Seeking advice about error: XtX is not a symmetric matrix

[Jesson-mark]

Hi everyone, I'm using mvSuSiE to do fine-mapping for two highly correlated traits (rg=0.6, estimated by LDSC) in UKBB at one 1Mb region.

Before running mvSuSiE , I performed the single-trait fine-mapping using SuSiE for each of the two traits at the same region and got some credible sets for these two traits.

Then I want to perform multi-trait fine-mapping for these two traits. I followed the vignette to prepare inputs for mvSuSiE. Using the criteria: INFO<0.9, MAF<0.01 and P < 1, I got 2636 SNPs in this region and extracted in-sample LD for these SNPs. Then I used the prior as specified in the vignette, with the code:

prior <- create_mixture_prior(list(matrices = simdata$par$U,
                                    weights = simdata$par$w),
                                null_weight = 0)

As for the estimate of residual variance, I also followed the codes in that vignette:

null_markers <- which(apply(abs(Z),1,max) < 2)
length(null_markers)

Z_null <- Z[null_markers,]
Vest <- cov(Z_null)
Vest

These codes filtered 922 null markers and the Vest is:

          trait1    trait2
trait1 1.6847297 0.4521737
trait2 0.4521737 0.8353627

Then I used the following codes to run mvSuSiE:

num_snps <- nrow(df) # number of snps used to perform fine-mapping
R <- load_R(ldfile, num_snps = num_snps) # load LD matrix

N <- 450000
tolerance <- 0.01

fit_rss <- mvsusie_rss(Z = Z, R = R, N = N,
                       prior_variance = prior,
                       residual_variance = Vest,
                       estimate_prior_variance = TRUE,
                       tol = tolerance)

However, mvsusie_rss exited with an error: Error in initialize(...) : XtX is not a symmetric matrix.

Does anyone could give some advice about why this error occured?

Any advice will help! Thanks for your reply!

[Jesson-mark]

Hi everyone, I have resolved the error above and figured out the reason. It is because the rownames and colnames of LD matrix are not same.

However, I have another question about the esidual variance matrix. I noticed that in your preprint paper, the esidual variance matrix of UKBB is estimated using 1,950 SNPs (2 SNPs with small z-scores were selected from each of the 975 fine-mapping regions). Is there only 2 SNPs at each region with small z-scores or you just selected 2 SNPs with the two smallest z-scores among each region?

I wonder if one could use all genome-wide SNPs with small z-scores (e.g. absolute z-score less than 1 or 2) or all SNPs with z-scores equaling to zero to estimate the esidual variance matrix. I also wonder if there is a suggestive minimum number of SNPs that could give an reasonable estimate of the esidual variance matrix.

Any advice will help! Thanks for your reply!