which can fit GAMLSS models across multiple sites without sharing patient-level data. We demonstrate the effectiveness of dGAMLSS in constructing population reference charts across clinical, genomics, and neuroimaging settings. Competing Interest Statement RTS receives consulting income from Octave Bioscience and compensation for reviewership duties from the American Medical Association. JS, RAIB and AA-B hold shares in Centile Bioscience, and JS and RAIB are directors of Centile Bioscience. Footnotes CRediT author statement: Fengling Hu: Conceptualization, Methodology, Software, Validation, Formal Analysis, Investigation, Data Curation, Writing – Original Draft, Writing – Review & Editing, Visualization. Jiayi Tong: Methodology, Validation, Formal Analysis, Resources, Investigation, Writing – Review & Editing. Margaret Gardner: Validation, Resources, Writing – Review & Editing. Andrew A. Chen: Validation, Resources, Writing – Review & Editing, Supervision. Richard A.I. Bethlehem: Validation, Resources, Writing – Review & Editing. Jakob Seidlitz: Validation, Resources, Writing – Review & Editing. Hongzhe Li: Validation, Formal Analysis, Writing – Review & Editing, Supervision. Aaron Alexander-Bloch: Validation, Resources, Writing – Review & Editing, Supervision. Yong Chen: Conceptualization, Methodology, Validation, Resources, Investigation, Writing – Review & Editing, Supervision. Russell T. Shinohara: Conceptualization, Methodology, Validation, Formal Analysis, Resources, Investigation, Writing – Review & Editing, Supervision, Project administration, Funding acquisition. Disclosures and Conflicts of Interest: RTS receives consulting income from Octave Bioscience and compensation for reviewership duties from the American Medical Association. JS, RAIB and AA-B hold shares in Centile Bioscience, and JS and RAIB are directors of Centile Bioscience. Funding: FH was supported by NIH Medical Scientist Training Program T32 GM07170. Funding sources were not involved in study design, data analysis, manuscript preparation, or submission decisions.