Covering Hierarchical Dirichlet Mixture Models on binary data to enhance genomic stratifications in Onco-Hematology

Onco-hematological studies are increasingly adopting statistical mixture models to support the advancement of the genetically-driven classification systems for blood cancer. Targeting enhanced patients stratification based on the sole role of molecular biology attracted much interest and contributes to bring personalized medicine closer to reality. In particular, Dirichlet processes have become the preferred method to approach the fit of mixture models. Usually, the multinomial distribution is at the core of such models. However, despite their advanced statistical formalism, these processes are not to be considered black box techniques and a better understanding of their working mechanisms enables to improve their employment and explainability. Focused on genomic data in Acute Myeloid Leukemia, this work unfolds the driving factors and rationale of the Hierarchical Dirichlet Mixture Models of multinomials on binary data. In addition, we introduce a novel approach to perform accurate patients clustering via multinomials based on statistical considerations. The newly reported adoption of the Multivariate Fisher’s Non-Central Hypergeometric distributions reveals promising results and outperformed the multinomials in clustering both on simulated and real onco-hematological data. Author summary Explainable models are particularly attractive nowadays since they have the advantage to convince clinicians and patients. In this work we show that a deeper understanding of the Hierarchical Dirichlet Mixture Model, a non-black box method, can lead to better data modelling. In onco-hematology Hierarchical Dirichlet Mixture Models typically help to cluster molecular alterations rather than patients. Here, an intuitive statistical approach is presented to tackle patient classification based on the Hierarchical Dirichlet Mixture Models outcome. Additionally, molecular alterations are usually modelled by Hierarchical Dirichlet Mixture Models as a mixture of multinomial distributions. This work highlights that the alternative Fisher’s Non-Central Hypergeometric distribution can provide even better results and can give a higher priority to rare molecular alterations for patient classification.