Federated generalized additive models for location, scale and shape

The generalized additive model for location, scale and shape (GAMLSS) is a flexible regression model with a wide range of applications. In particular, it is the standard method to estimate age-specific percentile curves for clinical parameters for children and adolescents. Deriving international percentile curves requires large datasets that cover a diverse population. Such datasets are typically obtained by pooling data from multiple studies. However, due to ethical and legal constraints, physically sharing and pooling sensitive individual-level data might not always be permitted. Therefore, we aimed to develop a privacy-enhancing method to fit a GAMLSS.

We developed a federated version of the GAMLSS algorithm which allows to co-analyze data from different sources, without physically transferring the data. Instead, data are analyzed locally within their secure home environments and only non-disclosive analysis results are shared. We implemented our method in DataSHIELD, an open-source software infrastructure for federated analysis in R, and investigated its theoretical properties. Considering two different use cases, we applied our algorithm to physically separated epidemiological study data and compared its results with the ones obtained by fitting a GAMLSS to the physically-pooled data. Furthermore, we evaluated the runtime of the federated GAMLSS against the original GAMLSS algorithm for varying number of observations and DataSHIELD servers.

We proved that, in theory, the federated GAMLSS yields identical results as the original GAMLSS algorithm, using the additivity of matrix multiplication in the fitting algorithm. Furthermore, we provided an implementation of the proposed algorithm and demonstrated that the federated GAMLSS implementation yielded the same results as the pooled GAMLSS in our examples, with only minor differences attributable to numerical computation. However, the runtime was more than 1000 times higher for fitting the federated compared to the pooled GAMLSS.

In this paper, we propose a privacy-enhancing federated GAMLSS that yields virtually identical results as the original GAMLSS algorithm, without the need to physically pool the data.