Question: Caclulate effect estimates and SE from Z scores
gravatar for muralinmars
3.9 years ago by
muralinmars80 wrote:


I am using a post-gwas analysis tools to test genetic overlap between different traits based on summary level data, and it requires the effect size(beta) and SE.

So for summary stats that has the Z score measures, beta and SE are estimated by using the following formula that was published in a large scale study on Alzheimers.



  • VP: phenotypic variance approximated to 1;
  • ES: effective sample size
  • pq: allele frequencies (p allele, q allele)
  • Z: Z scores

The summary stats that I currently have access to does not have allele frequency information.

head of the summary stats:

> Chr     Pos     MarkerName      EffectAllele    OtherAllele     Z    P.value TotalSampleSize 
> 1       744055  rs3131000               a           g         -1.60      0.10  23546

Is there a way to calculate the Betas and SE without contacting the study, with just relying on the information that is currently publicly available.

R meta-analysis gwas • 5.7k views
ADD COMMENTlink modified 12 months ago by atlas.akhan0 • written 3.9 years ago by muralinmars80

Hi, Would it be possible to send the link of the Alzheimers paper you found the equation in please?

ADD REPLYlink written 3.4 years ago by RLady0

I am somewhat pressed for time but it's not 100% clear which data-points you have. Please take a look here and see if you can work back from the Z-score calculation: A: SNP dataset and Z Score

Do you have the allele tallies?

ADD REPLYlink written 2.6 years ago by Kevin Blighe69k
gravatar for atlas.akhan
12 months ago by
atlas.akhan0 wrote:

You can use this equation:

Beta = z / sqrt(2p(1− p)(n + z^2)) and

SE =1 / sqrt(2p(1− p)(n + z^2))

Where p is the frequency of the imputed SNP, you could use out reference panel to calculate p. For reference please go to

ADD COMMENTlink written 12 months ago by atlas.akhan0
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