From this analysis, we can also estimate both the variance due to measurement error and variance explained by the GRS in the absence of measurement error, as follows. Let B = observed BP measurement, G = the GRS, E = residual genetic and environmental effect on BP, M = component of BP due to measurement error, and k = number of BP measurements. We assume that the measurement error is independent across multiple measures within an individual, and the additive model B=G+E+Mk for the average of k BP measurements. Let VB=Var(B), VG=Var(G), VE=Var(E), and VM=Var(M). For k BP measurements with independent measurement error, VMk=VM/k. The proportion H of BP variance attributable to the GRS is VG/(VG+VE+VM/k). Then 1/H = (1+VE/VG)+(VM/VG)/k=α+β(1/k) where α=1+VE/VG and β=VM/VG. We thus have a linear model of 1/H in terms of 1/k, and 1/α=VG/(VG+VE) is the proportion of variance due to the GRS in the absence of measurement error, and β/(α+β) is the proportion of variance in BP due to measurement error. Fitting a linear regression model to 1/H as a function of 1/k, we can
