Question: GWAS - approximate odds ratio and standard error
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gravatar for alessandrotestori7
23 months ago by
alessandrotestori7330 wrote:

Hello! I'm using ImpG-Summary (Pasaniuc et al, 2014) to perform genotype imputation from summary statistics. However, for each imputed SNP, I only get a z-score, while odds ratio and standard error are missing. The output file has - for each SNP - six columns: name of SNP, position of SNP, Ref allele, Alt allele, Z-score, r2pred; the higher this latter value is, the more confident one is about the result. Can I approximate Odds Ratio, effect size, and standard error somehow? Please let me know. Thanks in advance!

imputation gwas • 2.6k views
ADD COMMENTlink modified 23 months ago by Kevin Blighe48k • written 23 months ago by alessandrotestori7330

Hey, you will have to provide more information, as one can only hypothesise about the specifics of your analysis based on the current information that you've provided. For example, which imputation program have you used and in which format is your data currently?

If you are interested in obtaining odds ratios and standard errors (between 2 conditions of interest, I assume?), then the basic association test of PLINK is a good starting point: http://zzz.bwh.harvard.edu/plink/anal.shtml

ADD REPLYlink written 23 months ago by Kevin Blighe48k

Thanks Kevin for your comment, I have updated my post with more information.

ADD REPLYlink written 23 months ago by alessandrotestori7330

This is an interesting question but I do not believe that you have enough information such that you could calculate what you want. There was a similar question posted ~7 months ago: convert GWAS Zscore back to OR

If you had summary statistics prior to using ImpG-Summary, then what did these summary statistics contain?

ADD REPLYlink written 23 months ago by Kevin Blighe48k

I had summary statistics containing ref allele, alt allele, MAF in cases, MAF in controls, chisq, p-value, OR, L95, U95, ln(OR), SE of ln(OR)

ADD REPLYlink written 23 months ago by alessandrotestori7330
1

I would contact the authors. Their emails are at the beginning of the manual: http://bogdan.bioinformatics.ucla.edu/wp-content/uploads/sites/3/2013/07/ImpG_v1.0_User_Manual_31July13.pdf

From the Z-score alone, it may be difficult to calculate the OR - there is too much information missing. The formula is something like:

Z-score = ln(OR) / ln(OR StdErr)

ln is the natural log

OR StdErr is the standard error of the log odds, calculated as:

(ln(OR) - 95% CI of ln(OR)) / 1.96

I may try to work through this formula later on a scrap of paper.

ADD REPLYlink written 23 months ago by Kevin Blighe48k
1

One of the authors actually states that the imputed Z-score divided by the square root of the sample size yields the effect size (beta) under the standardized scale (i.e. when both phenotype and genotype are standardized to have mean 0 and variance 1). I already contacted them through their github repository: https://github.com/huwenboshi/ImpG/issues issue #5. Similarly in Pasaniuc & Price, 2017 (Nature Reviews Genetics)

ADD REPLYlink written 23 months ago by alessandrotestori7330

Okay, let me know what they say. I'd be interested.

It looks like we could calculate the ORs from the Z-scores but we would be making a few assumptions along the way without direct evidence.

ADD REPLYlink modified 23 months ago • written 23 months ago by Kevin Blighe48k

One thing I noticed is that in my dataset - being sample size fixed for all SNPs - SE of ln(OR) and allele frequency are well correlated, so that it is easy to approximate SE for various intervals of allele frequency. For example, all SNPs with allele frequency between 0.40 and 0.41 tend to have the same SE. I can thus obtain SE for different ranges of allele frequency starting from typed SNPs and assign it to imputed SNPs. ln(OR) is then easy to compute : z-score*SE. I guess SE is mainly a function of sample size and allele frequency

ADD REPLYlink written 23 months ago by alessandrotestori7330
2

There is a paper mentioned conversion of z-statistics back to effect size: https://www.ncbi.nlm.nih.gov/pubmed/27019110. See the online method part. Basically, beta=z/sqrt(2p(1-p)(n+sq(z)) , it requires allele frequency as well as sample size. Hopefully, this might help

ADD REPLYlink written 20 months ago by zpliu40

Sure it helps! Thanks a lot!

ADD REPLYlink written 20 months ago by alessandrotestori7330
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