Artificial intelligence (AI) can unveil novel personalized treatments based on drug screening and whole-exome sequencing experiments (WES). However, the concept of "black box" in AI limits the potential of this approach to be translated into the clinical practice. In contrast, explainable AI (XAI) focuses on making AI results understandable to humans. Here, we present a novel XAI method -called multi-dimensional module optimization (MOM)- that associates drug screening with genetic events, while guaranteeing that predictions are interpretable and robust. We applied MOM to an acute myeloid leukemia (AML) cohort of 319 ex-vivo tumor samples with 122 screened drugs and WES. MOM returned a therapeutic strategy based on the FLT3, CBF beta-MYH11, and NRAS status, which predicted AML patient response to Quizartinib, Trametinib, Selumetinib, and Crizotinib. We successfully validated the results in three different large-scale screening experiments. We believe that XAI will help healthcare providers and drug regulators better understand AI medical decisions.