MOTIVATION: Recent advances in DNA sequencing technologies have allowed the detailed characterization of genomes in large cohorts of tumors, highlighting their extreme heterogeneity, with no two tumors sharing the same complement of somatic mutations. Such heterogeneity hinders our ability to identify somatic mutations important for the disease, including mutations that determine clinically relevant phenotypes (e.g. cancer subtypes). Several tools have been developed to identify somatic mutations related to cancer phenotypes. However, such tools identify correlations between somatic mutations and cancer phenotypes, with no guarantee of highlighting causal relations. RESULTS: We describe ALLSTAR, a novel tool to infer reliable causal relations between somatic mutations and cancer phenotypes. ALLSTAR identifies reliable causal rules highlighting combinations of somatic mutations with the highest impact in terms of average effect on the phenotype. While we prove that the underlying computational problem is NP-hard, we develop a branch-and-bound approach that employs protein-protein interaction networks and novel bounds for pruning the search space, while properly correcting for multiple hypothesis testing. Our extensive experimental evaluation on synthetic data shows that our tool is able to identify reliable causal relations in large cancer cohorts. Moreover, the reliable causal rules identified by our tool in cancer data show that our approach identifies several somatic mutations known to be relevant for cancer phenotypes as well as novel biologically meaningful relations. AVAILABILITY AND IMPLEMENTATION: Code, data, and scripts to reproduce the experiments available at https://github.com/VandinLab/ALLSTAR.

Abstract Many algorithms have been proposed to learn local graphical structures around target variables of interest from observational data, focusing on two sets of variables. The first one, called Parent–Children (PC) set, contains all the variables that are direct causes or consequences of the target while the second one, known as Markov boundary (MB), is the minimal set of variables with optimal prediction performances of the target. In this paper we introduce two novel algorithms for the PC and MB discovery tasks with rigorous guarantees on the Family-Wise Error Rate (FWER), that is, the probability of reporting any false positive in output. Our algorithms use Rademacher averages, a key concept from statistical learning theory, to properly account for the multiple-hypothesis testing problem arising in such tasks. Our evaluation on simulated data shows that our algorithms properly control for the FWER, while widely used algorithms do not provide guarantees on false discoveries even when correcting for multiple-hypothesis testing. Our experiments also show that our algorithms identify meaningful relations in real-world data.

Causal discovery from observational data provides candidate causal relationships that need to be validated with ad-hoc experiments. Such experiments usually require major resources, and suitable techniques should therefore be applied to identify candidate relations while limiting false positives. Local causal discovery provides a detailed overview of the variables influencing a target, and it focuses on two sets of variables. The first one, the Parent-Children set, comprises all the elements that are direct causes of the target or that are its direct consequences, while the second one, called the Markov boundary, is the minimal set of variables for the optimal prediction of the target. In this paper we present RAveL, the first suite of algorithms for local causal discovery providing rigorous guarantees on false discoveries. Our algorithms exploit Rademacher averages, a key concept in statistical learning theory, to account for the multiple-hypothesis testing problem in high-dimensional scenarios. Moreover, we prove that state-of-the-art approaches cannot be adapted for the task due to their strong and untestable assumptions, and we complement our analyses with extensive experiments, on synthetic and real-world data.