andrew-slater
commented
9 years ago Upon further investigation, we observe Rsq values in minimac output are ~double what are produced by this formula and can be > 1. We can approximate these values using raw dose (not scaled) as counts and multiplying the denominator by 2 (9e1bff516f39250bf8a767f820e32418f75f7832):
#Calculate rsq - need to confirm this formula
xbar <- colMeans(dose[,-c(1,2)])
x2bar <- colMeans((dose[,-c(1,2)])^2)
#Rounding to 5 to match minimac output
info.df$Rsq = round((x2bar - xbar^2)/(2*(xbar/2)*(1-xbar/2)),5)
#Replacing NaNs due to division by 0 when xbar is 0 with 0
info.df$Rsq[is.na(info.df$Rsq)] = 0This formula does not give the exact same values as minimac since minimac calculates at the haplotype level, not genotype (per Toby).
The same relationship with Hardy-Weinberg equilibrium stands: Rsq 1 is perfect equilibrium. As doses deviate towards excess of hets, Rsq decreases towards 0. As doses deviate towards an excess of homozygotes, Rsq increases towards 2.
sks2772
Based on minimac formula, seems Rsq ranges from 0-1 if the "Counts" in the numerator are the doses divided by 2 to scale from 0-1 (0 for homozygote Al2, 0.5 for het, and 1 for homozygote Al1) and p is the allele frequency (Freq1 which is the mean of the doses divided by 2). This is the formula currently (45cb8a544af85c13fbf88c57df00b8adb1e93f1d) used:
With these conditions, when the genotypes are in perfect Hardy-Weinberg equilibrium, Rsq is 0.5. As they deviate towards an excess of hets, Rsq decreases towards 0. As they deviate towards an excess of homozygotes, Rsq increases towards 1.
Note, the statement as of the 31 January 2013 instance of the minimac wiki page referenced above, "poorly imputed genotype counts will shrink towards their expectations based on population allele frequencies alone," is somewhat confusing. It implies perfect Hardy-Weinberg equilibrium (Rsq 0.5) indicates a poorly imputed variant and deviations from this (Rsq greater than or less than 0.5) indicate higher quality imputation. The statement in Li et al 2009, "imputed allele counts for poorly imputed markers show less variability than expected based on allele frequency," is clearer. It implies that imputation quality decreases as the doses deviate from Hardy-Weinberg equilibrium (Rsq 0.5) towards an excess of hets (Rsq < 0.5). This aligns with the commonly used exclusion criteria of Rsq < 0.3.