  A pair of variables that tend to rise and fall either together or in
opposition are said to be monotonically associated. For certain phenomena, this
tendency is causally restricted to a subpopulation, as, for example, an
allergic reaction to an irritant. Previously, Yu et al. (2011) devised a method
of rearranging observations to test paired data to see if such an association
might be present in a subpopulation. However, the computational intensity of
the method limited its application to relatively small samples of data, and the
test itself only judges if association is present in some subpopulation; it
does not clearly identify the subsample that came from this subpopulation,
especially when the whole sample tests positive. The present paper adds a
"top-K" feature (Sampath and Verducci (2013)) based on a multistage ranking
model, that identifies a concise subsample that is likely to contain a high
proportion of observations from the subpopulation in which the association is
supported. Computational improvements incorporated into this top-K tau-path
(TKTP) algorithm now allow the method to be extended to thousands of pairs of
variables measured on sample sizes in the thousands. A description of the new
algorithm along with measures of computational complexity and practical
efficiency help to gauge its potential use in different settings. Simulation
studies catalog its accuracy in various settings, and an example from finance
illustrates its step-by-step use.
