The purpose of this study is to develop an innovative system for Coumarin-derived drug dosing, suitable for elderly patients. Recent research highlights that the pharmacological response of the patient is often affected by many exogenous factors other than the dosage prescribed and these factors could form a very complex relationship with the drug dosage. For this reason, new powerful computational tools are needed for approaching this problem. The system we propose is called Geometric Semantic Genetic Programming, and it is based on the use of recently defined geometric semantic genetic operators. In this paper, we present a new implementation of this Genetic Programming system, that allow us to use it for real-life applications in an efficient way, something that was impossible using the original definition. Experimental results show the suitability of the proposed system for managing anticoagulation therapy. In particular, results obtained with Geometric Semantic Genetic Programming are significantly better than the ones produced by standard Genetic Programming both on training and on out-of-sample test data.