Genome-wide association studies (GWAS) have identified many associated SNPs across a variety of different diseases. However, there remains a significant gap in the heritability explained by these GWAS results and the total heritability predicted for the diseases. This is the missing heritability problem in genetics. One of the sources of missing heritability is gene-gene interactions between SNPs. However, traditional methods for detecting genomic associations have low power to detect these interactions. Machine Learning methods allow us to detect these interactions. Here, we present a new method for identifying interacting SNPs, called Entanglement Mapping (EM). EM works in conjunction with a previously developed Random Forest based method called r2VIM, which can model gene-gene interactions with high power but cannot detect which genes are actually interacting. EM iteratively drops a single SNP and records the effect on importance score. We confirm this here by simulating a genetic model based on interacting and non-interacting SNPs. We have found that interacting SNPs exhibit a higher drop in importance score when one of the interacting SNPs is excluded from the analysis compared to when SNPs that are known to not be interacting are excluded. EM was applied to exome chip genotype data in a study of genetic risk factors for refractive error, a complex eye disorder, and yielded evidence of interaction between two pairs of genetic variants in different genes. EM will be a useful tool in identifying potential new targets for drug development that were missed by traditional GWAS.

BACKGROUND: Random forests (RF) have been increasingly used in applications such as genome-wide association and microarray studies where predictor correlation is frequently observed. Recent works on permutation-based variable importance measures (VIMs) used in RF have come to apparently contradictory conclusions. We present an extended simulation study to synthesize results. RESULTS: In the case when both predictor correlation was present and predictors were associated with the outcome (HA), the unconditional RF VIM attributed a higher share of importance to correlated predictors, while under the null hypothesis that no predictors are associated with the outcome (H0) the unconditional RF VIM was unbiased. Conditional VIMs showed a decrease in VIM values for correlated predictors versus the unconditional VIMs under HA and was unbiased under H0. Scaled VIMs were clearly biased under HA and H0. CONCLUSIONS: Unconditional unscaled VIMs are a computationally tractable choice for large datasets and are unbiased under the null hypothesis. Whether the observed increased VIMs for correlated predictors may be considered a "bias" - because they do not directly reflect the coefficients in the generating model - or if it is a beneficial attribute of these VIMs is dependent on the application. For example, in genetic association studies, where correlation between markers may help to localize the functionally relevant variant, the increased importance of correlated predictors may be an advantage. On the other hand, we show examples where this increased importance may result in spurious signals.

MOTIVATION: The advent of high-throughput genomics has produced studies with large numbers of predictors (e.g. genome-wide association, microarray studies). Machine learning algorithms (MLAs) are a computationally efficient way to identify phenotype-associated variables in high-dimensional data. There are important results from mathematical theory and numerous practical results documenting their value. One attractive feature of MLAs is that many operate in a fully multivariate environment, allowing for small-importance variables to be included when they act cooperatively. However, certain properties of MLAs under conditions common in genomic-related data have not been well-studied--in particular, correlations among predictors pose a problem. RESULTS: Using extensive simulation, we showed considering correlation within predictors is crucial in making valid inferences using variable importance measures (VIMs) from three MLAs: random forest (RF), conditional inference forest (CIF) and Monte Carlo logic regression (MCLR). Using a case-control illustration, we showed that the RF VIMs--even permutation-based--were less able to detect association than other algorithms at effect sizes encountered in complex disease studies. This reduction occurred when 'causal' predictors were correlated with other predictors, and was sharpest when RF tree building used the Gini index. Indeed, RF Gini VIMs are biased under correlation, dependent on predictor correlation strength/number and over-trained to random fluctuations in data when tree terminal node size was small. Permutation-based VIM distributions were less variable for correlated predictors and are unbiased, thus may be preferred when predictors are correlated. MLAs are a powerful tool for high-dimensional data analysis, but well-considered use of algorithms is necessary to draw valid conclusions. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.