genomic inflation factor and how to use it to estimate adjusted P-values in GWAS?

Question

[Ana]

Hi all, I have 3 questions regarding genomic inflation factor and how to use it to estimate adjusted p-value. I would appreciate any help. I am running genotype environment association analysis by using latent factor mixed model (LFMM). I am using this to estimate genomic inflation factor:

lambda = median(z.scores^2)/qchisq(1/2, df = 1)

This is a very naive question, please forgive me, but why df should be 1? I thought it should be the number of genetic cluster that I have in my data-set!

Second I am using the lambda value to adjust the P-values:

adjusted.p.values = pchisq(z.score^2/lambda, df = 1, lower = F)

Again here, df should be 1 or it should be the number of population clusters that I have in my data (K = 3)?

By the way, when I estimate lambda according to the above algebra, I am getting low values (0.3-0.4), this means p_values are deflated! What can cause such a Low inflation factors?

Answer 1

[Fabio Marroni]

1) The number of df is 1 because in the original work Devlin and Roeder (Biometrics, 1999) observed that the best estimator of lambda is obtained by dividing the median of the test statistics by 0.675^2 which incidentally is 0.455 which is the median of the chi-square distribution with one degree of freedom. This is what I found in this paper, I guess there is much more literature around. Googling "lambda inflation factor" or "lambda genomic control" should lead you to interesting results.

2) Your value of lambda is indeed very low, I never saw such a low value. Can you share the qqplot of your data? They should also show a strong deflation. What software are you using for LFMM? I am not very expert on that, but I noticed that the R function lfmm_test is automatically calibrating the results by genomic control.