enrichment_z does not equal to enrichment_mean/enrichment_se?

[WeiCSong]

Hi, From the output of module 8, I found that column enrichment_z does not equal to enrichment_mean/enrichment_se, does that mean that Z score is derived by a different method? How should the significance of enrichment be defined? Thanks for your help!

[danjweiner]

Hi there -- that's correct, enrichment_z = (enrichment_mean - 1)/(enrichment_se) (see line 99 of the code for AMM.py).

This is because the enrichment_z is relative to a null that enrichment_mean = 1, i.e. there is nothing interesting about your gene set. For example, if enrichment_mean = 2 and enrichment_se = 0.5, then enrichment_z should be equal to 2. I will add a note in the README about this.

Hope that helps!

[WeiCSong]

Thanks for your help! I'm a bit confused--usually we log-transformed the OR into a normal distribution where z score makes sense. For example, the opposite of enrichment=2 should be enrichment=0.5, but calculating enrichment-1/se would get asymmetric z for 2 and 0.5. Does that mean that the "enrichment" in AMM follows normal distribution in the >1 half, and the <1 half is meaningless and is simply ignored?

[danjweiner]

Thanks for asking -- while a log scale could be used, linear has the advantage of compatibility with negative estimates of heritability. Linear scales are used in other LD score-based publications as well. As to the question of interpretability, the linear scale implies greater power to discover a 2x enrichment than a 0.5x depletion, which is how we interpret in this context. Hope that helps!

[WeiCSong]

Got it, thanks!