Question: Is it valid to call this an "empirical p-value" ?
gravatar for Vincent Laufer
4.2 years ago by
Vincent Laufer1.1k
United States
Vincent Laufer1.1k wrote:

There is a well-known paper in the autoimmune disease literature that describes an algorithm called probabilistically identified causative SNPs, or PICS.

The paper identified ~9,000 PICS based on a posterior probability that the SNP is a true causal variant rather than a neutrally associated variant. I trimmed this to 1,865 LD independent PICS.

I wanted to see if the PICS were enriched for having p-values below a certain threshold in our lab's GWAS data. I could have set this up as an exact binomial test using the threshold as the probability of success, but this is problematic for a lot of reasons. For instance, although the genomic inflation in our study is well-controlled (lambda GC = 1.03), that still indicates a slight enrichment of lower p-values.

For this reason and many others, I think such an exact binomial test is a weak comparison and is likely to have a very high type I error rate. So, I searched for a more rigorous comparison.

Without going into substantial detail, after a lot of work I think a more appropriate test is to compare the association p-values of the PICS (from our study) to p-values of "SNPs like them" (e.g., SNPs that have similar numbers of nearby genes, or similar numbers of exonic variants, etc. etc.).

So, using SNPsnap I generated a list of 87,000 SNPs having characteristics matching those of the PICS. I call them "matched SNPs."

I then drew random samples of 1865 from from the ~87000 in the matched SNP list and compared the number of times the matched SNPs had more variants with an association p-value below the threshold than the PICS. I did this 100,000 times, and each time the matched SNP sample had more SNPs below the threshold than the PICS SNPs, I recorded this.

So, if 4650 of the 100,000 samples from the matched set had more SNPs below the p-value threshold than the PICS set, then I am saying p = 0.04650 and calling that an "empirical p-value."

I do not call this a permutation based test anywhere, because I have not scrambled any case-control statuses or anything like that. However I am thinking of calling it a "simulation test." Also, I would like to ask if it is valid to call this an "empirical p-value," and if not, I am unsure what to call it.

My question is, does either of these terms carry with it a denotation that would make it inaccurate to use that term in the above context?

ADD COMMENTlink modified 4.2 years ago by Devon Ryan96k • written 4.2 years ago by Vincent Laufer1.1k
gravatar for Devon Ryan
4.2 years ago by
Devon Ryan96k
Freiburg, Germany
Devon Ryan96k wrote:

Your general strategy sounds reasonable and yes this is an empirical p-value (do mention the simulation in the methods!). The appropriateness of the result is dependent on how "similar" the simulated data was, so I hope you put a good deal of thought into that. Regarding the p-value itself, that's the correct value assuming none of the simulations returned the exact same number of SNPs below threshold, since those should be included too.

Edit: Apparently there's an argument to be made that 1 should be added to the numerator and denominator when calculating the p-value. I've never thought about it, but it seems reasonable at first read.

ADD COMMENTlink modified 4.2 years ago • written 4.2 years ago by Devon Ryan96k

Devon - thank you so much for taking the time to write a response to my post. I will read the linked paper and I appreciate that.

As for the comment "The appropriateness of the result is dependent on how "similar" the simulated data was, so I hope you put a good deal of though in that." Yes, I agree completely. Also, the reasons for that are articulated in the manuscript. Ultimately this whole analysis was an attempt to be more rigorous rather than less, so I hope I have succeeded in that to some degree.

This is perhaps a separate issue, but I am also weary of using the term Monte Carlo. Monte Carlo samples must be mutually independent, I think. But in my case I have 100,000 samples of 1865 variants from a list of 87000. As such, many of the samples contain overlapping variants and are therefore not strictly independent from one another. Practically, I am not very worried about this, as I expect each sample to have relatively little dependence on the next, but I am just trying to be cautious.

Thanks again.

ADD REPLYlink written 4.2 years ago by Vincent Laufer1.1k

@Devon Ryan - this paper is very helpful as well and also addresses sampling with and without replacement. It is also written specifically for genomicists / bioinformaticians.

ADD REPLYlink written 4.2 years ago by Vincent Laufer1.1k
Please log in to add an answer.


Use of this site constitutes acceptance of our User Agreement and Privacy Policy.
Powered by Biostar version 2.3.0
Traffic: 1009 users visited in the last hour