# How to interpret false positive from QQ-plot in genome-wide association studies?

I am doing SNP association study, and the estimated p-values for each SNP are plotted as a QQ-plot. The question is, can one interpret false positive hits from a QQ-plot in GWAS (Genome-Wide Association Study)?

"...on the other hand, should show a solid line matching X=Y until it sharply curves at the end (representing the small number of true associations among thousands of unassociated SNPs)"

Is this always true, or may False Positive also deviate sharply at the end of the curve? How to tell from a QQ-plot if a deviation is because of a true association or a false association?

Under the null hypothesis, your p-values should adhere to a uniform distribution (I'm ignoring some issues with dependencies here, as they are not really relevant to the discussion). This includes the false positives: just by coincidence, you should get a few extreme p-values, but since this is exactly what is in the expected distribution, this will not distort the QQ-plot: false positives are already accounted for in this type of QQ-plot.

On the other hand, if some SNPs were tested where the null hypothesis is not true, typically this should show up as a lower p-value than expected, and these will indeed distort the image.

What the author of the article you link seems to mean is: if you have wicked strong distortion, there are unexpectedly (as per the uniform distribution) many extreme p-values, so something is likely to be wrong.

So, in short: a uniform QQ-plot of p-values (like this) should show relatively little digression from the straight line, and only in the extremely low p-values (showing you have more low p-values than if the null hypothesis were true everywhere).

• Thank you for your answer! If p-values of 0.01 and lower deviates from the expected distribution one can conclude that those p-values are very likely to be true positive? Commented Mar 14, 2013 at 13:29
• As much as everybody would like it, there is no such thing as a threshold for this, so I cannot make statements on whether 0.01 will work: you need (the relevant) multiple testing correction for this, which will depend on your design. Even then: I eschew using the results from a single GWAS without individual confirmation. Commented Mar 14, 2013 at 13:37
• Is it possible, to somehow estimate the possible number of "False Hits" from the deviated p-values on a QQ-plot? Commented Mar 17, 2013 at 11:34