I have two datasets from genome-wide association studies. The only
information available is the odds ratio and the p-value for the first
data set. For the second data set I have the Odds Ratio, p-value and allele frequencies (AFD= disease, AFC= controls) (e.g: 0.321). I'm trying to do a meta-analysis of these data but I
don't have the effect size parameter to perform this. Is there a
possibility to calculate the SE and OR confidence intervals for each of
these data only using the info that is provided??
Thank you in advance
example:
Data available:
Study SNP ID P OR Allele AFD AFC
1 rs12345 0.023 0.85
2 rs12345 0.014 0.91 C 0.32 0.25
With these data can I calculate the SE and CI95% OR ?
Thanks
Best Answer
You can calculate/approximate the standard errors via the p-values. First, convert the two-sided p-values into one-sided p-values by dividing them by 2. So you get $p = .0115$ and $p = .007$. Then convert these p-values to the corresponding z-values. For $p = .0115$, this is $z = -2.273$ and for $p = .007$, this is $z = -2.457$ (they are negative, since the odds ratios are below 1). These z-values are actually the test statistics calculated by taking the log of the odds ratios divided by the corresponding standard errors (i.e., $z = log(OR) / SE$). So, it follows that $SE = log(OR) / z$, which yields $SE = 0.071$ for the first and $SE = .038$ for the second study.
Now you have everything to do a meta-analysis. I'll illustrate how you can do the computations with R, using the metafor package:
Note that the meta-analysis is done using the log odds ratios. So, $-0.1095$ is the estimated pooled log odds ratio based on these two studies. Let's convert this back to an odds ratio:
So, the pooled odds ratio is .90 with 95% CI: .84 to .96.