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 beenidentified and high-throughput genotyping technologies havebeen rapidly developed, large-scale genomewide association studiesare soon within reach. However, since a genomewide associationstudy involves a large number of SNPs it is therefore nearlyimpossible to ensure a genomewide significance level of 0.05using the available statistics, although the multiple-test problemscan be alleviated, but not sufficiently, by the use of taggingSNPs. One strategy to circumvent the multiple-test problem associatedwith genome-wide association tests is to develop novel teststatistics with high power. In this report, we introduce severalnonlinear tests, which are based on nonlinear transformationof allele or haplotype frequencies. We investigate the powerof the nonlinear test statistics and demonstrate that undercertain conditions, some nonlinear test statistics have muchhigher power than the standard Formula

-test statistic. Type I error rates of the nonlinear tests are validatedusing simulation studies. We also show that a class of similaritymeasure-based test statistics is based on the quadratic functionof allele or haplotype frequencies, and thus they belong tononlinear tests. To evaluate their performance, the nonlineartest statistics are also applied to three real data sets. Ourstudy shows that nonlinear test statistics have great potentialin association studies of complex diseases.