Linear Mixed Modeling of Federated Data When Only the Mean, Covariance, and Sample Size Are Available

Abstract

In medical research, individual-level patient data provide invaluable information, but the patients' right to confidentiality remains of utmost priority. This poses a huge challenge when estimating statistical models such as a linear mixed model, which is an extension of linear regression models that can account for potential heterogeneity whenever data come from different data providers. Federated learning tackles this hurdle by estimating parameters without retrieving individual-level data. Instead, iterative communication of parameter estimate updates between the data providers and analysts is required. In this article, we propose an alternative framework to federated learning for fitting linear mixed models. Specifically, our approach only requires the mean, covariance, and sample size of multiple covariates from different data providers once. Using the principle of statistical sufficiency within the likelihood framework as theoretical support, this proposed strategy achieves estimates identical to those derived from actual individual-level data. We demonstrate this approach through real data on 15 068 patient records from 70 clinics at the Children's Hospital of Pennsylvania. Assuming that each clinic only shares summary statistics once, we model the COVID-19 polymerase chain reaction test cycle threshold as a function of patient information. Simplicity, communication efficiency, generalisability, and wider scope of implementation in any statistical software distinguish our approach from existing strategies in the literature.