Nonparametric Risk and Nonparametric Odds in Quantitative Genetic Association Studies

Abstract

The coefficient in a linear regression model is commonly employed to evaluate the genetic effect of a single nucleotide polymorphism associated with a quantitative trait under the assumption that the trait value follows a normal distribution or is appropriately normally distributed after a certain transformation. When this assumption is violated, the distribution-free tests are preferred. In this work, we propose the nonparametric risk (NR) and nonparametric odds (NO), obtain the asymptotic normal distribution of estimated NR and then construct the confidence intervals. We also define the genetic models using NR, construct the test statistic under a given genetic model and a robust test, which are free of the genetic uncertainty. Simulation studies show that the proposed confidence intervals have satisfactory cover probabilities and the proposed test can control the type I error rates and is more powerful than the exiting ones under most of the considered scenarios. Application to gene of PTPN22 and genomic region of 6p21.33 from the Genetic Analysis Workshop 16 for association with the anticyclic citrullinated protein antibody further show their performances.

Figure 1. The empirical power of the Kruskal-Wallis test (KW-R, KW-A and KW-D), the Jonckheere-Terpstra test (JT-R, JT-A and JT-D), the F test (F-R, F-A and F-D) and the proposed nonparametric test (Z_R, Z_A and Z_D) derived under a given genetic model.

The first column is for β₁ = 0.25 and the second column is for β₁ = 0.5.

Figure 2. The empirical power of KW-A, F-A, Z_A and MAX3.

The first column is for β₁ = 0.25 and the second column is for β₁ = 0.5.