nmax3 {AssocTests}

NMAX3 based on the maximum value of the three nonparametric trend tests under the recessive, additive, and dominant models

Description

Test for the association between a biallelic SNP and a quantitative trait using the maximum value of the three nonparametric trend tests derived for the recessive, additive, and dominant models. It is a robust procedure against the genetic models.

Usage

nmax3(y, g)

Arguments

y

a numeric vector of the observed quantitative trait values in which the ith element is the trait value of the ith subject.

g

a numeric vector of the observed genotype values (0, 1, or 2 denotes the number of risk alleles) in which the ith element is the genotype value of the ith subject for a biallelic SNP. g has the same length as y.

Details

Under the null hypothesis of no association, the vector of the three nonparametric tests under the recessive, additive, and dominant models asymptotically follows a three-dimensional normal distribution. The p-value can be calculated using the function pmvnorm in the R package "mvtnorm".

This test is different from the MAX3 test using in the function max3. On one hand, the NMAX3 applies to the quantitative traits association studies. However, the MAX3 is used in the case-control association studies. On the other hand, the NMAX3 is based on the nonparametric trend test. However, the MAX3 is based on the Cochran-Armitage trend test.

Value

A list with class "htest" containing the following components:

statistic
			the observed value of the test statistic.
p.value
			the p-value for the test.
alternative
			a character string describing the alternative hypothesis.
method
			a character string indicating the type of test performed.
data.name
			a character string giving the names of the data.

Author(s)

Lin Wang, Wei Zhang, and Qizhai Li.

References

Lin Wang, Wei Zhang, and Qizhai Li. AssocTests: An R Package for Genetic Association Studies. Journal of Statistical Software. 2020; 94(5): 1-26.

W Zhang and Q Li. Nonparametric Risk and Nonparametric Odds in Quantitative Genetic Association Studies. Science Reports (2nd revision). 2015.

B Freidlin, G Zheng, Z Li, and JL Gastwirth. Trend Tests for Case-Control Studies of Genetic Markers: Power, Sample Size and Robustness. Human Heredity. 2002; 53:146-152.

WG Cochran. Some Methods for Strengthening the Common Chi-Square Tests. Biometrics. 1954; 10:417-451.

P Armitage. Tests for Linear Trends in Proportions and Frequencies. Biometrics. 1955; 11:375-386.

Examples

g <- rbinom(1500, 2, 0.3)
y <- 0.5 + 0.25 * g + rgev(1500, 0, 0, 5)
nmax3(y, g)