Adaptive Fisher's method using weakly geometric grid for combining p-values with application to COVID-19 surveillance

In COVID-19 surveillance, detecting significant case increases within regions over specific periods is crucial. Classical methods, typically relying on strict parametric assumptions, struggle with the rare events characteristic of COVID-19's early spread. An alternative strategy is employing nonparametric approaches based on p-value combination methods. However, initial COVID-19 outbreaks across regions exhibit varying signal sparsity levels, while existing p-value combination methods demonstrate power in detecting either moderately sparse or ultra sparse signals in practice, but not both. We present a modified Fisher's method, utilizing a weakly geometric system-based search strategy to adapt across the entire spectrum of signal sparsity. Our method is theoretically and numerically powerful across the whole spectrum of sparsity. Under mild conditions, we examine the robustness of our method in combining approximated p-values, demonstrating its powerful performance even when the number of p-values far surpasses the sample sizes for their derivation, offering a novel nonparametric strategy for COVID-19 surveillance. An efficient algorithm is developed to calculate the p-value of our method. Focusing on the early COVID-19 surveillance in the United States, our method consistently detects outbreaks across regions with varying signal sparsity, uncovering diverse patterns of COVID-19's spread, while competing methods struggle with either ultra-sparse or moderately sparse signals.