Genome-wide association studies (GWASs) in identifying the disease-associated genetic variants have been proved to be a great pioneering work. Two-stage design and analysis are often adopted in GWASs. Considering the genetic model uncertainty, many robust procedures have been proposed and applied in GWASs. However, the existing approaches mostly focused on binary traits, and few work has been done on continuous (quantitative) traits, since the statistical significance of these robust tests is difficult to calculate. In this paper, we develop a powerful -statistic-based robust joint analysis method for quantitative traits using the combined raw data from both stages in the framework of two-staged GWASs. Explicit expressions are obtained to calculate the statistical significance and power. We show using simulations that the proposed method is substantially more robust than the -test based on the additive model when the underlying genetic model is unknown. An example for rheumatic arthritis (RA) is used for illustration. 1. Introduction Genome-wide association studies (GWASs) have identified a large number of genomic regions (especially single-nucleotide polymorphisms (SNPs)) with a wide variety of complex traits/diseases. In a GWAS, two most common types of data, qualitative (or binary) and quantitative (or continuous) traits, are analyzed and two contentious points are often faced; one is how to construct the test statistic considering the genetic model uncertainty and the other is how to evaluate the statistical significance for controlling the false positive rates efficiently (e.g., [1, 2]). Considering these issues, a lot of work has been done on the binary trait in the past 10 years (e.g., [3–7]). Computer algorithms have also been developed to calculated the significance level of robust tests in GWASs, taking into account the genetic model uncertainty [8]. However, few work has been done on continuous traits, only recently So and Sham [9] proposed a MAX3 based on score test statistics, and Li et al. [10] gave a MAX3 based on -test statistics. Note that these tests just focus on single-marker analysis in one-stage analysis. Although the costs of whole-genome genotyping are decreasing with the high-throughput biological technology, the total costs for a GWAS are still very expensive due to the thousands of sampling units and huge amounts of single-nucleotide polymorphisms. In order to save the costs, the two-stage design and the corresponding statistical analysis where all the SNPs are genotyped in Stage 1 on a portion of the samples and the promising
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