Statistical tests for detecting associations with groups of genetic variants: generalization, evaluation, and implementation

Abstract

With recent advances in sequencing, genotyping arrays, and imputation, GWAS now aim to identify associations with rare and uncommon genetic variants. Here, we describe and evaluate a class of statistics, generalized score statistics (GSS), that can test for an association between a group of genetic variants and a phenotype. GSS are a simple weighted sum of single-variant statistics and their cross-products. We show that the majority of statistics currently used to detect associations with rare variants are equivalent to choosing a specific set of weights within this framework. We then evaluate the power of various weighting schemes as a function of variant characteristics, such as MAF, the proportion associated with the phenotype, and the direction of effect. Ultimately, we find that two classical tests are robust and powerful, but details are provided as to when other GSS may perform favorably. The software package CRaVe is available at our website (http://dceg.cancer.gov/bb/tools/crave).

Figure 1

The power (y-axis) to detect an association between a gene with 40-independent SNPs and a disease is illustrated for four different test statistics (ROV, HOI, MDF, SUM), as a function of the number (x-axis) of those SNPs that increase disease risk.

Figure 2

The power (y-axis) to detect an association between a gene with 40-independent SNPs and a disease is illustrated for four different test statistics (MDF+, MDF, STZ+, STZ), as a function of the proportion (x-axis) of the 10-associated SNPs that reduce disease risk. The remaining associated SNPs increase risk.

Figure 3

The lines illustrate the number of SNVs that need to be influential in order for the SUM test to have higher power than the MDF test, as a function of the total number of independent SNVs in the tested region. Results are based on simulations where SNVs have MAF equally spaced between 0.005 and 0.02, and the influential SNVs are randomly distributed, have equal effect size, and increase risk. The effect size (β in equation (15)) was chosen so the MDF test had a specified power: 0.2 (brown), 0.5 (red), or 0.8 (orange).