Statistical analysis strategies for association studies involving rare variants.

Sample size requirements and statistical power for variants of different frequencies(A). Sample sizes necessary to detect an association between an allele with a specific effect size and a binary trait. The plots assume a standard z-test for the difference in the frequency of the allele between the two phenotypic categories. A genome-wide type I error rate of 10−9 was assumed, under the assumption that one may perform 2 orders of magnitude more tests in a complete sequence-based GWAS than a standard GWAS. (B). Similar setting to that provided in Figure 1A except the effect size depicted on the x axis gives the ratio of the frequency of the allele in the case vs. control groups. These curves give insight into the power gains associated with the collapsing strategy. Consider the black line in Figure 1B and testing a single rare variant with a frequency of 0.01 in the controls and 0.02 in the cases. This difference would require approximately 250,000 cases and controls to detect with 80% power at a super genome-wide level of significance. However, if one were to test 5 such variants with the same frequencies after collapsing them (assuming they are independent and no individual has more than one such variant), then one would effectively be testing a 0.05 frequency among the controls and a 0.10 frequency among the cases. From the red line in Figure 1B this difference would require only 3000 cases and controls. (C). Power to detect a quantitative trait locus with a sample of 1000 individuals as a function of fraction of phenotypic variation explained by the locus via standard linear regression analysis. A genome-wide type I error rate of 10−9 was assumed.

Scenarios in which DNA sequence variants distinguish cases and controlsBlue lines indicate genomic regions; red boxes indicate variants. A. Variants at a single locus with common alleles are more frequent in cases then controls. B. Multiple rare variations contribute to the phenotype such that the collective frequency of these variations is greater in cases. This would create a greater diversity of haplotypes or DNA sequences among the cases. C. Multiple rare variations contribute to the phenotype, but act in a synergistic fashion such that cases are likely to have more similar DNA sequences compared to controls. D. Multiple rare variations contribute to a phenotype, but the variations contributing to the phenotype reside in specific genomic regions. This situation would create greater sequence diversity among the cases, as in setting B, but only within the genomic regions of relevance.