SUMMARY: Combinatorial association mapping aims to assess the statistical association of higher-order interactions of genetic markers with a phenotype of interest. This article presents combinatorial association mapping (CASMAP), a software package that leverages recent advances in significant pattern mining to overcome the statistical and computational challenges that have hindered combinatorial association mapping. CASMAP can be used to perform region-based association studies and to detect higher-order epistatic interactions of genetic variants. Most importantly, unlike other existing significant pattern mining-based tools, CASMAP allows for the correction of categorical covariates such as age or gender, making it suitable for genome-wide association studies. AVAILABILITY AND IMPLEMENTATION: The R and Python packages can be downloaded from our GitHub repository http://github.com/BorgwardtLab/CASMAP. The R package is also available on CRAN. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Genetic heterogeneity is the phenomenon that distinct genetic variants may give rise to the same phenotype. The recently introduced algorithm Fast Automatic Interval Search ( FAIS ) enables the genome-wide search of candidate regions for genetic heterogeneity in the form of any contiguous sequence of variants, and achieves high computational efficiency and statistical power. Although FAIS can test all possible genomic regions for association with a phenotype, a key limitation is its inability to correct for confounders such as gender or population structure, which may lead to numerous false-positive associations. RESULTS: We propose FastCMH , a method that overcomes this problem by properly accounting for categorical confounders, while still retaining statistical power and computational efficiency. Experiments comparing FastCMH with FAIS and multiple kinds of burden tests on simulated data, as well as on human and Arabidopsis samples, demonstrate that FastCMH can drastically reduce genomic inflation and discover associations that are missed by standard burden tests. AVAILABILITY AND IMPLEMENTATION: An R package fastcmh is available on CRAN and the source code can be found at: https://www.bsse.ethz.ch/mlcb/research/bioinformatics-and-computational-biology/fastcmh.html. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

In high-dimensional settings, where the number of features p is typically much larger than the number of samples n, methods which can systematically examine arbitrary combinations of features, a huge 2^p-dimensional space, have recently begun to be explored. However, none of the current methods is able to assess the association between feature combinations and a target variable while conditioning on a categorical covariate, in order to correct for potential confounding effects. We propose the Fast Automatic Conditional Search (FACS) algorithm, a significant discriminative itemset mining method which conditions on categorical covariates and only scales as O(k log k), where k is the number of states of the categorical covariate. Based on the Cochran-Mantel-Haenszel Test, FACS demonstrates superior speed and statistical power on simulated and real-world datasets compared to the state of the art, opening the door to numerous applications in biomedicine.

MOTIVATION: Genetic heterogeneity, the fact that several sequence variants give rise to the same phenotype, is a phenomenon that is of the utmost interest in the analysis of complex phenotypes. Current approaches for finding regions in the genome that exhibit genetic heterogeneity suffer from at least one of two shortcomings: (i) they require the definition of an exact interval in the genome that is to be tested for genetic heterogeneity, potentially missing intervals of high relevance, or (ii) they suffer from an enormous multiple hypothesis testing problem due to the large number of potential candidate intervals being tested, which results in either many false positives or a lack of power to detect true intervals. RESULTS: Here, we present an approach that overcomes both problems: it allows one to automatically find all contiguous sequences of single nucleotide polymorphisms in the genome that are jointly associated with the phenotype. It also solves both the inherent computational efficiency problem and the statistical problem of multiple hypothesis testing, which are both caused by the huge number of candidate intervals. We demonstrate on Arabidopsis thaliana genome-wide association study data that our approach can discover regions that exhibit genetic heterogeneity and would be missed by single-locus mapping. CONCLUSIONS: Our novel approach can contribute to the genome-wide discovery of intervals that are involved in the genetic heterogeneity underlying complex phenotypes. AVAILABILITY AND IMPLEMENTATION: The code can be obtained at: http://www.bsse.ethz.ch/mlcb/research/bioinformatics-and-computational-biology/sis.html.