rare/common variants • Assume • Formulation • Assume and , where F() is a arbitral distribution. • Correlation of coefficients: and • Test hypothesis: • Score test for • should be pre-specified • Iuliana et al. (2013) recommend to use → and have same variance Other covariates Genotype vector of rare variants Genotype vector of common variants Yi = ↵0 + Xi↵ + Grare i 1 + Gcommon i 2 + " " ⇠ N(0, 2) 2j ⇠ F(0, w2 2j ⌧) 1j ⇠ F(0, w2 1j (1 )⌧) H0 : 1 = 2 = 0 , H0 : ⌧ = 0 cor( 1j, 1k) = ⇢1 cor( 2j, 2k) = ⇢2 ⌧ = 0 Q( , ⇢1, ⇢2) = (1 )Qrare + Qcommon ⇠ Mixture of 2 1 = SD(Qrare) SD(Qrare) + SD(Qcommon) (1 )Qrare Qcommon