Early outbreak data analysis is critical for informing about their potential impact and interventions. However, data obtained early in outbreaks are often sensitive and subject to strict privacy restrictions. Thus, federated analysis, which implies decentralised collaborative analysis where no raw data sharing is required, emerged as an attractive paradigm to solve issues around data privacy and confidentiality. In the present study, we propose two approaches which require neither data sharing nor direct communication between devices/servers. The first approach approximates the joint posterior distributions via a multivariate normal distribution and uses this information to update prior distributions sequentially. The second approach uses summaries from parameters' posteriors obtained locally at different locations (sites) to perform a meta-analysis via a hierarchical model. We test these models on simulated and on real outbreak data to estimate the incubation period of multiple infectious diseases. Results indicate that both approaches can recover incubation period parameters accurately, but they present different inferential advantages. While the approximation approach permits to work with full posterior distributions, thus providing a better quantification of uncertainty; the meta-analysis approach allows for an explicit hierarchical structure, which can make some parameters more interpretable. We provide a framework for federated analysis of early outbreak data where the public health contexts are complex.

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