Federated Mixed Effects Logistic Regression Based on One-Time Shared Summary Statistics

Upholding data privacy, especially in medical research, has become tantamount to facing difficulties in accessing individual-level patient data. Estimating mixed effects binary logistic regression models involving data from multiple data providers, like hospitals, thus becomes more challenging. Federated learning has emerged as an option to preserve the privacy of individual observations while still estimating a global model that can be interpreted on the individual level, but it usually involves iterative communication between the data providers and the data analyst. In this paper, we present a strategy to estimate a mixed effects binary logistic regression model that requires data providers to share summary statistics only once. It involves generating pseudo-data whose summary statistics match those of the actual data and using these in the model estimation process instead of the actual unavailable data. Our strategy is able to include multiple predictors, which can be a combination of continuous and categorical variables. Through simulation, we show that our approach estimates the true model at least as good as the one that requires the pooled individual observations. An illustrative example using real data is provided. Unlike typical federated learning algorithms, our approach eliminates infrastructure requirements and security issues while being communication efficient and while accounting for heterogeneity.