Most genetic or environmental factors work together in determining complex disease risk. Detecting gene-environment interactions may allow us to elucidate novel and targetable molecular mechanisms on how environmental exposures modify genetic effects. Unfortunately, standard logistic regression (LR) assumes a convenient mathematical structure for the null hypothesis that however results in both poor detection power and type 1 error, and is also susceptible to missing factor, imperfect surrogate, and disease heterogeneity confounding effects. Here we describe a new baseline framework, the asymmetric independence model (AIM) in case-control studies, and provide mathematical proofs and simulation studies verifying its validity across a wide range of conditions. We show that AIM mathematically preserves the asymmetric nature of maintaining health versus acquiring a disease, unlike LR, and thus is more powerful and robust to detect synergistic interactions. We present examples from four clinically discrete domains where AIM identified interactions that were previously either inconsistent or recognized with less statistical certainty.