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Originally published as Genetics Published Articles Ahead of Print on July 2, 2006.
Genetics, Vol. 174, 1529-1538, November 2006, Copyright © 2006
doi:10.1534/genetics.106.060491
Nonlinear Tests for Genomewide Association Studies
Jinying Zhao*,
Li Jin
,
and
Momiao Xiong*,,1
* Human Genetics Center, University of Texas Health Science Center, Houston, Texas 77030, Laboratory of Theoretical Systems Biology, School of Life Science, Fudan University, Shanghai 200433, China and CAS-MPG Partner Institute of Computational Biology, SIBS, CAS, Shanghai 200031, China
1 Corresponding author: Human Genetics Center, School of Public Health, University of Texas Health Science Center, 1200 Herman Pressler, Houston, TX 77030.
E-mail: momiao.xiong{at}uth.tmc.edu
As millions of single-nucleotide polymorphisms (SNPs) have been identified and high-throughput genotyping technologies have been rapidly developed, large-scale genomewide association studies are soon within reach. However, since a genomewide association study involves a large number of SNPs it is therefore nearly impossible to ensure a genomewide significance level of 0.05 using the available statistics, although the multiple-test problems can be alleviated, but not sufficiently, by the use of tagging SNPs. One strategy to circumvent the multiple-test problem associated with genome-wide association tests is to develop novel test statistics with high power. In this report, we introduce several nonlinear tests, which are based on nonlinear transformation of allele or haplotype frequencies. We investigate the power of the nonlinear test statistics and demonstrate that under certain conditions, some nonlinear test statistics have much higher power than the standard 
-test statistic. Type I error rates of the nonlinear tests are validated using simulation studies. We also show that a class of similarity measure-based test statistics is based on the quadratic function of allele or haplotype frequencies, and thus they belong to nonlinear tests. To evaluate their performance, the nonlinear test statistics are also applied to three real data sets. Our study shows that nonlinear test statistics have great potential in association studies of complex diseases.
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