  The surveillance of a pandemic is a challenging task, especially when crucial
data is distributed and stakeholders cannot or are unwilling to share. To
overcome this obstacle, federated methodologies should be developed to
incorporate less sensitive evidence that entities are willing to provide. This
study aims to explore the feasibility of pushing hypothesis tests behind each
custodian's firewall and then meta-analysis to combine the results, and to
determine the optimal approach for reconstructing the hypothesis test and
optimizing the inference. We propose a hypothesis testing framework to identify
a surge in the indicators and conduct power analyses and experiments on real
and semi-synthetic data to showcase the properties of our proposed hypothesis
test and suggest suitable methods for combining $p$-values. Our findings
highlight the potential of using $p$-value combination as a federated
methodology for pandemic surveillance and provide valuable insights into
integrating available data sources.
