Test for a Difference in Two Odds Ratios

Testing for a statistical difference between two odds ratio estimates can be useful in determining if an association has statistically different effects in different groups or strata of a variable.  For example, maybe an association is stronger for older individuals than younger individuals.  To test for such a difference we need the odds ratio estimate (or more precisely the natural log of the odds ratio estimate, aka the beta estimate from a logistic regression) and the standard error of the log odds ratio.

If you don't have access to the primary data and need to estimate the standard error from a 95% confidence interval (95% CI), see this blog entry.  If you have forgotten how to calculate the standard error of the log odds ratio use this formula:
SE(logOR)=1n1+1n2+1n3+1n4−−−−−−−−−−−−−−−√

To test if two odds ratios are significantly different and get a p-value for the difference follow these steps:
(1) Take the absolute value of the difference between the two log odds ratios. We will call this value δ.
(2) Calculate the standard error for δ, SE(δ), using the formula:
SE21+SE22−−−−−−−−−
√

(3) Calculate the Z score for the test: z=δ/SE(δ)
(4) Calculate the p-value from the z score. The p-value can be easily calculated in R or Microsoft Excel using the below formulas.

R: P-value=2*(1-pnorm(Z))
MS Excel: P-value=2*(1-(NORMDIST(Z,0,1,TRUE)))

Is there a GWAS on that?

A great online resource to find whether a genome-wide association study (GWAS) has been published on a certain trait or disease is the National Human Genome Research Institute (NHGRI) webpage where they maintain a curated catalog of published GWAS.  Here trained curators are constantly scanning PubMed publications and other genomic resources looking for association studies linking a genomic position (usually a tagging SNP) to a disease trait of interest.  Details listed include study size, population, locus, risk allele, odds ratio, p-value, and other pertinent statistics.  Recently, the NHGRI in collaboration with the European Bioinformatics Institute (EBI) released an interactive version of the GWAS catalog called the GWAS Diagram Browser.  This provides a great way to visualize and filter many of the genome-wide significant findings from genome-wide associations studies.  Highlights include filtering by disease, time series views, and some useful downloads.

Another noteworthy resource is the HuGE Navigator GWAS Interagator.  This is a search tool similar to the NHGRI GWAS catalog, but more focused on a search terms.  Handy links are provided to other resources.  Of particular interest are links to visualize the variants in the UCSC Browser.

I am sure other GWAS resources exist as well, but these were the two main ones that first came to mind for me.  If you know other great GWAS resources capable of linking a genomic marker with a disease, please share in the comments below.