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Qualitative interactions occur when a treatment effect or measure ofassociation varies in sign by sub-population. Of particular interest in manybiomedical settings are absence/presence qualitative interactions, which occurwhen an effect is present in one sub-population but absent in another.Absence/presence interactions arise in emerging applications in precisionmedicine, where the objective is to identify a set of predictive biomarkersthat have prognostic value for clinical outcomes in some sub-population but notothers. They also arise naturally in gene regulatory network inference, wherethe goal is to identify differences in networks corresponding to diseased andhealthy individuals, or to different subtypes of disease; such differences leadto identification of network-based biomarkers for diseases. In this paper, weargue that while the absence/presence hypothesis is important, developing astatistical test for this hypothesis is an intractable problem. To overcomethis challenge, we approximate the problem in a novel inference framework. Inparticular, we propose to make inferences about absence/presence interactionsby quantifying the relative difference in effect size, reasoning that when therelative difference is large, an absence/presence interaction occurs. Theproposed methodology is illustrated through a simulation study as well as ananalysis of breast cancer data from the Cancer Genome Atlas.

Statistical Inference for Qualitative Interactions with Applications to Precision Medicine and Differential Network Analysis