A Graph-Based Approach to Mitigate Drug-Drug Interactions and Optimize Therapeutic Regimens

Drug-drug interactions (DDIs) pose a significant issue in modern healthcare, potentially compromising treatment efficacy and patient safety. DDIs arise when significant alterations occur in the pharmacological action of a drug due to its co-administration with another drug, leading to potential adverse drug reactions (ADRs), toxicity or diminished therapeutic efficacy. Apart from the obvious cases of drug combinations that should be avoided, there are instances where risk-benefit analysis may allow co-administration. Hence, DDIs may represent clinically significant cases depending on the clinical outcome, time point of administration, etc. The issue is especially critical in cases of patients with multimorbidity and complex therapeutic regimens with different time points in drug administrations. This work employs a graph-based approach aimed at optimizing therapeutic regiments while considering the minimization of DDIs potential. In this approach each drug is represented as a node, and edges represent the clinical significance of DDIs. We aim to identify sets of drugs that either have no DDIs or exhibit minor to moderate clinical significance (referred to as Maximal Independent Sets), indicating that they can be taken together. In practice, we solved the complementary problem, which is finding Maximal Cliques. Both problems are NP-hard, but for small graphs, they can be solved exactly. From all the cliques we identify, those selected to be a part of each proposed therapeutic regimen must consist of nodes that appear only once. This problem is once again reduced to clique finding. The above approach is demonstrated using two clinical scenarios involving two patients who are experiencing polypharmacy and are at risk for ADRs due to potential DDIs of varying clinical significance. By applying our approach, the therapeutic schemes are optimized towards minimizing the risk of ADRs.