Abstract
BackgroundDeveloping binary classification rules based on SNP observations has been a major challenge for many modern bioinformatics applications, e.g., predicting risk of future disease events in complex conditions such as cancer. Small-sample, high-dimensional nature of SNP data, weak effect of each SNP on the outcome, and highly non-linear SNP interactions are several key factors complicating the analysis. Additionally, SNPs take a finite number of values which may be best understood as ordinal or categorical variables, but are treated as continuous ones by many algorithms.MethodsWe use the theory of high dimensional model representation (HDMR) to build appropriate low dimensional glass-box models, allowing us to account for the effects of feature interactions. We compute the second order HDMR expansion of the log-likelihood ratio to account for the effects of single SNPs and their pairwise interactions. We propose a regression based approach, called linear approximation for block second order HDMR expansion of categorical observations (LABS-HDMR-CO), to approximate the HDMR coefficients. We show how HDMR can be used to detect pairwise SNP interactions, and propose the fixed pattern test (FPT) to identify statistically significant pairwise interactions.ResultsWe apply LABS-HDMR-CO and FPT to synthetically generated HAPGEN2 data as well as to two GWAS cancer datasets. In these examples LABS-HDMR-CO enjoys superior accuracy compared with several algorithms used for SNP classification, while also taking pairwise interactions into account. FPT declares very few significant interactions in the small sample GWAS datasets when bounding false discovery rate (FDR) by 5%, due to the large number of tests performed. On the other hand, LABS-HDMR-CO utilizes a large number of SNP pairs to improve its prediction accuracy. In the larger HAPGEN2 dataset FTP declares a larger portion of SNP pairs used by LABS-HDMR-CO as significant.ConclusionLABS-HDMR-CO and FPT are interesting methods to design prediction rules and detect pairwise feature interactions for SNP data. Reliably detecting pairwise SNP interactions and taking advantage of potential interactions to improve prediction accuracy are two different objectives addressed by these methods. While the large number of potential SNP interactions may result in low power of detection, potentially interacting SNP pairs, of which many might be false alarms, can still be used to improve prediction accuracy.
Highlights
Developing binary classification rules based on single nucleotide polymorphism (SNP) observations has been a major challenge for many modern bioinformatics applications, e.g., predicting risk of future disease events in complex conditions such as cancer
While the large number of potential SNP interactions may result in low power of detection, potentially interacting SNP pairs, of which many might be false alarms, can still be used to improve prediction accuracy
Given that many studies may measure several hundred thousand or a few million SNPs, they all cannot be directly inputted to a classifier, that we aim to account for pairwise SNP interactions, i.e., the second order terms of the high dimensional model representation (HDMR) expansion
Summary
Developing binary classification rules based on SNP observations has been a major challenge for many modern bioinformatics applications, e.g., predicting risk of future disease events in complex conditions such as cancer. Data encountered in bioinformatics is typically “smallsample high-dimensional”, a challenge not encountered in many classical statistics problems and machine learning applications. While being a small-sample high-dimensional problem is typical of many bioinformatics applications, it seems to be more pronounced when analyzing SNPs as (a) current technologies measure hundreds of thousands of SNPs, and (b) sample size can be much smaller than the number of disease associated SNPs. many molecular features, and in particular SNPs, can be weak markers, meaning each individual feature alone cannot reliably predict the disease outcome, and a large collection of features need to be considered together to obtain reliable predictions. That a specific mutation increases cancer risk by some amount, or presence of a combination of mutations is an indicator of high risk
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