Using Iterative Ridge Regression to Explore Associations Between Conditioned Variables

We address a specific case of joint probability mapping, where the information presented is the probabilistic associations of random variables under a certain condition variable (conditioned associations). Bayesian and dependency networks graphically map the joint probabilities of random variables, though both networks may identify associations that are independent of the condition (background associations). Since the background associations have the same topological features as conditioned associations, it is difficult to discriminate between conditioned and non-conditioned associations, which results in a major increase in the search space. We introduce a modification of the dependency network method, which produces a directed graph, containing only condition-related associations. The graph nodes represent the random variables and the graph edges represent the associations that arise under the condition variable. This method is based on ridge-regression, where one can utilize a numerically robust and computationally efficient algorithm implementation. We illustrate the method's efficiency in the context of a medically relevant process, the emergence of drug-resistant variants of human immunodeficiency virus (HIV) in drug-treated, HIV-infected people. Our mapping was used to discover associations between variants that are conditioned by the initiation of a particular drug treatment regimen. We have demonstrated that our method can recover known associations of such treatment with selected resistance mutations as well as documented associations between different mutations. Moreover, our method revealed novel associations that are statistically significant and biologically plausible.