So far, our simulations have been based on European UK10K data, with genomic regions chosen at random from chromosome 22. The LD of these regions was not quantified and a common question from talks has been how our method performs in high/ low LD regions.
For this reason, I have reran the results but now using either high or low LD regions from Europeans (eur) or African (afr) data. The following results are for regions with 726 SNPs (corrcov
function only takes ~ 2 mins).
There doesn’t seem to be any huge descrepencies between populations or LD structures. However, on closer examination of the correlation plots, it seems that there is a bug in the function.
I can’t see any obvious problems with the code - as long as the il2ra region 10p-6030000-6220000 has high LD and low LD comes from the first 5000 snps.
It was suggested at GSK to facet relative error plots by OR and bin by MAF at the CV.
It was suggested that LD is positively correlated with MAF so it is expected that the claimed coverage would perform less bad under sufficently powered scenarios. If something is rare, then it can only be in LD with those things which are also rare. As it becomes more common, then as will the things it is in LD with.
The \(Z\) scores are a function of OR and MAF (and sample sizes) –> think about calculating \(V\). However, this is picked up by our \(\mu\), which is also a function of these things.
The simulations below are for \(N0 = N1 = 10000\) and further illustrate that our method shouldn’t be used in lower powered scenarioes (\(OR = 1.05\)).
summary(x[x$OR==1.05, c(10,11)])
## true.mu mu.est
## Min. :1.076 Min. :0.8296
## 1st Qu.:1.589 1st Qu.:1.6593
## Median :2.028 Median :2.0764
## Mean :1.937 Mean :2.2446
## 3rd Qu.:2.327 3rd Qu.:2.6687
## Max. :2.439 Max. :5.8542
Key inference here is that \(MAF\) doesn’t have much of an effect on the coverage estimates.
predict(glm, newdata = data.frame(true.mu = 2))
## 1
## 2.24322
2 * pnorm( - abs ( 2.5 ) )
## [1] 0.01241933
Gold Standard: Haplotypes used for the simulations are derived from the 1000 genomes project data so that all low-frequency and common variant spectrum is covered.
GWAS scenario: Filtered whole-genome data to those present on custom arrays, such as the Immunochip. These variants were subsequently imputed up to the 1000 genomes panel.
GWAS with failure: Representing a GWAS with a genotype missingness rate per cohort. For each of the cohorts (i.e. 1 study with 1000 cases and controls) they removed all genotypes from 5% of the variants (after downsampling). This means that the CV could now be missing along with influential variants required for accurate imputation. For this scenario, ABFs must be rescaled by maximum effective sample size to compensate for genotype missingness. They found that this scenario only lead to problems in low power scenarioes and that is “led to only modest attrition of the causal variant coverage” in higher powered scenarios.
“We performed these analyses using an unfiltered set of 1000 Genome-derived genotypes, equivalent to an association study performed on genome-wide sequence data (“gold standard” scenario). To represent a more typical fine-mapping scenario, variants from each study were downsampled to the content of an Illumina HumanOmni2.5 BeadChip array (“GWAS” scenario). This is also a similar density to that achieved within established GWAS regions using recent custom arrays such as Metabochip or Immunochip. To capture the effects of genotyping failure, downsampling was performed with and without 5% random variant failure per cohort (n = 1000 cases or controls) in each simulated GWAS (“GWAS with failure” scenario). These GWAS genotypes were then imputed (using IMPUTE2 [22]) up to the 1000G Phase 1, all ancestries release 3 panel before analysis as above. Only well-imputed variants (INFO score >0.4) with a MAF > = 1% were included in further analyses.”
I think it would be useful to apply our approach to simulations representing the GWAS and GWAS with failure scenarios (We’ve only simulated gold standard which may not be representative of real GWAS or sufficient for the research paper).
# TRIMMED (discarding snps after QC)
load(aligned9.build37.RData)
# FULL (not discarding any snps)
load("/home/ah2011/rds/rds-cew54-wallace-share/anna/ichip-control-data.RData")
## Index_SNP nvar_diff_cut nvar_diff_snps nsnps_cut nsnps_all
## 1: rs10277986 0 0 362 372
## 2: rs11203202 -1 0 201 206
## 3: rs11954020 -7 -6 397 406
## 4: rs12416116 0 NA 300 306
## 5: rs12453507 -43 NA 790 816
## 6: rs12927355 3 12 482 605
## 7: rs13415583 -63 8 747 873
## 8: rs1456988 -23 1 382 395
## 9: rs151234 -1 0 248 268
## 10: rs1538171 20 36 702 761
## 11: rs1615504 -20 1 173 189
## 12: rs1893217 1 15 262 283
## 13: rs193778 -2 -1 293 374
## 14: rs2111485 -2 1 320 423
## 15: rs229533 0 0 208 211
## 16: rs2476601 0 0 639 658
## 17: rs3024505 0 NA 337 377
## 18: rs3087243 4 7 512 532
## 19: rs34593439 0 0 296 305
## 20: rs402072 -1 -1 151 152
## 21: rs4820830 5 11 778 797
## 22: rs516246 0 0 183 189
## 23: rs56994090 -1 -1 79 81
## 24: rs61839660 1 5 339 350
## 25: rs62447205 3 5 313 369
## 26: rs6476839 -1 NA 641 660
## 27: rs6518350 -2 -2 248 255
## 28: rs653178 2 3 160 181
## 29: rs705705 4 12 468 499
## 30: rs72727394 -2 0 64 78
## 31: rs757411 -5 NA 200 208
## 32: rs75793288 2 24 268 276
## 33: rs8056814 3 11 160 182
## Index_SNP nvar_diff_cut nvar_diff_snps nsnps_cut nsnps_all
index_snp | muhat | claim | corrcov | CI95 | req_thr | new_corrcov | new.CI95 | orig.nvar | new.nvar |
---|---|---|---|---|---|---|---|---|---|
rs10277986 | 6.192332 | 0.9889960 | 0.9171811 | (0.905031421384125,0.920389729140967) | 0.9749174 | 0.9500912 | (0.944702726685179,0.956265598673255) | 10 | 10 |
rs11203202 | 7.401054 | 0.9993207 | 0.9797289 | (0.973796670212908,0.986942265708181) | 0.8567383 | 0.9500548 | (0.93652935629839,0.950879137822264) | 4 | 3 |
rs11954020 | 4.303493 | 0.9502686 | 0.9696898 | (0.96284170064125,0.972591762859335) | 0.9247803 | 0.9500230 | (0.942877945935695,0.953687011415271) | 58 | 51 |
rs12416116 | 6.658150 | 0.9718870 | 0.9720422 | (0.96259014624179,0.978497390609567) | 0.9085938 | 0.9500149 | (0.941479734429351,0.960069411691902) | 2 | 2 |
rs12453507 | 5.108095 | 0.9503553 | 0.9520961 | (0.949520126831509,0.960313467323529) | NA | NA | NA | 44 | 1 |
rs12927355 | 8.599211 | 0.9601493 | 0.9122280 | (0.908272976009575,0.920105924495373) | 0.9792358 | 0.9500874 | (0.947007682593116,0.954576610636093) | 16 | 19 |
rs13415583 | 4.708329 | 0.9524107 | 0.9507262 | (0.942947566692847,0.9550754295913) | NA | NA | NA | 64 | 1 |
rs1456988 | 4.731193 | 0.9535380 | 0.9484886 | (0.941969187050749,0.956656664408099) | NA | NA | NA | 24 | 1 |
rs151234 | 6.449380 | 0.9775408 | 0.9458466 | (0.937614815814998,0.956531242702797) | NA | NA | NA | 2 | 1 |
rs1538171 | 6.153422 | 0.9509100 | 0.9082384 | (0.898833977355817,0.911081303456883) | 0.9813232 | 0.9500459 | (0.948553395120825,0.958570294604208) | 56 | 76 |
rs1615504 | 5.068904 | 0.9622248 | 0.9535018 | (0.948275013353071,0.960927379786153) | NA | NA | NA | 21 | 1 |
rs1893217 | 8.653968 | 0.9724025 | 0.8665701 | (0.852517466103629,0.869130993478309) | 0.9901186 | 0.9502427 | (0.942105287485973,0.951064259229036) | 10 | 11 |
rs193778 | 5.413262 | 0.9663249 | 0.9694273 | (0.963595016104752,0.973130676069367) | 0.9179688 | 0.9500951 | (0.948018997443917,0.958495326355909) | 14 | 12 |
rs2111485 | 7.648895 | 0.9669121 | 0.9511314 | (0.947141459790681,0.958967231244364) | NA | NA | NA | 3 | 1 |
rs229533 | 5.273287 | 0.9861805 | 0.9839880 | (0.972124741546224,0.984999121932125) | 0.9031772 | 0.9498967 | (0.941412154266199,0.956959036419462) | 5 | 5 |
rs2476601 | 20.777874 | 1.0000000 | 0.7543202 | (0.742903302679327,0.759711692734404) | 1.0000000 | 0.9494079 | (0.945239826213084,0.953695588462255) | 2 | 2 |
rs3024505 | 5.794417 | 0.9565988 | 0.9655758 | (0.961644787515928,0.974222283296569) | 0.9273438 | 0.9500078 | (0.949564851733834,0.964254490448463) | 3 | 3 |
rs3087243 | 8.168146 | 0.9546426 | 0.8812576 | (0.874040294034052,0.886986171445653) | 0.9903320 | 0.9500064 | (0.946791615062543,0.955898241861903) | 17 | 21 |
rs34593439 | 7.303685 | 0.9913195 | 0.9777350 | (0.968035132337749,0.981173891509216) | 0.8722656 | 0.9500235 | (0.928891413093434,0.951067311403487) | 2 | 2 |
rs402072 | 5.289199 | 0.9647504 | 0.9613291 | (0.961804677633936,0.975538030279231) | 0.9331299 | 0.9500087 | (0.951340120077907,0.965068611400695) | 9 | 8 |
rs4820830 | 6.161197 | 0.9518170 | 0.9274551 | (0.915215847325519,0.932633578047537) | 0.9645508 | 0.9500382 | (0.936496684601527,0.949899596508437) | 40 | 45 |
rs516246 | 6.681179 | 0.9742401 | 0.9394157 | (0.936299319899232,0.948388285065363) | 0.9571533 | 0.9500628 | (0.944432115584242,0.955560261926702) | 10 | 10 |
rs56994090 | 5.946041 | 0.9568165 | 0.9780607 | (0.974381965767013,0.984743432858352) | 0.9115613 | 0.9496209 | (0.951748918036831,0.96404534046064) | 6 | 5 |
rs61839660 | 11.919212 | 0.9774293 | 0.9166875 | (0.908349607106025,0.923133075504424) | 0.9883911 | 0.9500310 | (0.94164903808023,0.956010571336561) | 3 | 4 |
rs62447205 | 5.733063 | 0.9518484 | 0.9165577 | (0.91373104008924,0.921540159252631) | 0.9734863 | 0.9500312 | (0.948076142297674,0.954857195474714) | 25 | 28 |
rs6476839 | 5.733596 | 0.9638376 | 0.9644591 | (0.954895328006516,0.965745767664582) | 0.9342285 | 0.9500743 | (0.940005667540812,0.951278374208736) | 14 | 13 |
rs6518350 | 4.121487 | 0.9500279 | 0.9845063 | (0.973656030980636,0.985633967416089) | 0.8974609 | 0.9500373 | (0.938125660447938,0.956000420921729) | 10 | 8 |
rs653178 | 12.990950 | 0.9995797 | 0.7933128 | (0.782169194691251,0.799808097929654) | 0.9999866 | 0.9500326 | (0.94730144658252,0.95791150144775) | 2 | 4 |
rs705705 | 9.333459 | 0.9885632 | 0.8658267 | (0.861270144526212,0.871214931968482) | 0.9969193 | 0.9500892 | (0.951131563038664,0.957724474640495) | 8 | 12 |
rs72727394 | 5.380735 | 0.9681648 | 0.9666902 | (0.96422246654253,0.975833278299069) | 0.9135010 | 0.9500558 | (0.935365170767039,0.950294436352534) | 18 | 16 |
rs757411 | 4.762107 | 0.9531139 | 0.9561126 | (0.952113509776672,0.965919442078425) | 0.9299805 | 0.9500716 | (0.934909045219952,0.951468802544647) | 36 | 31 |
rs75793288 | 7.145365 | 0.9576472 | 0.9338571 | (0.921168658570848,0.937848269344194) | 0.9742711 | 0.9497165 | (0.944763610926613,0.95796537472138) | 17 | 19 |
rs8056814 | 8.496126 | 0.9719188 | 0.9111199 | (0.903902711839319,0.92854566640944) | 0.9838323 | 0.9507970 | (0.947286688243211,0.965032976174906) | 3 | 6 |
index_snp | muhat | claim | corrcov | CI95 | req_thr | new_corrcov | new.CI95 | orig.nvar | new.nvar |
---|---|---|---|---|---|---|---|---|---|
rs10277986 | 6.192332 | 0.9889959 | 0.9014786 | (0.891590206499145,0.90690820567881) | 0.9803348 | 0.9501245 | (0.940990797337965,0.952543524250967) | 10 | 10 |
rs11203202 | 7.401054 | 0.9993207 | 0.9664616 | (0.957810036683282,0.969656505562841) | 0.9219845 | 0.9504321 | (0.944160040956813,0.960243424652539) | 4 | 4 |
rs11954020 | 4.410225 | 0.9525516 | 0.9625245 | (0.957239901678519,0.96748062421015) | 0.9344299 | 0.9500884 | (0.943210327878538,0.954719928324372) | 58 | 52 |
rs12416116 | 6.658150 | 0.9718870 | 0.9485367 | (0.944144347283846,0.962696103851946) | NA | NA | NA | 2 | NA |
rs12453507 | 5.108034 | 0.9503121 | 0.9421846 | (0.941461553480529,0.950992199195379) | NA | NA | NA | 44 | NA |
rs12927355 | 8.663089 | 0.9580670 | 0.8114088 | (0.807444346468706,0.818382514959271) | 0.9998505 | 0.9500357 | (0.947562898562167,0.953085557818951) | 19 | 31 |
rs13415583 | 4.707577 | 0.9519610 | 0.9190704 | (0.917096059079171,0.9277348102117) | 0.9705078 | 0.9500173 | (0.943878843499672,0.95340191842997) | 64 | 72 |
rs1456988 | 4.730915 | 0.9533186 | 0.9394653 | (0.928392340433027,0.942117522596469) | 0.9632812 | 0.9500649 | (0.943153438052082,0.954690789746775) | 24 | 25 |
rs151234 | 6.448421 | 0.9759145 | 0.9325581 | (0.922975813032841,0.942706200653203) | 0.9620686 | 0.9503173 | (0.934618081902837,0.951296499047157) | 2 | 2 |
rs1538171 | 6.153095 | 0.9506085 | 0.8625061 | (0.852371085117067,0.863878926702973) | 0.9924316 | 0.9500298 | (0.944601672117194,0.953554634451195) | 57 | 93 |
rs1615504 | 5.068859 | 0.9621981 | 0.9224031 | (0.920087977649948,0.930161880519238) | 0.9735352 | 0.9500858 | (0.949023608331084,0.957529845999764) | 21 | 22 |
rs1893217 | 8.653907 | 0.9722646 | 0.8171646 | (0.809927312892616,0.824711074942543) | 0.9992873 | 0.9498141 | (0.945637308496857,0.954060950897155) | 10 | 25 |
rs193778 | 5.401205 | 0.9550472 | 0.9641863 | (0.952990214529146,0.963550396727136) | 0.9308594 | 0.9500743 | (0.94208550733159,0.952795971529675) | 20 | 19 |
rs2111485 | 7.648881 | 0.9668856 | 0.8747255 | (0.868432560370803,0.890674170252034) | 0.9884763 | 0.9495767 | (0.937258801311748,0.95165399014313) | 3 | 4 |
rs229533 | 5.273250 | 0.9861513 | 0.9771505 | (0.968250588283412,0.980047568519119) | 0.9173828 | 0.9500294 | (0.945972249156555,0.960317969094521) | 5 | 5 |
rs2476601 | 20.777874 | 1.0000000 | 0.7410395 | (0.72926325850916,0.749370515809894) | 1.0000000 | 0.9500482 | (0.944163790007028,0.953110029446778) | 2 | 2 |
rs3024505 | 5.793979 | 0.9561899 | 0.9562823 | (0.94522903435999,0.961402389414939) | NA | NA | NA | 3 | NA |
rs3087243 | 8.166220 | 0.9567886 | 0.8467156 | (0.845589789911689,0.85561940772028) | 0.9971436 | 0.9500850 | (0.947799831740829,0.955646229342681) | 18 | 25 |
rs34593439 | 7.303685 | 0.9913195 | 0.9623038 | (0.958689789500348,0.973590008018769) | 0.9013924 | 0.9495579 | (0.936719263543682,0.952135412729876) | 2 | 2 |
rs402072 | 5.289197 | 0.9647492 | 0.9649470 | (0.960837856865493,0.972821435346712) | 0.9226941 | 0.9499812 | (0.938677951537735,0.954924820954295) | 9 | 8 |
rs4820830 | 6.161197 | 0.9518169 | 0.9154805 | (0.902864652889133,0.918459364733653) | 0.9785156 | 0.9500378 | (0.947089026791078,0.959292116888197) | 40 | 51 |
rs516246 | 6.681178 | 0.9742396 | 0.9255047 | (0.919388436088101,0.930880817953164) | 0.9672852 | 0.9500158 | (0.940335507875494,0.948048162292157) | 10 | 10 |
rs56994090 | 5.946041 | 0.9568164 | 0.9672253 | (0.962901209413509,0.971980446487158) | 0.9120605 | 0.9500881 | (0.941043243370255,0.953508025286184) | 6 | 5 |
rs61839660 | 11.918420 | 0.9739596 | 0.8479311 | (0.831120279212552,0.850244553707156) | 0.9999934 | 0.9502889 | (0.946206834737962,0.955787248653584) | 3 | 8 |
rs62447205 | 5.733062 | 0.9518477 | 0.9089545 | (0.902829398641674,0.912296737757696) | 0.9776367 | 0.9500923 | (0.945927098592844,0.951788888910147) | 25 | 30 |
rs6476839 | 5.733595 | 0.9638373 | 0.9486432 | (0.945279306334145,0.954233711645975) | NA | NA | NA | 14 | NA |
rs6518350 | 4.117693 | 0.9520511 | 0.9656494 | (0.965202979897874,0.975972416530343) | 0.9230469 | 0.9500999 | (0.945952365403909,0.960034128135237) | 11 | 9 |
rs653178 | 12.990950 | 0.9995797 | 0.7393082 | (0.736558330299006,0.751685814495494) | 1.0000000 | 0.9498252 | (0.947152395916529,0.955937282190789) | 2 | 5 |
rs705705 | 9.333454 | 0.9885560 | 0.7493139 | (0.737879101689105,0.748519087602328) | 0.9999832 | 0.9500619 | (0.946895387011591,0.953905963371889) | 8 | 20 |
rs72727394 | 5.380730 | 0.9681623 | 0.9258840 | (0.923941440519498,0.937299633279572) | 0.9672363 | 0.9500725 | (0.945283850688224,0.956364728295462) | 18 | 18 |
rs757411 | 4.760895 | 0.9518965 | 0.9398577 | (0.935150890788473,0.951116598629495) | NA | NA | NA | 36 | NA |
rs75793288 | 7.320964 | 0.9508133 | 0.8087144 | (0.789900998257295,0.818328493262857) | 0.9988281 | 0.9500007 | (0.939062027225274,0.956077646314689) | 10 | 34 |
rs8056814 | 8.496009 | 0.9716798 | 0.8697871 | (0.854383825197285,0.875065668605961) | 0.9993168 | 0.9504280 | (0.94508617334529,0.958353604514732) | 3 | 14 |
Comments, next steps and questions
Continue with fine-mapping methods vignette.
Document playing around with SuSiE: https://annahutch.github.io/PhD/SuSiE.html
Next steps: Prepare for a meeting with Rob to discuss the re-weighting prior method?
P.S. I made a hex sticker!