Mining large datasets using machine learning approaches often leads to models that are hard to interpret and not amenable to the generation of hypotheses that can be experimentally tested. We present 'Logic Optimization for Binary Input to Continuous Output' (LOBICO), a computational approach that infers small and easily interpretable logic models of binary input features that explain a continuous output variable. Applying LOBICO to a large cancer cell line panel, we find that logic combinations of multiple mutations are more predictive of drug response than single gene predictors. Importantly, we show that the use of the continuous information leads to robust and more accurate logic models. LOBICO implements the ability to uncover logic models around predefined operating points in terms of sensitivity and specificity. As such, it represents an important step towards practical application of interpretable logic models.

Cancer hallmarks are evolutionary traits required by a tumour to develop. While extensively characterised, the way these traits are achieved through the accumulation of somatic mutations in key biological pathways is not fully understood. To shed light on this subject, we characterised the landscape of pathway alterations associated with somatic mutations observed in 4,415 patients across ten cancer types, using 374 orthogonal pathway gene-sets mapped onto canonical cancer hallmarks. Towards this end, we developed SLAPenrich: a computational method based on population-level statistics, freely available as an open source R package. Assembling the identified pathway alterations into sets of hallmark signatures allowed us to connect somatic mutations to clinically interpretable cancer mechanisms. Further, we explored the heterogeneity of these signatures, in terms of ratio of altered pathways associated with each individual hallmark, assuming that this is reflective of the extent of selective advantage provided to the cancer type under consideration. Our analysis revealed the predominance of certain hallmarks in specific cancer types, thus suggesting different evolutionary trajectories across cancer lineages. Finally, although many pathway alteration enrichments are guided by somatic mutations in frequently altered high-confidence cancer genes, excluding these driver mutations preserves the hallmark heterogeneity signatures, thus the detected hallmarks' predominance across cancer types. As a consequence, we propose the hallmark signatures as a ground truth to characterise tails of infrequent genomic alterations and identify potential novel cancer driver genes and networks.