Fig. 1: Summary of methods under MTAR framework.
From: Multi-trait analysis of rare-variant association summary statistics using MTAR
In this illustration, the number of variants is m = 10 and the number of traits is K = 5. The degree of heterogeneity of among-variant effects is controlled by ρ1. MTAR methods are robust to various patterns of genetic effects across variants by combining variance-component test P-values from different specifications of ρ1. The degree of heterogeneity of among-trait effects is controlled by ρ2. By changing the value of ρ2, the degree of heterogeneity of among-trait effects can be weakly, moderately, or strongly dictated by genetic correlation Ckk′. By setting ρ2 = 0, iMTAR and cMTAR structures assume genetic effects become completely heterogeneous and homogeneous, respectively. MTAR methods are robust to various patterns of genetic effects across traits by combining variance-component test P-values from different specifications of ρ2. The cctP that combines the single-trait burden and SKAT tests P-values is particularly powerful when only a small number of traits are associated with the set of rare variants. The omnibus test MTAR-O that combines iMTAR, cMTAR, and cctP is robust to all the aforementioned patterns of genetic effects across traits and variants.
