PPubMed9 Jan 2026Cited 2×

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

Fengling Hu, Jiayi Tong, Margaret Gardner, Andrew A. Chen, Richard A.I. Bethlehem, Jakob Seidlitz, Hongzhe Li, Aaron Alexander-Bloch, Yong Chen, Russell T. Shinohara, Christina Kendziorski

Abstract

Distributed GAMLSS (dGAMLSS) provides machinery for estimating semi-parametric coefficients across a broad family of GAMLSS distributions defined by up to four parameters, including mean, variance, skewness, and kurtosis, across multiple sites without sharing any patient-level data. Once coefficients are estimated, dGAMLSS allows for inference and estimation of model-based centiles, defined as quantiles multiplied by 100. Notation for dGAMLSS is defined in [btaf625-T1]. Briefly, the proposed dGAMLSS algorithm adapts the pooled GAMLSS fitting algorithm, where the terminology “pooled” refers to

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dGAMLSS enables exact, privacy‑preserving fitting of GAMLSS models across sites, reproducing pooled reference charts with negligible differences.

What’s new

i.Developed dGAMLSS, an exact distributed algorithm for fitting GAMLSS without sharing patient‑level data
ii.Demonstrated dGAMLSS in clinical (BMI), genomics (Proteobacteria), and neuroimaging (brain volume) applications
iii.Showed dGAMLSS reproduces pooled GAMLSS results with >0.9999 correlation in quantile predictions
iv.Provided an R package implementing dGAMLSS and site‑level aggregation functions

How they did it

The pooled GAMLSS Newton‑Raphson fitting was reformulated as a distributed RS algorithm where each site computes and sends summary matrices M_{i1} and M_{i2} to a central node, achieving the exact pooled weighted‑least‑squares solution with one communication per inner iteration. After convergence, a final communication round aggregates site‑wise Hessians to obtain global covariance for Wald‑type inference. The approach was applied to multiple multi‑site datasets using fixed‑effect smooth, fixed‑penalty, and automated‑penalty spline models.

What they found

Correlation between dGAMLSS and pooled quantile predictions for BMI >0.9999
Correlation for Proteobacteria quantiles 0.9994; BIC dGAMLSS -2360.2 vs pooled -2365.2
Correlation for brain‑volume quantiles >0.9999
Proteobacteria model required 2 communication rounds to set spline basis, 117 rounds to converge, and 1 round to obtain centiles

Caveats

✕Exact inference is not implemented for smooth terms in the automated‑penalty setting
✕Standardization of data measurement, processing, and storage across sites is required for robust models
✕Inference for penalized smooth terms may be liberal and is not fully addressed

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