Caclulate effect estimates and SE from Z scores

Question

[muralinmars]

Hi,

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.

SE~=sqrt(VP/(ES×2pq))
    Beta=SE×Z

where:

• 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.

[RLady]

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

[Kevin Blighe]

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?

Answer 1

[atlas.akhan]

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

https://images.nature.com/full/nature-assets/ng/journal/v48/n5/extref/ng.3538-S1.pdf