Estimation of p-values with Two Dimensional Null Distributions from Genomic Data Set

Abstract

When an observable is described by a single value, the statistic significance may be estimated by construction of null distribution using permutation and counting the portion of it that exceeds the observed value by chance. Genome-wide association study usually focuses on the association measure between a single or interacting genotypes with a single phenotype. However investigation of common genotypes associated simultaneously on multiple phenotypes may involve the observables that should be described with multiple numbers. Statistical significance for such an observable would involve null distribution in multiple dimensions. In this study, extension of the p-value estimation process using null distribution in one dimension has been sought that may be applicable to two dimensional case. Comparison of the position of points within the set of points they form has been proposed to use a positioning parameter inspired by the extension of the Kolmogorov- Smirnov statistic to two dimensions.