Hi all,

I have (an imputed) GWAS that only has z-score and p-values. I want to convert z-score into beta and SE. My ultimate goal is to use log(odds ratio) with its corresponding standard error to run COJO analysis. I came across this post [Caclulate effect estimates and SE from Z scores] that describes the formula to convert z-score into SE. I tested it on a SNP whose SE I have from GWAS but answers are not matching.

Formula = SE = 1/ sqrt(2p(1− p)(n + z^2))
 zscore = z = 0.50795203
 frequency = p = 0.123274
 sample size = n = 375752

when I run the code in R, it gives

> SE = 1/sqrt((2*p)*(1-p)*(n+z^2))  
> SE
 [1] 0.003508864

However, the real SE as in my GWAS is 0.0252602590 and beta is 0.012831. A snippet from my GWAS is

    variant_id  panel_variant_id    chromosome  position    effect_allele   non_effect_allele   current_build   frequency   sample_size zscore  pvalue  effect_size standard_error  imputation_status   n_cases
    rs143225517 chr1_816376_T_C_b38 chr1            816376                 C    T                   hg38            0.123274    375752      0.50795203   0.611487 0.012831  0.025260259097695255    original  59674.0 

I am not sure where I am going wrong. Can anyone please point me in right direction?