Can't fit generalized Pareto distribution because all tail values are the same.

[yfeiiii]

Hi, I got warnings when fitting results. Although I got 50 warning messages, all were: "Can't fit generalized Pareto distribution because all tail values are the same."

I still could get summary(res) ,which was significant.

p-value testing that causal model is a better fit: 0.007 Posterior medians and 95 % credible intervals: model gamma eta q [1,] "Sharing" NA "0 (-0.12, 0.12)" "0.07 (0, 0.31)" [2,] "Causal" "0 (-0.12, 0.12)" "0 (-0.12, 0.12)" "0.07 (0, 0.31)"

elpd were:

model1 model2 delta_elpd se_delta_elpd z p 1 null sharing 5.2e-13 3.4e-14 15.0 1.000 2 null causal 4.7e-13 3.4e-14 14.0 1.000 3 sharing causal -4.2e-14 1.7e-14 -2.5 0.007

And I tried

res$loos[[2]]

Does this mean the significant results were not reliable?

Thanks!

YF

[jean997]

Hello! I have occasionally seen warnings for the Pareto k diagnostic values but it is suspicious to me that 84% are in the very bad category. It seems like something may be odd with your data. I've never seen the "tail values are the same" warning which I think may also point to something in your data. Can you give me more information about the source of the data and how you created it?

[yfeiiii]

Hello! I have occasionally seen warnings for the Pareto k diagnostic values but it is suspicious to me that 84% are in the very bad category. It seems like something may be odd with your data. I've never seen the "tail values are the same" warning which I think may also point to something in your data. Can you give me more information about the source of the data and how you created it?

Hi,

I guess I found the reason might be there is not enough statistical power. Thank you

[jean997]

I would be surprised if that was the explanation -- at least I have not seen this when I did tests with simulated low power GWAS. How many variants did you use for the parameter calculation step and how many did you use for the posterior fitting step?

[yfeiiii]

Sorry for the late reply. After several times of trying, LD clumping step I used for the CAUSE ranging from 24 to 1921.(using r2= 0.01, kb = 1000kb, value = 5e-5), same as I used for other MR methods, i.e., MBE, MR-EGGER. As most of the models were insignificant in CAUSE while significant for MBE and MR-EGGER, I am wondering how many variants are enough for CAUSE analysis.

Thank you so much!

[jean997]

I usually recommend to use a genome-wide set of LD-pruned SNPs for parameter estimation and down to a p-value of 1e-3 for model fitting. The model fit should not be too sensitive to the p-value threshold. If you are finding that it is, that could indicate something unusual.