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June 29

“Try using zscores to build sigma, plot of number of SNPs with low zscores”

  1. plot of number of SNPs with low zscores

In this section, I am going to check how the estimated Sigma \(\hat{\Sigma}_{K}\) (correlation matrix of zscores/residule expression across genes) can affect PCO’s pvalues. Use eQTLGen zscores. Consider two \(\hat{\Sigma}\)’s. (1) \(\hat{\Sigma}_{DGN}\), computed by \(cor(\tilde{Y}_{n \times K}^{DGN})\), where \(\tilde{Y}\) is the residual expression data from DGN, n is sample size, K is gene module size. (2) \(\hat{\Sigma}_{nullz}\), computed by \(cor(\tilde{Z}_{m \times K}^{eQTLGen})\), where z is genome-wide independent null zscores from eQTLGen, m is the number of null SNPs (m is in fact much less than genome-wide, but should be sufficient?).

Since for each null SNP, we should have its zscores on all genes (or at least all genes in the module we consider), but eQTLGen doesn’t provide zscores for all genome-wide SNPs (only disease-related variants for trans-eQTLs and close-to-gene variants for cis-eQTLs). Therefore, I will first extract the common SNPs for each module. Main steps include:

  • Combine the zscores of all the significant/non-significant gene-SNP pairs in both eQTLGen cis-eQTL and trans-eQTL results.

  • For each module, extract the common SNPs that have zscores available for all genes in the module.

  • For each module, further extract the common SNPs that are “NULL SNPs”. A snp for a module is defined as a “null snp” if its z-scores for all genes in this module are below some z-score cutoff (i.e. all z-scores are small z’s").

  • Among these common null SNPs, check how many of them are independent. (Use DGN genotype ‘plink –indep-pairwise 50 5 0.2’ ??? in this case, some SNPs not included in DGN are also considered as "independent. ref panel including all eQTLGen snps?)

Version Author Date
1b79abb liliw-w 2021-06-29

Here I explain the above figure. x-axis is for each module (75), y-axis is for number of SNPs under various scenarios that can be used for computing \(\hat{\Sigma}_{nullz}\). Color is for various z-scores cutoff for defining “NULL SNPs”. The cutoff is pvalue of z. Smaller cutoff, more insignificant z. Point shape is for unique SNPs and independent SNPs. The barplot in the lower panel gives the number of genes in each module.

Observations

  1. For larger gene module, the common null SNPs (unique and independent) are fewer.

  2. The average number of the unique null SNPs is ~8000 (under pvalue of z > 0.001). The independent null SNPs is ~4000.

  3. Since we were particularly interested at eQTLGen’s module1, (as all eQTLGen trans-variants are significant for module1,) next I will focus on module1. I use the 2282 independent null SNPs (under pvalue of z > 0.001) for module1 to calculate \(\hat{\Sigma}_{nullz}(module1)\).

Build Sigma \(\hat{\Sigma}_{DGN}\) and \(\hat{\Sigma}_{nullz}\) and check PCO pvalues.

eQTLGen’s module1. Run PCO based on two Sigmas, \(\hat{\Sigma}_{DGN}\) and \(\hat{\Sigma}_{nullz}\) built on 2282 independent null SNPs. Calculate pvalues of 9918 SNPs across chromosomes.

Version Author Date
1b79abb liliw-w 2021-06-29

In the above figure, x-axis is for snp across chromosomes, y-axis is for log(p) for the module1, color is for different \(\hat{\Sigma}\), grey dashed line is the Bonferroni pvalue threshold (~1e-8).

Version Author Date
1b79abb liliw-w 2021-06-29

The above figure gives QQ-plot for all pvalues across 22 chr’s of module1.

Observations

  1. Using \(\hat{\Sigma}_{nullz}\) gives larger PCO pvalues, than using \(\hat{\Sigma}_{DGN}\). Number of signals decreases. Under Bonferroni pvalue threshold (~1e-8), when using \(\hat{\Sigma}_{nullz}\), there are 790 out of 9918 SNPs are significant, compared to 9794 significant SNPs using \(\hat{\Sigma}_{DGN}\).

June 25

Replication of eQTLGen results in trans-PCO of eQTLGen summary stats?

I first give some data statistics here.

Dataset Method #(gene, SNP)/(module, SNP) #unique genes/modules unique SNPs
eQTGen FDR<0.05 59786 6298 3853
eQTGen filter 20394 1857 2469
eQTLGen_trans-PCO qvalue 406729 75 9918
eQTLGen_trans-PCO Bonferroni 55634 74 9915

  • The eQTGen’s original result here gives 59786 (gene, trans-eQTL) pairs under FDR \(<0.05\), corresponding to 6298 unique genes and 3853 unique SNPs.

  • After some filtering, to make sure the eQTGen trans-eQTLs and genes are included in out trans-PCO result using eQTLGen summary stats. There are 20394 (gene, trans-eQTL) pairs left, corresponding to 1857 unique genes and 2469 unique SNPs.

  • Orignal eQTLGen_trans-PCO result (under qvalue FDR correction): 406729 (module, trans-eQTL) pairs, corresponding to all 75 unique modules and 9918 unique SNPs.

  • Under Bonferroni correction (p<6.721785e-08): 55634, 74, 9915.

Next, I will check how eQTGen signals are replicated in eQTLGen_trans-PCO results (see bold text above). The basic idea is, for an eQTGen trans-eQTL, find its trans-target genes, then look at how these genes are distributed in each gene modules we used for eQTLGen_trans-PCO, and whether the corresponding (module, trans-eQTL) are identified by eQTLGen_trans-PCO. Specifically, I will check two things.

  1. For a trans-eQTL whose trans-target genes are included in one of our PCO module, is this (module, trans-eQTL) identified by eQTLGen_trans-PCO? (Power)

    Since in previous analysis, the intuition is PCO tends to pick modules where there are multiple trans-target genes for a SNP. Therefore, in the below figure, I picked out all the eQTGen trans-eQTLs that have >2 target genes and plotted them on x-axis. The target genes are distributed on the Y-axis for each PCO module. Number/color is for #target genes. These (module, SNP) pairs should be significant in eQTLGen_trans-PCO. I circled out (red) those (module, SNP) pairs that are missed by eQTLGen_trans-PCO. As a result, 11 (module, SNP) (11 unique SNPs) are missed.

Power

Power

Version Author Date
0f60720 liliw-w 2021-06-25

Check here for clearer version.

  1. For a trans-eQTL whose trans-target genes are not included in any PCO modules (or only 1 or 2), is this (module, trans-eQTL) identified by eQTLGen_trans-PCO? (TIE)

    Similar plot, except Number/color is SNP with 0, 1, or 2 target genes in each module. These (module, SNP) pairs are less likely to be identified by eQTLGen_trans-PCO. Yet, I circled out (green) those (module, SNP) pairs that are still identified by eQTLGen_trans-PCO.

TIE

TIE

Version Author Date
0f60720 liliw-w 2021-06-25

Check here for clearer version.

Observation

  1. Almost all eQTGen trans-eQTLs with >2 target genes and their corresponding module are identified by eQTLGen_trans-PCO. This may suggest a good power of eQTLGen_trans-PCO.

  2. However, the false positiva rate may be inflated, as a large amount of SNPs that has no target genes in the modules are also identified. (Maybe although none of the genes in the module are target genes for the SNPs, the genes may be cross-mappable with the SNP’s other traget genes that are filter out?)

How does zero values affect qvalue?

Short answer:

June 14

Why there are so many eQTLGen signals using PCO_\({\lambda<0.1}\)?

Check the QQ-plot of the observed pvalues from eQTLGen using PCO_\({\lambda<0.1}\) (9918 unique SNPs, all eQTLGen variants) and PCO_\({\lambda<1}\) (909 unique SNPs).

Version Author Date
4fc3dff liliw-w 2021-06-14

June 11

Compare with truncated ‘DGN_transeQTL_battle2014’

In this section, I removed trans-eGenes from Battle’s result that are not included in our analysis for being cross-mappable or poorly mapped. I do this to makes sure univariate and multivariate are based on the same set of genes. I go through the same analysis as below.

  • Summary of the new version Battle trans-eQTL signals

After filter our some trans-eGenes, there are 157 (v.s. 736) significant (gene, SNP) pairs left, corresponding to 84 unique trans-eQTLs and 47 unique trans-eGenes.

The following is a a table of the number of trans-target genes of these 84 unique trans-eQTLs.


 1  2  3  4  5 15 16 29 
75  1  1  3  1  1  1  1

We have identified 313 unique trans-eQTLs, among which 24 are also detected by Battle’s univariate method. The above table gives which Battle’s signals are replicated by trans-PCO.

Among 84 Battle’s trans-eQTLs, 24 (~28.57%) are also detected by trans-PCO. For 9 signals with more than one trans-target genes included in our analysis, all of them are detected by trans-PCO. Trans-PCO also detected other 15 signals with only one trans-target gene used in our analysis. For the other 60 univariate signals that are missed by trans-PCO, they have only one trans-target gene included in trans-PCO.

            sig N_transeGene if_transPCO num_included
 1:  3:56849749           29        TRUE           29
 2:  3:56858686           16        TRUE           16
 3:  3:56865776           15        TRUE           15
 4:  3:56880444            5        TRUE            5
 5:  3:56871432            4        TRUE            4
 6:  3:56874033            4        TRUE            4
 7:  7:50366637            4        TRUE            4
 8:  3:56851387            3        TRUE            3
 9:  7:50428445            2        TRUE            2
10: 7:106337250            1       FALSE            1
11: 12:54723028            1       FALSE            1
12: 12:54729872            1       FALSE            1
13: 4:103432974            1       FALSE            1
14: 4:103443569            1       FALSE            1
15: 4:103448582            1       FALSE            1
16: 4:103511114            1       FALSE            1
17: 1:118147675            1       FALSE            1
18: 1:118158079            1       FALSE            1
19: 19:37441365            1       FALSE            1
20: 19:37469098            1       FALSE            1
21: 19:37503899            1       FALSE            1
22: 19:37504596            1       FALSE            1
23: 19:37507729            1       FALSE            1
24: 19:37516220            1       FALSE            1
25: 19:37520927            1       FALSE            1
26: 19:37547219            1       FALSE            1
27: 19:37563211            1       FALSE            1
28: 19:37573074            1       FALSE            1
29: 19:37582471            1       FALSE            1
30: 19:37584650            1       FALSE            1
31: 19:37597395            1       FALSE            1
32: 19:37620248            1       FALSE            1
33: 19:37627113            1       FALSE            1
34: 19:37632877            1       FALSE            1
35: 19:37634291            1       FALSE            1
36: 19:37642165            1       FALSE            1
37: 19:37649577            1       FALSE            1
38: 19:37650929            1       FALSE            1
39: 19:37684966            1       FALSE            1
40: 17:33875262            1       FALSE            1
41: 1:248039451            1        TRUE            1
42: 1:248039713            1       FALSE            1
43: 1:248041182            1       FALSE            1
44: 1:248058265            1       FALSE            1
45: 19:44889660            1       FALSE            1
46: 19:44930738            1        TRUE            1
47: 19:44931995            1       FALSE            1
48: 19:44932972            1        TRUE            1
49: 19:44933947            1        TRUE            1
50: 19:44938980            1        TRUE            1
51: 19:44947050            1       FALSE            1
52: 19:44947184            1        TRUE            1
53: 19:44959866            1       FALSE            1
54: 19:44973969            1       FALSE            1
55: 19:44978298            1       FALSE            1
56: 19:44979443            1       FALSE            1
57: 19:44995990            1       FALSE            1
58: 19:45001346            1       FALSE            1
59: 19:45001619            1       FALSE            1
60: 14:35523266            1       FALSE            1
61: 14:35571651            1        TRUE            1
62: 14:35624831            1       FALSE            1
63: 21:44473062            1       FALSE            1
64: 21:44473425            1       FALSE            1
65: 21:44473446            1       FALSE            1
66:  12:8142798            1        TRUE            1
67:  12:8143483            1        TRUE            1
68:  12:8161503            1        TRUE            1
69:  12:8179891            1       FALSE            1
70:  12:8185853            1       FALSE            1
71:  12:8190206            1       FALSE            1
72: 6:159498130            1       FALSE            1
73: 15:80260554            1        TRUE            1
74: 15:80263217            1        TRUE            1
75: 15:80263345            1        TRUE            1
76: 15:80263406            1        TRUE            1
77:  7:50435777            1       FALSE            1
78: 6:169749100            1       FALSE            1
79: 14:20811332            1        TRUE            1
80: 17:33902635            1       FALSE            1
81: 17:34019488            1       FALSE            1
82: 17:34043021            1       FALSE            1
83: 17:34051176            1       FALSE            1
84:  9:99288951            1       FALSE            1
            sig N_transeGene if_transPCO num_included

Compare with ‘DGN_transeQTL_battle2014’

  • Summary of Battle trans-eQTL signals

They gave 736 significant (gene, SNP) pairs, corresponding to 350 unique trans-eQTLs and 138 unique trans-eGenes.

The following is a a table of the number of trans-target genes of these 350 unique trans-eQTLs. We can see most of the trans-eQTLs have only 1 or 2 trans-target genes (\(283+34=317, \approx 91\%\)).


  1   2   3   4   5   6   7   8  11  13  14  22  23  24  29  33  59 
283  34   3   1  12   1   2   2   2   1   2   1   2   1   1   1   1

Let’s take a look at the trans-eQTLs with more than 2 target genes. We can see these trans-eQTLs are mainly located around the regions 3:56849749, 3:101043565, 7:50366637, 17:33875262.

            sig N_transeGene if_transPCO num_included
 1:  3:56849749           59        TRUE           29
 2:  3:56858686           33        TRUE           16
 3:  3:56865776           29        TRUE           15
 4: 3:101242751           24       FALSE            0
 5: 3:101043565           23       FALSE            0
 6: 3:101106527           23       FALSE            0
 7: 3:101232736           22       FALSE            0
 8: 3:100963761           14       FALSE            0
 9: 3:100970240           14       FALSE            0
10: 3:100994497           13       FALSE            0
11:  3:56851387           11        TRUE            3
12:  3:56880444           11        TRUE            5
13: 3:100915962            8       FALSE            0
14:  7:50366637            8        TRUE            4
15:  3:56874033            7        TRUE            4
16: 3:101068620            7       FALSE            0
17:  3:56871432            6        TRUE            4
18: 3:101042594            5       FALSE            0
19: 3:101080694            5       FALSE            0
20: 3:101085413            5       FALSE            0
21: 3:101135210            5       FALSE            0
22: 3:101160339            5       FALSE            0
23: 3:101184134            5       FALSE            0
24: 3:101191663            5       FALSE            0
25: 3:101231921            5       FALSE            0
26: 3:101237307            5       FALSE            0
27: 3:101252514            5       FALSE            0
28: 3:101253091            5       FALSE            0
29: 3:101253605            5       FALSE            0
30:  7:50428445            4        TRUE            2
31:  7:50435777            3       FALSE            1
32: 17:33875262            3       FALSE            1
33: 17:33902635            3       FALSE            1
            sig N_transeGene if_transPCO num_included
  • As for our results from trans-PCO

We have identified 313 unique trans-eQTLs, among which 24 are also detected by Battle’s univariate method. The above table gives which Battle’s signals are replicated by trans-PCO.

Table of the number of target genes for replicated trans-eQTLs.


 1  2  4  6  7  8 11 29 33 59 
12  3  1  1  1  1  2  1  1  1

  1. Signals detected by univariate but missed by trans-PCO.

    Since trans-PCO tends to identify SNPs that have effects on multiple genes, I will focus on the univariate trans-eQTLs that correspond to multiple genes (\(>2\)). For this type of signals, there are 33 trans-eQTLs in total, among which 9 are detected by trans-PCO. For the rest of 24 missed trans-eQTLs, there are basically three types: (1) 21 near the region “3:101043565”, (2) 1 at “7:50435777”, (3) 2 at “17:33875262” and “17:33875262”.

    1. Even though the 20 missed trans-eQTLs correspond to multiple genes, ranging from 5 ~ 24, they are still missed by trans-PCO. So I checked their trans-target genes, and it turns out that all of the target genes are filtered out at the beginning of our analysis for being cross-mappable or poorly mapped.

    2. As for the rest of three trans-eQTLs that are missed by trans-PCO, only one of their 3 trans-target genes are included in our analysis.

Take-aways

  1. Trans-PCO tends to be more likely to detect trans-eQTLs with effects on multiple target genes.

  2. Some signals could be missed at the step of filtering out genes.

May 26

Are trans-eQTLs cis-eQTLs?

Updated the way to define cis-eQTLs. Previously, cis-eQTL signals are gene-based (from Pheonix using fastQTL). In this section, I compare trans signals with SNP-based cis-eQTLs from two datasets, i.e. GTEx_v7 (whole blood) and DGN.

  • GTEx_v7. Here provides all significant variant-gene associations.

  • DGN. Two steps to obtain SNP-based significant associations.

    1. Gene-based associations. (eGenes using fastQTL, result from Pheonix)

    2. Find all cis-eQTLs for each gene.

      See “4.2 cis-eQTL mapping” described here. (p.s. I checked GTEx source code and turns out that the actual code GTEx used is a bit different. See below for key lines.)

pt = mean(c(max(eGene$bpval), min(eGene$bpval)))
eGene$pval_nominal_threshold = signif(qbeta(pt,
                                            eGene$shape1, eGene$shape2, ncp=0, lower.tail=TRUE, log.p=FALSE), 6)
Dataset #signal GTEx_v7_is_ciseQTL(SNP-based) GTEx_v7_cis-eGene DGN_is_ciseQTL(SNP-based) DGN_cis-eGene DGN_is_cissQTL(SNP-based) DGN_cis-sIntro DGN_cis-e/sQTL
DGN 313 51 16 156 39 101 71 182
eQTLGen_DGN 784 221 32 502 83 381 182 551

A diagram version:

Are trans-eQTLs cis-e/sQTLs?

Are trans-eQTLs cis-e/sQTLs?

Version Author Date
1f02e91 liliw-w 2021-05-26

Observations:

  • For DGN, among 313 trans signals, 156 (~49.8%) are also cis-eQTLs, corresponding to 39 eGenes, including:

AC016753.7, BECN1, C17orf50, C2orf68, CFL2, CTD-2562J15.6, ERN1, FAM177A1, FIGNL1, FKRP, GGCX, HABP4, HSD17B1P1, ICAM2, KIAA0391, MAT2A, MLX, NEK6, NFE2, NFKBIA, OR2W3, PARP2, PEX12, PPP2R3C, PRKD2, PSMC3IP, RETSAT, RNF181, RP11-1094M14.8, RP11-69M1.4, RP11-85K15.2, SLC1A5, SLC2A3, SLFN12L, SYMPK, TMEM150A, TTC5, VAMP8, ZNF782

  • For DGN, 101 (~32.3%) out of 313 trans signals are cis-sQTLs, corresponding to 71 introns. 26 trans-eQTLs are only sQTLs but not eQTLs. These signals are located on chromosome 15 and 19.

  • Among 313 trans signals, 182 (~58.1%) are either cis-eQTLs or cis-sQTLs.

May 19

How many trans-eQTLs detected in DGN/GTEx whole blood are replicated in eQTLGen?

Replication of DGN signals in eQTLGen. Based on updated results, i.e. smaller and more gene modules & PCO\(_{\lambda>0.1}\).

Are trans-eQTLs cis-eQTLs?

  1. Dataset: DGN
Dataset #signal is_ciseQTL(gene-based) is_cissQTL(SNP-based) is_cise(s)QTL(gene-based)
DGN 313 7 9 15
eQTLGen_DGN 784 17 30 45

Observations:

1.1 DGN

  • Among 313 trans signals, 7 are also (gene-based) cis-eQTLs, corresponding to 5~7 independent SNPs. The cis-eGenes include SLC2A3, NFE2, KIAA0391, NFKBIA, ERN1, AC016753.7, MAT2A.

  • Among 313 unique trans signals, 229 (~73%) have a neareset gene that are eGenes (with cis-eQTLs). Among 28 independent trans signals, 19 (~68%) have a neareset gene that are eGenes (with cis-eQTLs).

  • Among 313 trans signals, 9 are also cis-sQTLs, corresponding to 6 independent SNPs.

1.2 eQTLGen_DGN

  • Among 784 trans signals, 17 are also (gene-based) cis-eQTLs, corresponding to 9 independent SNPs. The cis-eGenes include AC016753.7, CPEB4, KIAA0391, MAT2A, MRFAP1, NFKBIA, PAQR6, PWP1, RNF181, RP11-539L10.2, RP11-69M1.4, S100P, SENP7, SLC25A44, SLC2A3, SMG5, TMEM79, ZNF782.

  • Among 784 unique trans signals, 590 (~75%) have a neareset gene that are eGenes (with cis-eQTLs). Among 50 independent trans signals, 29 (~58%) have a neareset gene that are eGenes (with cis-eQTLs).

  • Among 784 trans signals, 30 are also cis-sQTLs, corresponding to 10 independent SNPs.

  1. Dataset: TCGA

  2. eQTLGen?

March 8

Muscle

  • Less modules, PCO\(_{\{\lambda: \lambda>0.1\}}\). 1 independent signal, large p.

  • More modules, PCO\(_{\{\lambda: \lambda>0.1\}}\). 5 independent signal, small p.

  • More modules, PCO\(_{\{\lambda: \lambda>1\}}\). 5 independent signal, relatively large p.

March 1

Real data analysis by PCO using more \(\lambda\)’s

Dataset: Muscle_Skeletal.

Fewer (independent) signals. \(PCO_{\{\lambda: \lambda>0.1\}}\) (1 signal) v.s. \(PCO_{\{\lambda: \lambda>1\}}\) (3 signals).

proteomics data

See the google doc here.

Other stuff

  • RCC account storage

Feb 23

Updated simulation

  1. Adjusted variance of effects

  • tests

    • Oracle: \(\beta^T \Sigma^{-1}Z \approx \beta^T \hat\Sigma^{-1}Z = \beta^T (\sum_{\{\lambda_k: \lambda_k>0.1\}}\lambda_k u_k u_k^T) Z\)

    • PCO: Use \(\{\lambda_k: \lambda_k>0.1\}\).

  • scenerios (\(K=100,K=105\))

    • N: var.b = 0.003; caus = 30%; N.seq = c(200, 400, 600, 800, 1000)

    • caus: var.b = 0.003; N = 500; caus.seq = c(1, 5, 10, 30, 50, 70, 100)

    • caus_fix: var.b.fix = 0.1; N = 500; caus.seq = c(1, 5, 10, 30, 50, 70, 100)

  1. Run for other \(\Sigma\)’s. \(K=100,K=105\)

  2. FDR level

The minimum null pvalue of PCO is \(\ge 10^{-9}\), similar as the significance threshold we use here \(10^{-9}\).

  1. Results
power under Bonferroni corretion cutoff

power under Bonferroni corretion cutoff

Version Author Date
cbbe319 Lili Wang 2021-02-23
Another Sigma (K=105)

Another Sigma (K=105)

Version Author Date
cbbe319 Lili Wang 2021-02-23

Feb 16

simulation

  • tests

    • Oracle: \(\beta^T \Sigma^{-1}Z \approx \beta^T \hat\Sigma^{-1}Z = \beta^T (\sum_{\{\lambda_k: \lambda_k>1\}}\lambda_k u_k u_k^T) Z\)

    • PC1;

    • minp = \(min\{p_1, \dots, p_K \} \times K\)

    • PCO: Use \(\{\lambda_k: \lambda_k>1\}\).

  • Multiple testing

    The significance threshold is set based on the Bofferroni correction as the \(\frac{0.05}{50\times10^6} = 10^{-9}\) for univariate test and PC-based tests.

  • scenerios (\(K=100\))

    • N: var.b = 0.01; caus = 100 (100%); N.seq = c(200, 400, 600, 800, 1000)

    • caus: var.b = 0.02; N = 500; caus.seq = c(1, 10, 30, 50, 70, 100)

    • caus_fix: var.b.fix = 0.2; N = 500; caus.seq = c(1, 10, 30, 50, 70, 100)

  • results

power under Bonferroni corretion cutoff

power under Bonferroni corretion cutoff

Version Author Date
cbbe319 Lili Wang 2021-02-23
8960692 Lili Wang 2021-02-16

  • Try other tests

    • Oracle: \(\beta^T \Sigma^{-1}Z \approx \beta^T \hat\Sigma^{-1}Z = \beta^T (\sum_{\{\lambda_k: \lambda_k>0.1\}}\lambda_k u_k u_k^T) Z\)

    • PCO: Use \(\{\lambda_k: \lambda_k>0.1\}\).

power under Bonferroni corretion cutoff

power under Bonferroni corretion cutoff

Version Author Date
cbbe319 Lili Wang 2021-02-23
8960692 Lili Wang 2021-02-16
  • For talk

(This figure should be updated as for the case of ‘u1’, the threshold is falsely set as 0.05, which should be \(10^{-9}\).)

PC1 v.s. PCO

PC1 v.s. PCO

Version Author Date
cbbe319 Lili Wang 2021-02-23
8960692 Lili Wang 2021-02-16

Jan 26

simulation

  • Methods: Oracle, PC1, PCO, MinP, minp.

  • Models: \(z \sim N(\sqrt{N} \beta, \Sigma)\). \(\beta \sim N(0, \sigma_{b}^2 I_{K \times K})\).

  1. various sample size \(N\). 200, 400, 600, 800, 1000.

  2. various \(\sigma_{b}^2\). 0.005, 0.01, 0.05, 0.1, 0.2.

  3. various causality percentage. ???

  • simulation.

    Generate \(10^4\) zscores under each model. \(10^4\) simulations.

The following plot gives the boxplot, mean plot with standard deviation, and mean plot with standard error of the mean. Which one to use?

power under cutoff 0.05

power under cutoff 0.05

Version Author Date
8960692 Lili Wang 2021-02-16
power comparison

power comparison

Version Author Date
8960692 Lili Wang 2021-02-16
bar plot

bar plot

Version Author Date
912acee Lili Wang 2021-02-06

Larger FDR level, #signals in large and small module?

Here I will look at how the number of signals changes in the original large and current small modules when I increase the FDR level.

The plot below is based on Muscle tissue from GTEx_v8. The x-axis is for various FDR levels, including 5%, 10%, 15%, and 20%. The y-axis is for the number of signals under these FDR levels. I plot three types of signals, i.e. module and SNP pairs (left subplot), unique SNPs (middle subplot), independent SNPs (right subplot). The two colors represent our previous WGCNA modules (red) and current smaller WGCNA modules (blue).

We can observe (1) When increasing FDR levels, number of signals only increase a little bit, say 3-5 more signals. This means that the corrected pvalues are bipolar, i.e. either very small or very large. (2) Signals based on smaller modules are similar to that of previous standard modules.

Muscle: #signals v.s.FDR

Muscle: #signals v.s.FDR

Version Author Date
0b5d8d3 Lili Wang 2021-02-02
DGN: #signals v.s.FDR

DGN: #signals v.s.FDR

Version Author Date
0b5d8d3 Lili Wang 2021-02-02

Smaller gene modules, more signals?

I changed the parameter deepSplit in function cutreeDynamic from package WGCNA to get modules with smaller size. I run it on the Muscle tissue from GTEx (see GTEx_v8.Muscle_Skeletal.WGCNA in the GTEx results table). Compared to GTEx_v8.Muscle_Skeletal, though more modules (32 v.s. 18), they have same independent signals (3), located on chr5, chr10, and chr22.

The corresponding modules of these signals from small and large WGCNA share a large proportion of genes.

signal.Chr module.small (#genes) module.big (#genes) #overlapped genes
chr5 module21 (89) module15 (114) 88
chr10 module21 (89) module15 (114) 88
chr22 module2 (297) module4 (350) 257

The above table is for clusters obtained by method ‘WGCNA.min20_deep2’ (big) and ‘WGCNA.min20_deep4’ (small). Next, I give more info about the clusters by more methods, i.e. #genes in modules (A), #unclassfied genes (B), and #modules (C) by the six methods. I also give the pvalue distribution corresponding to these clusters below.

Generally, funcExplorer gives more modules, smaller module, and much more unclassified genes. Though the smaller modules, there aren’t many extreme pvalues. Say, the minimum p of all is about \(10^{-9}\), as compared to \(10^{-14}\) by other methods.

From the pvalue plot, it looks like ‘WGCNA.min10_deep4’ gives smaller clusters and some extreme pvalues. So next step I will run the whole pipleline for this setting.

Modules v.s. methods/parameters

Modules v.s. methods/parameters

Version Author Date
0b5d8d3 Lili Wang 2021-02-02
af77a67 Lili Wang 2021-01-30
3017262 Lili Wang 2021-01-30
p distribution of Muscle

p distribution of Muscle

Version Author Date
74c629e Lili Wang 2021-02-06

Jan 05, Jan 19

Simulation

The simulations here aim to compare the power of PC-based tests including PC1 (using only the primary PC) and PCO (using combined PC’s), and non-PC based test MinP. The simulations consist of two parts: (1) verify that type 1 error is well controlled; (2) compare power of tests. At this time, I simply assume there is no LD among SNPs, i.e. tests are independent.

  1. Verify that type 1 error is well controlled.

Since the tests are assumed to be independent, the null pvalues should be uniformly distributed. To verify that, I estimate the null pvalues by empirical p’s obtained from the following steps.

Step1. Generate \(z_0 \sim N(0, \Sigma) | H_0\).

Step2. Run tests including PC1, PCO, MinP for \(10^6\) times and obtain \(10^6\) p’s for each test.

Step3. Compute the empirical T1E at significance \(\alpha\) by \(\frac{I\{p<\alpha\}}{10^6}\). Draw qqplot of \(-log_{10}p\).

The correlation matrix \(\Sigma\) is the correlation of genes in module15 of GTEx dataset Muscle_Skeletal (Sigma.Muscle_Skeletal.module15.chr7.rds).

alpha PC1 PCO MinP
5e-02 0.050356 0.053584
1e-04 0.000093 0.000114
qqplot.simulation.null

qqplot.simulation.null

Version Author Date
11c79eb Lili Wang 2021-01-19
  1. Compare power of tests.

To compare the power of non-/PC-based tests, I will run the oracle test in addition to PC1, PCO, and MinP to benchmark the power. It’s mentioned in the PCO paper that given a fixed correlation relationship among the phenotypes, the power of a test depends on the relationship bewteen the true effects (\(\beta\)) and the phenotype correlation (\(\Sigma\)). Therefore, to see which tests perform well in what cases, I will consider different models, including (1) \(\beta=10 u_1\); (2) \(\beta=4 u_k\); (3) \(\beta=1.5 u_K\); (4) \(\beta=rnorm(K)\); (5) \(\beta=rnorm(0.7K)\); (6) \(\beta=rnorm(0.3K)\).

Step1. Generate \(z_0 \sim N(\beta, \Sigma) | H_1\).

Step2. Run tests including Oracle, PC1, PCO, MinP for \(10^6\) times and obtain \(10^6\) p’s for each test.

Step3. Compute the power at significance \(\alpha\) by \(\frac{I\{p<\alpha\}}{10^6}\).

Model Oracle PC1 PCO MinP
u1 0.946341 0.902540 0.746301
uPCO 0.989835 0.050178 0.713434
uK 0.953727 0.049719 0.054140
100% 1.000000 0.058867 0.945918
70% 1.000000 0.058910 0.580368
30% 0.999995 0.050201 0.149904

GTEx

Results

The table below summarizes all results I have so far, followed by figures of the distributions of pvalues in various datasets.

Dataset Nsample All Annotated Filtered Filtered_info Final Nmodule FDR Nperm QTL_Module unique_QTL independent_QTL
DGN 913 13634 11979 8120 0;165;1663;8073 3859 21 combined chr+module 20 659 623 40
DGN_new 913 13634 12585 9939 1;453;1798;8705 3695 19 combined chr+module 10 331 275 26
TCGA 788 17656 15994 12694 336;3504;10697;598 4962
GTEx_v8.Whole_Blood 670 20315 20315 15245 619;4544;3677;13096 5070 22 combined chr+module 10 4 4 2
GTEx_v8.Muscle_Skeletal 706 21031 21031 15601 675;4447;3631;13490 5430 18 combined chr+module 10 38 38 3
GTEx_v8.Skin_Sun_Exposed_Lower_leg 605 25196 25196 18801 807;6458;4557;15650 6395 30 combined chr+module 10 1 1 1
GTEx_v8.Artery_Tibial 584 23304 23304 17390 795;5588;4202;14730 5914 20 combined chr+module 10 0 0 0
GTEx_v8.Muscle_Skeletal.cross 706 21031 21031 7141 675;4447;3631;0 13890 39 combined chr+module 10 43 43 4
GTEx_v8.Muscle_Skeletal.WGCNA 706 21031 21031 15601 675;4447;3631;13490 5430 32 combined chr+module 10 44 44 3
DGN_new.WGCNA 913 13634 12585 9939 1;453;1798;8705 3695 40 combined chr+module 10
TCGA_new
DGN

DGN

Version Author Date
b110975 Lili Wang 2020-12-17
DGN_new

DGN_new

Version Author Date
361c43e Lili Wang 2021-01-04
Whole_Blood

Whole_Blood

Version Author Date
361c43e Lili Wang 2021-01-04
Muscle_Skeletal

Muscle_Skeletal

Version Author Date
361c43e Lili Wang 2021-01-04
Skin_Sun_Exposed_Lower_leg

Skin_Sun_Exposed_Lower_leg

Version Author Date
361c43e Lili Wang 2021-01-04
Artery_Tibial

Artery_Tibial

Version Author Date
361c43e Lili Wang 2021-01-04
Muscle_Skeletal.cross

Muscle_Skeletal.cross

Version Author Date
60cf10e Lili Wang 2021-01-17

Remarks

  1. The dataset “DGN_new” represents DGN through the standard filtering (see “Gene filter” on Dec 10).

  2. GTEx datasets generally have few significant signals and relatively large pvalues (compared to DGN).

  3. The dataset “GTEx_v8.Muscle_Skeletal.cross” uses Muscle_Skeletal samples from GTEx_v8 (similar as GTEx_v8.Muscle_Skeletal), but without removing cross-mapped genes before constructing gene modules. Therefore, there are 13890 genes (v.s. 5430 in GTEx_v8.Muscle_Skeletal) in total which result in 39 modules (v.s. 18 in GTEx_v8.Muscle_Skeletal). We do this step because we observed that there are relatively few signals using our original pipeline and we wonder if the reason to this observation is us filtering too many genes in the first step and leaving too few signals. To check on this, we put the “filtering” to the last step, i.e. including potentially cross-mapped genes into the analysis and generate significant variant-module pairs. We then exclude those where target eGene in the module is cross-mappable with any gene within 1Mb of the variant. Hopefully we could have more signals.

    However, though the increased genes and modules, the number of identified signals (43) is similar as that using the original pipeline (38). Next, I will look into these signals.

GTEx_v8.Muscle_Skeletal
variant-module p q
module15:10:48930105 8.63e-10 8.33e-03
module15:5:132440814 1.56e-09 2.16e-02
module15:5:132448891 3.36e-09 4.74e-02
module15:5:132450078 5.81e-12 0.00e+00
module15:5:132450726 5.96e-12 0.00e+00
module15:5:132450916 8.89e-12 0.00e+00
module15:5:132451361 5.97e-11 0.00e+00
module15:5:132451586 1.11e-11 0.00e+00
module15:5:132453865 1.05e-12 0.00e+00
module15:5:132454053 9.94e-13 0.00e+00
module15:5:132454171 1.03e-12 0.00e+00
module15:5:132454631 1.44e-12 0.00e+00
module15:5:132454724 1.08e-12 0.00e+00
module15:5:132455672 1.07e-12 0.00e+00
module15:5:132455979 1.04e-12 0.00e+00
module15:5:132456154 9.96e-13 0.00e+00
module15:5:132456710 6.04e-11 0.00e+00
module15:5:132458606 5.33e-11 0.00e+00
module15:5:132459905 4.84e-11 0.00e+00
module15:5:132459971 5.04e-11 0.00e+00
module15:5:132460190 5.05e-11 0.00e+00
module15:5:132460375 5.56e-11 0.00e+00
module15:5:132460917 5.03e-11 0.00e+00
module15:5:132461111 5.17e-11 0.00e+00
module15:5:132463834 5.47e-11 0.00e+00
module15:5:132464413 3.90e-11 0.00e+00
module15:5:132464907 1.01e-12 0.00e+00
module15:5:132466034 4.56e-11 0.00e+00
module15:5:132468333 1.32e-10 0.00e+00
module15:5:132468353 5.74e-11 0.00e+00
module15:5:132468564 8.53e-11 0.00e+00
module15:5:132469724 5.63e-11 0.00e+00
module15:5:132469899 6.96e-11 0.00e+00
module15:5:132470043 1.03e-10 0.00e+00
module15:5:132470796 5.42e-11 0.00e+00
module15:5:132471932 8.01e-11 0.00e+00
module15:5:132474927 2.71e-10 2.94e-03
module4:22:23508295 3.76e-10 5.71e-03
GTEx_v8.Muscle_Skeletal.cross
variant-module p q
module8:1:123955560 9.97e-12 0.00e+00
module8:1:123955561 1.06e-11 0.00e+00
module8:16:36353041 3.49e-11 6.67e-03
module8:16:36353056 8.29e-11 1.25e-02
module8:5:132453865 1.56e-09 3.12e-02
module8:5:132454053 1.59e-09 2.86e-02
module8:5:132454171 1.52e-09 3.33e-02
module8:5:132454631 1.43e-09 3.57e-02
module8:5:132454724 1.53e-09 3.23e-02
module8:5:132455672 1.50e-09 3.45e-02
module8:5:132455979 1.56e-09 3.03e-02
module8:5:132456154 1.78e-09 3.42e-02
module8:5:132456710 1.36e-09 3.33e-02
module8:5:132458606 3.37e-10 1.76e-02
module8:5:132459905 6.50e-10 1.74e-02
module8:5:132459971 3.92e-10 1.43e-02
module8:5:132460190 3.50e-10 1.58e-02
module8:5:132460375 3.37e-10 1.67e-02
module8:5:132460917 3.98e-10 1.36e-02
module8:5:132461111 3.57e-10 1.50e-02
module8:5:132463834 8.21e-10 2.40e-02
module8:5:132464413 9.93e-10 2.69e-02
module8:5:132466034 6.75e-10 1.67e-02
module8:5:132468333 1.86e-09 3.50e-02
module8:5:132468353 1.69e-09 3.06e-02
module8:5:132468564 2.43e-09 4.19e-02
module8:5:132469724 1.93e-09 3.66e-02
module8:5:132469899 1.73e-09 3.24e-02
module8:5:132470043 1.56e-09 2.94e-02
module8:5:132470796 1.85e-09 3.33e-02
module8:5:132471932 2.37e-09 4.29e-02
module8:5:46659000 9.86e-13 0.00e+00
module8:5:46906585 2.34e-11 7.14e-03
module8:5:47027928 0.00e+00 0.00e+00
module8:5:47068540 0.00e+00 0.00e+00
module8:5:47166316 3.33e-16 0.00e+00
module8:5:47210790 0.00e+00 0.00e+00
module8:5:47210990 0.00e+00 0.00e+00
module8:5:47258679 4.44e-16 0.00e+00
module8:5:47258917 3.33e-16 0.00e+00
module8:5:49809727 2.70e-13 0.00e+00
module8:5:49930686 0.00e+00 0.00e+00
module8:5:49936394 1.10e-11 0.00e+00 
For GTEx_v8.Muscle_Skeletal, there are 38 variant-module pairs, corresponding to 2 module (module 15, module4) and 3 independent loci on (chr5, chr10, chr22). GTEx_v8.Muscle_Skeletal.cross has 43 variant-module pairs, corresponding to 1 module (module 8) and 4 independent loci on (chr1, chr5, chr16).

The signal on chr5 is significant for both module 15 (114 genes) and module 8 (394 genes) in two datasets, which have 82 shared genes. Take SNP [rs2706381][rs2706381 GTEx ref] (chr5:132474927) for example. It is ["in cis with IRF1 ($P \le 2\times10^{-10}$; Fig. 6c), a transcription factor that facilitates regulation of the interferon-induced immune response"][rs2706381 GTEx ref]. It is also ["associated in trans with PSME1 ($P \le 1.1\times10^{-11}$) and PARP10 ($P \le 7.8\times10^{-10}$)"][rs2706381 GTEx ref]. These two genes are included in module 15. The reference also gives additional results to "suggest that cis-regulatory loci affecting IRF1 are regulators of interferon-responsive inflammatory processes involving genes including PSME1 and PARP10, with implications for complex traits specific to muscle tissue".

I also looked at the enrichment of the genes in module 15. These genes are mainly enriched in immunity-related terms and tuberculosis. To reproduce, use the gene list [here](./gene.GTEx_v8.Muscle_Skeletal.module15.txt).

SNP 10:48930105. module 15.

module4:22:23508295

+ Check if the signals' nearby genes are cross-mapped with genes in their corresponding module. The signal on chr5 corresponding to module8 has 20 genes +/- 500Kb away from its TSS. Many of them are crosspable with genes in the module 8. The number of of genes in the module crossmapped with each of the 20 genes are: `1, 144, 0, 62, 54, 0, 63, 4, 0, 0, 0, 59, 145, 0, 0, 128, 0, 23, 53`, where the nearest gene is crossmappable with 1 gene in the module.

  • The other signals on chr1, chr16, and chr5:47210790 don’t have any nearby genes around its TSS.

  • See the following plot for number of cross-mapped genes in each module.

Version Author Date
d22021e Lili Wang 2021-01-19

New TCGA by the standard filtering

eQTLGen

  1. eQTLGen description

    This full dataset includes 19942 genes that showed expression in blood tested and 10317 SNPs that are trait-associated SNPs based on GWAS Catalog.

    After gene filter steps described in Dec 10, there are 4963 genes left. Applying the same filtering to 13634 DGN genes, there are 3695 genes left, among which 3642 are also included in eQTLGen. So, I will use these genes to do the downstream analysis, e.g. constructing co-expressed gene modules. These 3642 genes result in 19 gene modules.

  2. Replication of DGN signals in eQTLGen

    The table below gives the signals found in eQTLGen and DGN.

    The first two rows give results based on eQTLGen zscores, with row 1 using qvalue for FDR correction (threshold \(0.05\)) and row 2 using \(\frac{0.05}{\#DGN signals}\) as significance threshold. The third row is based on the same gene modules and SNPs but tensorQTL zscores using DGN expression data. The FDR correction uses the empirical distribution of pvalues from the combined chr’s and modules (10 permutations).

Dataset FDR minp (QTL, module) unique QTL independent QTL
eQTLGen qvalue 5.82e-04 2195 909 348
eQTLGen 0.05/#DGN signals 1.18e-04 1707 762 286
eQTLGen_DGN combined chr+module #10-perms 1.00e-07 420 374 28

Among 374 eQTLGen_DGN signals, 16 are replicated in 762 eQTLGen signals. These 16 replicated signals consists of 6 independent SNPs, including (based on GRCh37),

  1. Replication of DGN signals in eQTLGen
DGN

DGN

Version Author Date
60cf10e Lili Wang 2021-01-17 

R version 4.1.0 (2021-05-18)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Catalina 10.15.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] data.table_1.14.0 workflowr_1.6.2  

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.6        whisker_0.4       knitr_1.33        magrittr_2.0.1   
 [5] R6_2.5.0          rlang_0.4.11      fansi_0.5.0       highr_0.9        
 [9] stringr_1.4.0     tools_4.1.0       xfun_0.23         utf8_1.2.1       
[13] git2r_0.28.0      htmltools_0.5.1.1 ellipsis_0.3.2    rprojroot_2.0.2  
[17] yaml_2.2.1        digest_0.6.27     tibble_3.1.2      lifecycle_1.0.0  
[21] crayon_1.4.1      later_1.2.0       vctrs_0.3.8       promises_1.2.0.1 
[25] fs_1.5.0          glue_1.4.2        evaluate_0.14     rmarkdown_2.8    
[29] stringi_1.6.2     compiler_4.1.0    pillar_1.6.1      httpuv_1.6.1     
[33] pkgconfig_2.0.3