Signal-noise ratio of genetic associations and statistical power of SNP-set tests

The SNP-set analysis is a powerful tool for dissecting the genetics of complex human diseases. There are three fundamental genetic association approaches to SNR-set analysis: the marginal model fitting approach, the joint model fitting approach, and the decorrelation approach. A problem of primary interest is how these approaches compare with each other. To address this problem, we develop a theoretical platform to compare the signal-to-noise ratio (SNR) of these approaches under the generalized linear model. We elaborate how causal genetic effects give rise to statistically detectable association signals, and show that when causal effects spread over blocks of strong linkage disequilibrium (LD), the SNR of the marginal model fitting is usually higher than that of the decorrelation approach, which in turn is higher than that of the unbiased joint model fitting approach. We also scrutinize dense effects and LDs by a bivariate model and extensive simulations using the 1000 Genome Project data. Last, we compare the statistical power of two generic types of SNP-set tests (summation-based and supremum-based) by simulations and an osteoporosis study using large data from UK Biobank. Our results help develop powerful tools for SNP-set analysis and understand the signal detection problem in the presence of colored noise.