<p>Those odds ratio aren't calculated from the raw allele frequencies. They're calculated from coefficients estimated from complex linear models with a bunch of covariates that are run on subsets of the data then meta-analysed together. </p>

<p>It is a bit surprising that the odds ratio is less than one when the frequency is higher in cases, but the p-value indicates that the OR is not significantly different from 1 so it may be down to statistical noise. It's possible that within populations one allele is more common in cases than in controls but that cases are primarily sampled from populations where that allele is uncommon, causing it to be more common in controls overall.  See <a href="https://en.wikipedia.org/wiki/Simpson%27s_paradox" rel="nofollow noreferrer">here</a>. Alternatively, 1/0.98 is pretty close to the value you calculated, so it's possible that the reference allele got switched around at some point.</p>

CC BY-SA 4.0
2018-07-11T23:38:28.293Z
2018-07-12T00:04:53.140Z
2018-07-12T00:04:53.140Z
heathobrien
<p>Posting here because the reddit thread I made didn't gain any traction. </p>

<p>I'm having a little bit of trouble understanding how the odds ratio was calculated in this table, specifically the OR marked in red:</p>

<p><a href="https://i.sstatic.net/nQYVo.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/nQYVo.png" alt="enter image description here"></a></p>

<p>To my understanding, an odds ratio = $$[(\text{# of cases with exposure}) / (\text{# of controls with exposure})] / [(\text{# of cases without exposure}) / (\text{# of controls without exposure})]$$</p>

<p>In the red-highlighted case, my odds ratio is</p>

<p>$$(0.661 / 0.6580) / [(1-0.661) / (1-0.6580)] = 1.0134$$</p>

<p>which is very off from $0.98$. Also, I know I'm using frequencies rather than absolute counts, but it shouldn't matter because if I were to multiply each frequency by the corresponding population values, all the population values would cancel out.</p>

<p>So, what have I done wrong?</p>

<p><a href="https://doi.org/10.1016/j.cell.2018.05.046" rel="nofollow noreferrer">Link to the paper</a></p>

<gwas>
Odds ratio calculations in GWAS paper
# Odds ratio calculations in GWAS paper

(Asked by: username_0 on 2018-07-11)

Posting here because the reddit thread I made didn't gain any traction.

I'm having a little bit of trouble understanding how the odds ratio was calculated in this table, specifically the OR marked in red:

[![enter image description here](https://i.sstatic.net/nQYVo.png)](https://i.sstatic.net/nQYVo.png)

To my understanding, an odds ratio = $$[(\text{# of cases with exposure}) / (\text{# of controls with exposure})] / [(\text{# of cases without exposure}) / (\text{# of controls without exposure})]$$

In the red-highlighted case, my odds ratio is

$$(0.661 / 0.6580) / [(1-0.661) / (1-0.6580)] = 1.0134$$

which is very off from $0.98$. Also, I know I'm using frequencies rather than absolute counts, but it shouldn't matter because if I were to multiply each frequency by the corresponding population values, all the population values would cancel out.

So, what have I done wrong?

[Link to the paper](https://doi.org/10.1016/j.cell.2018.05.046)

**Tags:** gwas

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## 1 answers

### Answer by username_1 on 2018-07-11. Score: 2 | Accepted answer

Those odds ratio aren't calculated from the raw allele frequencies. They're calculated from coefficients estimated from complex linear models with a bunch of covariates that are run on subsets of the data then meta-analysed together.

It is a bit surprising that the odds ratio is less than one when the frequency is higher in cases, but the p-value indicates that the OR is not significantly different from 1 so it may be down to statistical noise. It's possible that within populations one allele is more common in cases than in controls but that cases are primarily sampled from populations where that allele is uncommon, causing it to be more common in controls overall. See [here](https://en.wikipedia.org/wiki/Simpson%27s_paradox). Alternatively, 1/0.98 is pretty close to the value you calculated, so it's possible that the reference allele got switched around at some point.


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