1. Facet Simulations by LD and Population




“Low” (left) and “high” (right) European LD blocks

“Low” (left) and “high” (right) African LD blocks


2. Investigate Effect of MAF


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.


4. Incorporate some drop-out rate


  1. 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.

  2. 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.

  3. 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.



5. New T1D Results


# 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

Original results (cut snps)

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

New results (all snps)

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


#### CASE CONTROL:

# coloc
function (f, N, s) 
{
    1/(2 * N * f * (1 - f) * s * (1 - s))
}

# fGWAS
function (N0, N1, f){
  (N0 + N1)/(2 * N0 * N1 * f * ( 1 - f ))
}

# results differ only very slightly


#### QUANTITATIVE TRAITS:

# coloc
function (f, N) 
{
    1/(2 * N * f * (1 - f))
}

# fGWAS
function (N, f){
  1/(N[i] * f[i] (1 - f[i]))
} # N[i] here is the number of individuals in the association study for SNP i