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 genomically-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 onco-hematology, Hierarchical Dirichlet Mixture Models (HDMM) have become one of the preferred method to cluster the genomics data, that include the presence or absence of gene mutations and cytogenetics anomalies, into components. This work unfolds the standard workflow used in onco-hematology to improve patient stratification and proposes alternative approaches to characterize the components and to assign patient to them, as they are crucial tasks usually supported by a priori clinical knowledge. We propose (a) to compute the parameters of the multinomial components of the HDMM or (b) to estimate the parameters of the HDMM components as if they were Multivariate Fisher's Non-Central Hypergeometric (MFNCH) distributions. Then, our approach to perform patients assignments to the HDMM components is designed to essentially determine for each patient its most likely component. We show on simulated data that the patients assignment using the MFNCH-based approach can be superior, if not comparable, to using the multinomial-based approach. Lastly, we illustrate on real Acute Myeloid Leukemia data how the utilization of MFNCH-based approach emerges as a good trade-off between the rigorous multinomial-based characterization of the HDMM components and the common refinement of them based on a priori clinical knowledge. Explainable models are particularly attractive nowadays since they have the advantage to convince clinicians and patients. In this work we show that the standard workflow used in onco-hematology that leverages on the Hierarchical Dirichlet Mixture Model (HDMM) can benefit from the usage of alternative statistical approaches to better model genomics data. First, HDMMs are typically utilized to cluster the presence or absence of genomic alterations into components. Second, the components are characterized by genomic drivers according to the HDMM outcome, along with to clinical considerations, and eventually patients stratification is performed based on the sole occurrence of the drivers. Here, we present a multinomial-based approach and a Multivariate Fisher's Non-Central Hypergeometric (MFNCH) based approach to tackle components characterization and patients stratification. This work highlights that the MFNCH-based approach performs as good as, if not better, than the multinomial-based approach on simulated data. At the same time the characterization provided by the MFNCH-based approach on real data succeeds to outline all genomic drivers suggested by the standard workflow, which is a result that the rigorous multinomial-based approach fails to accomplish.