Meta-analytical federated surveillance for incubation period with interval- and right-censored data with stochastic variational inference.

Accurate estimation of incubation period is fundamental to surveillance for infectious diseases. This task faces two major challenges: (1) surveillance data are often coarsely observed, comprising interval- and right-censored observations, and (2) patient-level data are frequently fragmented across multiple facilities and cannot be pooled due to privacy constraints. While traditional meta-analysis (MA) aggregates summary statistics, its one-shot nature limits the ability to fit complex hierarchical models. We propose a novel federated Bayesian framework, Federated Stochastic Variational Inference (Fed-SVI), which extends the summary-statistic philosophy of MA into an iterative, model-based federated approach. Our method fits a hierarchical lognormal model, explicitly modeling heterogeneity while estimating a global distribution. To fit this model privately, Fed-SVI iteratively exchanges summary statistics (local variational parameters). Each facility analytically computes these local parameters, rigorously incorporating the likelihood contributions of coarsely-observed data via expectations of the truncated normal distribution. A central server aggregates these parameters using stochastic natural-gradient ascent, enabling efficient information borrowing and mini-batch updates. Through extensive simulations, we demonstrate that Fed-SVI achieves accuracy nearly identical to a fully centralized analysis, while substantially outperforming naive federated or MA methods that discard censored information. We apply Fed-SVI to a distributed COVID-19 line list from 177 facilities, yielding results consistent with centralized estimates. Fed-SVI provides a scalable, accurate, and privacy-preserving solution for robust surveillance in modern data networks.