Genome-wide association studies have discovered a large number of genetic variants associated with complex diseases such as Alzheimer's disease. However, the genetic background of such diseases is largely unknown due to the complex mechanisms underlying genetic effects on traits, as well as a small sample size (e.g., 1000) and a large number of genetic variants (e.g., 1 million). Fortunately, datasets that contain genotypes, transcripts, and phenotypes are becoming more readily available, creating new opportunities for detecting disease-associated genetic variants. In this paper, we present a novel approach called "Backward Three-way Association Mapping" (BTAM) for detecting three-way associations among genotypes, transcripts, and phenotypes. Assuming that genotypes affect transcript levels, which in turn affect phenotypes, we first find transcripts associated with the phenotypes, and then find genotypes associated with the chosen transcripts. The backward ordering of association mappings allows us to avoid a large number of association testings between all genotypes and all transcripts, making it possible to identify three-way associations with a small computational cost. In our simulation study, we demonstrate that BTAM significantly improves the statistical power over "forward" three-way association mapping that finds genotypes associated with both transcripts and phenotypes and genotype-phenotype association mapping. Furthermore, we apply BTAM on an Alzheimer's disease dataset and report top 10 genotype-transcript-phenotype associations.
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