Should you filter GWAS hits with high standard error? I'm trying to figure out if I should be filtering out GWAS hits that have high standard error and I'm not quite sure what to do.  It seems like it might not matter, because the standard error is used to calculate the t-statistic, which is then used to calculate the p-value.  So in a way it's already built in.  But reporting SNPs that have very high standard error doesn't seem quite right.  What's the best way to handle this?
I am curious about the relationship between your p-value (or effect sizes) and standard error. I would expect the significant signals to have smaller stand error compared to the non-significant, background signals. If this is the case, there is no need to do filter.