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Directional association measured by functional dependency can answer important questions on relationships between variables, for example, in discovery of molecular interactions in biological systems. However, when one has no prior information about the functional form of a directional association, there is not a widely established statistical procedure to detect such an association. To address this issue, here we introduce an exact functional test for directional association by examining the strength of functional dependency. It is effective in promoting functional patterns by reducing statistical power on dependent non-functional patterns. We designed an algorithm to carry out the test using a fast branch-and-bound strategy, which achieved a substantial speedup over brute-force enumeration. On data from an epidemiological study of liver cancer, the test identified the hepatitis status of a subject as the most influential risk factor among others for the cancer phenotype. On human lung cancer transcriptome data, the test selected 1068 transcription start sites of putative noncoding RNAs directionally associated with the presence or absence of lung cancer, stronger than 95 percent transcription start sites of 694 curated cancer genes. These predictions include non-monotonic interaction patterns, to which other routine tests were insensitive. Complementing symmetric (non-directional) association methods such as Fisher's exact test, the exact functional test is a unique exact statistical test for evaluating evidence for causal relationships.

A Fast Exact Functional Test for Directional Association and Cancer Biology Applications