  Qualitative interactions occur when a treatment effect or measure of
association varies in sign by sub-population. Of particular interest in many
biomedical settings are absence/presence qualitative interactions, which occur
when an effect is present in one sub-population but absent in another.
Absence/presence interactions arise in emerging applications in precision
medicine, where the objective is to identify a set of predictive biomarkers
that have prognostic value for clinical outcomes in some sub-population but not
others. They also arise naturally in gene regulatory network inference, where
the goal is to identify differences in networks corresponding to diseased and
healthy individuals, or to different subtypes of disease; such differences lead
to identification of network-based biomarkers for diseases. In this paper, we
argue that while the absence/presence hypothesis is important, developing a
statistical test for this hypothesis is an intractable problem. To overcome
this challenge, we approximate the problem in a novel inference framework. In
particular, we propose to make inferences about absence/presence interactions
by quantifying the relative difference in effect size, reasoning that when the
relative difference is large, an absence/presence interaction occurs. The
proposed methodology is illustrated through a simulation study as well as an
analysis of breast cancer data from the Cancer Genome Atlas.
