  Handling multiplicity without losing much power has been a persistent
challenge in various fields that often face the necessity of managing numerous
statistical tests simultaneously. Recently, $p$-value combination methods based
on heavy-tailed distributions, such as a Cauchy distribution, have received
much attention for their ability to handle multiplicity without the prescribed
knowledge of the dependence structure. This paper delves into these types of
$p$-value combinations through the lens of extreme value theory. Distributions
with regularly varying tails, a subclass of heavy tail distributions, are found
to be useful in constructing such $p$-value combinations. Three $p$-value
combination statistics (sum, max cumulative sum, and max) are introduced, of
which left tail probabilities are shown to be approximately uniform when the
global null is true. The primary objective of this paper is to bridge the gap
between current developments in $p$-value combination methods and the
literature on extreme value theory, while also offering guidance on selecting
the calibrator and its associated parameters.
