Diagnostic for fine-mapping with summary
statistics
Yuxin Zou
2022-09-05
This vignette demonstrates diagnostic plot for consistency between
summary statistics and reference LD matrix.
The susie_rss assumes the LD matrix accurately estimate
the correlations among SNPs from the original GWAS genotype data.
Typically, the LD matrix comes from some public database of genotypes in
a suitable reference population. The inaccurate LD information leads to
unreliable fine-mapping result.
The diagnostic for consistency between summary statistics and
refenrence LD matrix is based on the RSS model under the null with
regularized LD matrix. \[
\hat{z} | R, \lambda \sim N(0, (1-\lambda)R + \lambda I),
0<\lambda<1
\] The parameter \(\lambda\) is
estimated by maximum likelihood. A larger \(\lambda\) means a greater inconsistency
between summary statistics and the LD matrix. The expected z score is
computed for each SNP, \(E(\hat{z}_j |
\hat{z}_{-j})\), and plotted against the observed z scores.
library(susieR)
library(curl)
LD information from the reference panel
We use another simulated data where the LD matrix is estimated from a
reference panel. There is one signal in the simulated data (red point).
There is one SNP with mismatched reference and alternative allele
between summary statistics and the reference panel (yellow point).
data_file <- tempfile(fileext = ".RData")
data_url <- paste0("https://raw.githubusercontent.com/stephenslab/susieR/",
"master/inst/datafiles/SummaryConsistency1k.RData")
curl_download(data_url,data_file)
load(data_file)
zflip = SummaryConsistency$z
ld = SummaryConsistency$ldref
n=10000
b = numeric(length(zflip))
b[SummaryConsistency$signal_id] = zflip[SummaryConsistency$signal_id]
plot(zflip, pch = 16, col = "#767676", main = "Marginal Associations",
xlab="SNP", ylab = "z scores")
points(SummaryConsistency$signal_id, zflip[SummaryConsistency$signal_id], col=2, pch=16)
points(SummaryConsistency$flip_id, zflip[SummaryConsistency$flip_id], col=7, pch=16)
Using the data with misaligned allele, SuSiE-RSS identifies a true
positive CS containing the true effect SNP; and a false positive CS that
incorrectly contains the mismatched SNP.
fit = susie_rss(zflip, ld, n=n)
susie_plot(fit, y='PIP', b=b)
points(SummaryConsistency$flip_id, fit$pip[SummaryConsistency$flip_id], col=7, pch=16)
The estimated \(\lambda\) is
lambda = estimate_s_rss(zflip, ld, n=n)
lambda
# [1] 0.005005011
In the diagnostic plot, the mismatched SNP shows the largest
difference between observed and expected z-scores, and therefore appears
furthest away from the diagonal.
condz = kriging_rss(zflip, ld, n=n)
condz$plot
After fixing the allele encoding, SuSiE-RSS identifies a single true
positive CS containing the true-effect SNP, and the formerly mismatched
SNP is (correctly) not included in a CS.
z = zflip
z[SummaryConsistency$flip_id] = -z[SummaryConsistency$flip_id]
fit = susie_rss(z, ld, n=n)
susie_plot(fit, y='PIP', b=b)
