Asymmetric Independence Model for Detecting Interactions between Variables

TL;DR

The paper introduces the Asymmetric Independence Model (AIM), a new approach for detecting variable interactions in case-control studies that outperforms logistic regression, especially under confounding conditions, with proven theoretical and empirical advantages.

Contribution

AIM offers a biologically-inspired, robust alternative to logistic regression for interaction detection, with proven theoretical superiority and demonstrated empirical performance.

Findings

AIM is mathematically robust under confounding scenarios.

AIM has better power than LR for synergistic interactions.

AIM outperforms LR in simulations and real datasets.

Abstract

Detecting complex interactions among risk factors in case-control studies is a fundamental task in clinical and population research. However, though hypothesis testing using logistic regression (LR) is a convenient solution, the LR framework is poorly powered and ill-suited under several common circumstances in practice including missing or unmeasured risk factors, imperfectly correlated "surrogates", and multiple disease sub-types. The weakness of LR in these settings is related to the way in which the null hypothesis is defined. Here we propose the Asymmetric Independence Model (AIM) as a biologically-inspired alternative to LR, based on the key observation that the mechanisms associated with acquiring a "disease" versus maintaining "health" are asymmetric. We prove mathematically that, unlike LR, AIM is a robust model under the abovementioned confounding scenarios. Further, we provide a mathematical definition of a "synergistic" interaction, and prove that theoretically AIM has better power than LR for such interactions. We then experimentally show the superior performance of AIM as compared to LR on both simulations and four real datasets. While the principal application here involves genetic or environmental variables in the life sciences, our methodology is readily applied to other types of measurements and inferences, e.g. in the social sciences.