Last updated: 2017-03-06
Code version: f0c2ef6
Read in \(z\) scores and look at correlations between “nullish” (very non-significant) \(z\) scores. In this case I define nullish as absolute value <2.
source("../code/SumstatQuery.R")
Loading required package: rhdf5
Loading required package: RSQLite
##
# Load data for a random subset of eqtls
dat <- GetSS("null", "../data/MatrixEQTLSumStats.Portable.h5")
bc = "Brain_Cerebellum"
bch = "Brain_Cerebellar_Hemisphere"
plot(dat$z[,bc],dat$z[,bch])
nullish = abs(dat$z[,bc])<2 & abs(dat$z[,bch])<2
cor(dat$z[nullish,bc],dat$z[nullish,bch])
[1] 0.2333828
Compare whole blood and cerebellum:
wb = "Whole_Blood"
plot(dat$z[,bc],dat$z[,wb])
nullish = abs(dat$z[,wb])<2 & abs(dat$z[,bc])<2
cor(dat$z[nullish,wb],dat$z[nullish,bc])
[1] 0.03799596
Assume \[z^r_j = \mu^r_j + e_j\] where \(e_1,e_2\) are joint normal with variance 1 and some covariance (same as correlation since they are variance 1). Then \(E((z^r_1 - z^r_2)^2) = E(\mu^r_1-\mu^r_2)^2 + 2(1-cov(e_1,e_2)) > 2(1-cov(e_1,e_2))\).
Thus \[cov(e_1,e_2) > 1- 0.5E((z^r_1 - z^r_2)^2)\] gives a lower bound on the covariance. The following therefore suggests that the correlation between the two tissues is at least 0.2469158.
hist(dat$z[,bc]-dat$z[,bch])
1-0.5*mean((dat$z[,bc]-dat$z[,bch])^2)
[1] 0.2469158
But for wb we have a lower bound of -0.2472646 so we cannot be sure of any correlation in this case.
max_absz = apply(abs(dat$z),1, max)
nullish = which(max_absz < 2)
nz = dat$z[nullish,]
vhat = cor(nz)
saveRDS(vhat,file = "../data/vhat.RDS")
vhat[bc,bch]
[1] 0.1857079
vhat[bc,wb]
[1] 0.02045105
eigen(vhat)
$values
[1] 2.3266675 1.8704651 1.2475605 1.2021521 1.1580008 1.1353868 1.1102434 1.0894189 1.0637345 1.0530726 1.0368490
[12] 1.0293853 1.0252985 1.0115447 1.0046156 0.9993881 0.9888896 0.9785565 0.9746995 0.9715746 0.9646358 0.9597148
[23] 0.9461157 0.9388400 0.9282310 0.9225111 0.9120085 0.9048764 0.8978758 0.8829140 0.8790108 0.8727914 0.8587505
[34] 0.8545009 0.8453241 0.8390861 0.8296191 0.8180433 0.8108569 0.7957429 0.7933229 0.7712908 0.7591681 0.7372654
$vectors
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] -0.21859378 -0.058570939 -0.155530072 -0.1563725806 -0.2154016707 0.314058677 -0.019873474 -0.185446320
[2,] -0.15313863 -0.108477224 -0.091687800 -0.1996134270 0.2438854249 0.076902203 -0.071964726 -0.037814592
[3,] -0.11689139 -0.114146790 0.133171209 0.1785438623 0.0022366988 -0.141212839 0.172894764 -0.062079252
[4,] -0.18779187 -0.093252167 0.018187197 -0.1310995714 -0.0938131752 -0.076656761 0.012814112 0.072675349
[5,] -0.14753690 -0.084952974 0.024271587 0.0519624818 -0.0021110095 -0.242734833 -0.147073160 -0.016307120
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[7,] -0.11795613 0.251035395 0.004545913 0.1027359366 0.0325042787 0.027549524 0.040891034 0.256521098
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[1,] 0.03715477 -0.111755271 0.0036957714 -0.094898293 -0.028453671 0.046055483 -0.0653907087 0.010073943
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[4,] -0.1957987556 0.120213756 -0.113628409 0.024117598 -0.0364067157 -0.244001075 0.4498214627 0.217332150
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[8,] 0.0102143245 0.068409977 -0.106118985 -0.101420558 0.1087971906 -0.035957626 0.0714477702 -0.028396635
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[15,] 0.3010364413 0.062748704 -0.015022432 -0.048485862 0.1428847010 0.008715654 -0.0825013332 0.179004493
[16,] 0.2381483023 0.117281613 -0.089568673 0.028100099 -0.0118428579 -0.105870328 0.0042369574 0.008245093
[17,] 0.1444429351 0.010429249 -0.085691138 0.219496717 -0.1206458800 0.144959816 0.1055116631 0.096754384
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[20,] 0.0099961432 0.071707977 0.003088724 -0.260690890 -0.2010508381 0.014517467 0.2013546322 -0.125094392
[21,] -0.0105933901 -0.143303882 -0.055773850 0.117601276 -0.0990298864 0.145197761 -0.0679779863 -0.404941215
[22,] 0.2082507076 -0.002458300 -0.046945714 -0.016016188 0.0524725524 -0.280423805 -0.0947293262 0.181194880
[,25] [,26] [,27] [,28] [,29] [,30] [,31] [,32]
[1,] -0.114170729 0.1387142253 -0.071509856 0.084466897 -0.222476655 -0.108194651 0.166282719 0.119244098
[2,] 0.255365426 0.1958003233 -0.305661279 0.133214084 -0.088441102 0.014701602 0.073851377 0.070488801
[3,] -0.072052744 -0.0514987289 -0.042843336 -0.090129525 0.127133640 0.224979657 0.140013515 -0.065068552
[4,] 0.122293086 -0.1054334435 -0.041056813 0.106141600 -0.049105085 -0.109697818 -0.260087404 0.032705648
[5,] 0.078557486 0.2503783417 0.093872165 0.084649098 0.019119670 0.101781006 0.375140071 0.001336805
[6,] -0.058341557 -0.1641756565 0.015403309 0.002509917 -0.021012079 0.306338778 -0.002393278 -0.536020049
[7,] 0.033496715 -0.0494122654 -0.330673798 -0.190874705 -0.069729803 0.239974038 0.072772666 0.023063686
[8,] -0.094784727 -0.0903777954 -0.049099708 -0.010299439 -0.026427138 -0.036049219 0.039304972 0.042207262
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[21,] -0.062430602 -0.0006670498 0.115615715 -0.089912789 0.033291512 -0.138867103 -0.129721512 0.032492435
[22,] -0.071904052 0.1039994203 0.170049885 0.064509738 -0.024983212 0.195834176 0.279095411 -0.034561954
[,33] [,34] [,35] [,36] [,37] [,38] [,39] [,40]
[1,] 0.108012946 -0.202863995 -0.080561781 0.0188235144 -0.335318785 0.1770354502 0.168508514 -0.290150795
[2,] 0.142171324 -0.022797981 0.481779197 -0.0829884800 0.099358273 -0.0815300613 -0.025585519 -0.003902323
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[8,] 0.132943999 -0.5703081263 -0.381120851 -0.0865802214
[9,] 0.036420501 0.0613884788 0.055783617 0.5130916785
[10,] 0.079831306 0.0203651516 -0.084085630 -0.5286014196
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[12,] 0.101800499 0.0465450459 0.209695573 -0.2378918713
[13,] 0.202628726 -0.0620288651 -0.053203427 0.0383527964
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[15,] 0.147633498 0.0326467206 0.650200122 -0.0513150030
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[21,] -0.098143782 0.1163501163 0.105246195 0.0843052457
[22,] 0.173916897 0.2364151598 -0.171253782 -0.0597908174
[ reached getOption("max.print") -- omitted 22 rows ]
dimnames(vhat)=NULL #had to do this to make the figure nice
corrplot::corrplot(as.matrix(vhat),xlab="")
sessionInfo()
R version 3.3.2 (2016-10-31)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: OS X El Capitan 10.11.6
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] RSQLite_1.1-2 rhdf5_2.18.0
loaded via a namespace (and not attached):
[1] workflowr_0.3.0 Rcpp_0.12.9 digest_0.6.12 rprojroot_1.2 DBI_0.5-1 backports_1.0.5 git2r_0.18.0
[8] magrittr_1.5 evaluate_0.10 stringi_1.1.2 zlibbioc_1.20.0 rmarkdown_1.3 tools_3.3.2 stringr_1.2.0
[15] yaml_2.1.14 corrplot_0.77 memoise_1.0.0 htmltools_0.3.5 knitr_1.15.1
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