Description Usage Arguments Details Value Author(s) References Examples

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.

1 | ```
nmax3(y, g)
``` |

`y` |
a numeric vector of the observed quantitative trait
values in which the |

`g` |
a numeric vector of the observed genotype values ( |

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.

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. |

Lin Wang, Wei Zhang, and Qizhai Li.

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.

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