grammar: GRAMMAR test for association in samples with genetic...
In GenABEL: genome-wide SNP association analysis
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Fast approximate test for association between a trait and
genetic polymorphisms, in samples with genetic
sub-structure (e.g. relatives). The function implements
several varieties of GRAMMAR ('gamma','gc', and 'raw').
Usage
1
2
Arguments
polyObject
object returned by
polygenic function
data
object of gwaa.data-class
method
to be used, one of 'gamma','gc', or 'raw'
propPs
proportion of non-corrected P-values used
to estimate the inflation factor Lambda, passed directly
to the estlambda
...
arguments passed to the function used for
computations, (qtscore)
Details
With 'raw' argument, the original GRAMMAR (Aulchenko et
al., 2007) is implemented. This method is conservative
and generates biased estimates of regression
coefficients.
With 'gc' argument, the GRAMMAR-GC (Amin et al., 2007) is
implemented. This method solves the conservativity of the
test, but the Genomic Control (GC) lambda is by
definition "1" and can not serve as an indicator of
goodness of the model; also, the estimates of regression
coefficients are biased (the same as in 'raw' GRAMMAR).
GRAMMAR-Gamma (default 'gamma' argument) solves these
problems, producing a correct distribution of the test
statistic, interpretable value of GC Lambda, and unbiased
estimates of the regression coefficients. All together,
the default 'gamma' method is recommended for use.
Value
Object of scan.gwaa-class
Author(s)
Gulnara Svischeva, Yurii Aulchenko
References
GRAMMAR-Raw: Aulchenko YS, de Koning DJ, Haley C.
Genomewide rapid association using mixed model and
regression: a fast and simple method for genomewide
pedigree-based quantitative trait loci association
analysis. Genetics. 2007 Sep;177(1):577-85.
GRAMMAR-GC: Amin N, van Duijn CM, Aulchenko YS. A genomic
background based method for association analysis in
related individuals. PLoS One. 2007 Dec 5;2(12):e1274.
GRAMMAR-Gamma: Svischeva G, Axenovich TI, Belonogova NM,
van Duijn CM, Aulchenko YS. Rapid variance
components-based method for whole-genome association
analysis. Nature Genetics. 2012 44:1166-1170.
doi:10.1038/ng.2410
See Also
Examples
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# Using clean ge03d2 data
require(GenABEL.data)
data(ge03d2.clean)
# take only a small piece for speed
ge03d2.clean <- ge03d2.clean[1:200,]
# estimate genomic kinship
gkin <- ibs(ge03d2.clean[,sample(autosomal(ge03d2.clean),1000)], w="freq")
# perform polygenic analysis
h2ht <- polygenic(height ~ sex + age, kin=gkin, ge03d2.clean)
h2ht$est
# compute mmscore stats
mm <- mmscore(h2ht, data=ge03d2.clean)
# compute grammar-gc
grGc <- grammar(h2ht, data=ge03d2.clean, method="gc")
# compute grammar-gamma
grGamma <- grammar(h2ht, data=ge03d2.clean, method="gamma")
# compare lambdas
lambda(mm)
estlambda(mm[,"chi2.1df"])
lambda(grGamma)
estlambda(grGamma[,"chi2.1df"])
lambda(grGc)
estlambda(grGc[,"chi2.1df"])
# compare top results
summary(mm)
summary(grGamma)
summary(grGc)
Example output
Loading required package: MASS
Loading required package: GenABEL.data
LM estimates of fixed parameters:
desmat(Intercept) desmatsex desmatage
0.11651925 1.23453121 -0.01704133
iteration = 0
Step:
[1] 0 0 0 0 0
Parameter:
[1] 0.11651925 1.23453121 -0.01704133 0.30000000 0.56832793
Function Value
[1] 89.87921
Gradient:
[1] -1.061380 -4.246806 -5.815243 26.732438 -13.566868
iteration = 1
Step:
[1] 1.075834e-05 4.304638e-05 5.894433e-05 -2.709647e-04 1.375162e-04
Parameter:
[1] 0.11653001 1.23457426 -0.01698238 0.29972904 0.56846544
Function Value
[1] 89.87432
Gradient:
[1] 1.979885 -2.394381 155.957289 26.694853 -13.454761
iteration = 2
Step:
[1] 2.628014e-04 1.155500e-03 -2.265721e-05 -7.390687e-03 3.749879e-03
Parameter:
[1] 0.11679281 1.23572976 -0.01700504 0.29233835 0.57221532
Function Value
[1] 89.63131
Gradient:
[1] 1.797861 -2.170466 141.325218 25.576060 -10.239625
iteration = 3
Step:
[1] 0.0029385946 0.0129220964 -0.0002451896 -0.0828199740 0.0416949746
Parameter:
[1] 0.11973141 1.24865185 -0.01725023 0.20951837 0.61391030
Function Value
[1] 88.16933
Gradient:
[1] 0.4232801 0.3662474 19.7069061 15.1389873 19.3499897
iteration = 4
Step:
[1] 6.139895e-04 2.700878e-03 -4.932103e-05 -1.750270e-02 8.488991e-03
Parameter:
[1] 0.12034540 1.25135273 -0.01729955 0.19201568 0.62239929
Function Value
[1] 88.10673
Gradient:
[1] 0.2623950 0.8999993 2.4421952 13.3512515 24.2057816
iteration = 5
Step:
[1] 2.177535e-04 9.586542e-04 -1.697442e-05 -6.425734e-03 2.774330e-03
Parameter:
[1] 0.12056315 1.25231139 -0.01731653 0.18558994 0.62517362
Function Value
[1] 88.09325
Gradient:
[1] 0.2291314 1.1010952 -2.3436799 12.7406456 25.7517118
iteration = 6
Step:
[1] 2.497896e-04 1.101197e-03 -1.915382e-05 -7.796971e-03 2.725423e-03
Parameter:
[1] 0.12081294 1.25341258 -0.01733568 0.17779297 0.62789904
Function Value
[1] 88.07044
Gradient:
[1] 0.2060923 1.3433700 -7.0447692 12.0488119 27.3051850
iteration = 7
Step:
[1] 4.738517e-04 2.092856e-03 -3.591166e-05 -1.589951e-02 3.988192e-03
Parameter:
[1] 0.12128679 1.25550544 -0.01737159 0.16189346 0.63188723
Function Value
[1] 88.00679
Gradient:
[1] 0.184047 1.822799 -14.828292 10.751654 29.699901
iteration = 8
Step:
[1] 7.718745e-04 3.417875e-03 -5.773777e-05 -2.845054e-02 3.794478e-03
Parameter:
[1] 0.12205866 1.25892331 -0.01742933 0.13344292 0.63568171
Function Value
[1] 87.8579
Gradient:
[1] 0.1851475 2.6427793 -25.4501919 8.6367267 32.3593859
iteration = 9
Step:
[1] 1.217179e-03 5.408498e-03 -8.951109e-05 -5.056697e-02 -1.688116e-05
Parameter:
[1] 0.12327584 1.26433181 -0.01751884 0.08287595 0.63566483
Function Value
[1] 87.53159
Gradient:
[1] 0.2497556 4.0251007 -38.2882063 5.0435165 33.8085009
iteration = 10
Step:
[1] 1.318754e-03 5.895294e-03 -9.431383e-05 -6.625823e-02 -1.202102e-02
Parameter:
[1] 0.12459460 1.27022711 -0.01761315 0.01661773 0.62364381
Function Value
[1] 87.01577
Gradient:
[1] 0.4152722 5.7522646 -46.0170678 -0.3173002 29.7316738
iteration = 11
Step:
[1] 2.381536e-05 1.131750e-04 -1.285606e-06 -3.510845e-03 -2.631429e-03
Parameter:
[1] 0.12461841 1.27034028 -0.01761444 0.01310688 0.62101238
Function Value
[1] 86.94141
Gradient:
[1] 0.4382928 5.8385777 -45.3644019 -0.6494334 28.6226381
iteration = 12
Step:
[1] -1.467428e-04 -6.272553e-04 1.243517e-05 -2.755534e-03 -9.195834e-03
Parameter:
[1] 0.12447167 1.26971303 -0.01760200 0.01035135 0.61181655
Function Value
[1] 86.69443
Gradient:
[1] 0.5169688 5.8931143 -40.9548879 -0.9143002 24.5835931
iteration = 13
Step:
[1] -0.0014454485 -0.0062753561 0.0001180949 0.0050407505 -0.0567211402
Parameter:
[1] 0.12302622 1.26343767 -0.01748391 0.01539210 0.55509541
Function Value
[1] 86.09035
Gradient:
[1] 1.1153909 5.6572645 -1.8154223 -0.2558896 -6.8794239
iteration = 14
Step:
[1] 1.065194e-04 4.386146e-04 -7.663540e-06 6.058351e-03 1.129072e-02
Parameter:
[1] 0.12313274 1.26387628 -0.01749157 0.02145045 0.56638613
Function Value
[1] 86.0575
Gradient:
[1] 1.0778905 5.5525128 -3.3922638 0.4175381 0.4081793
iteration = 15
Step:
[1] -7.606184e-05 -3.388397e-04 6.463317e-06 1.312406e-03 -1.458151e-03
Parameter:
[1] 0.12305668 1.26353744 -0.01748511 0.02276286 0.56492798
Function Value
[1] 86.05625
Gradient:
[1] 1.1140196 5.5147359 -0.8338465 0.5774545 -0.5060683
iteration = 16
Step:
[1] -4.103823e-05 -1.889406e-04 3.515644e-06 6.210880e-04 -3.817184e-04
Parameter:
[1] 0.12301564 1.26334850 -0.01748159 0.02338394 0.56454626
Function Value
[1] 86.05578
Gradient:
[1] 1.1311945 5.4891718 0.4742630 0.6521680 -0.7474911
iteration = 17
Step:
[1] -1.589290e-04 -7.459876e-04 1.319486e-05 1.672453e-03 -9.648692e-04
Parameter:
[1] 0.1228567 1.2626025 -0.0174684 0.0250564 0.5635814
Function Value
[1] 86.05384
Gradient:
[1] 1.1754009 5.3768328 4.3962897 0.8557264 -1.3593902
iteration = 18
Step:
[1] -3.169631e-04 -1.510996e-03 2.529739e-05 2.003729e-03 -1.199914e-03
Parameter:
[1] 0.12253975 1.26109152 -0.01744310 0.02706012 0.56238148
Function Value
[1] 86.04973
Gradient:
[1] 1.215000 5.125732 9.681021 1.106875 -2.122185
iteration = 19
Step:
[1] -7.655672e-04 -3.689513e-03 5.910652e-05 2.496814e-03 -1.684974e-03
Parameter:
[1] 0.12177418 1.25740201 -0.01738400 0.02955694 0.56069650
Function Value
[1] 86.03951
Gradient:
[1] 1.217237 4.466678 17.548818 1.441639 -3.193369
iteration = 20
Step:
[1] -0.0014535945 -0.0070654690 0.0001090949 0.0011786754 -0.0013891727
Parameter:
[1] 0.12032059 1.25033654 -0.01727490 0.03073561 0.55930733
Function Value
[1] 86.02005
Gradient:
[1] 1.074382 3.133432 24.746057 1.662613 -4.060041
iteration = 21
Step:
[1] -0.002012655 -0.009862492 0.000146854 -0.003143938 0.000458561
Parameter:
[1] 0.11830793 1.24047405 -0.01712805 0.02759168 0.55976589
Function Value
[1] 85.99382
Gradient:
[1] 0.682195 1.191626 24.349985 1.404159 -3.700420
iteration = 22
Step:
[1] -1.283226e-03 -6.371026e-03 8.907643e-05 -7.026871e-03 2.796214e-03
Parameter:
[1] 0.11702471 1.23410302 -0.01703897 0.02056481 0.56256210
Function Value
[1] 85.97652
Gradient:
[1] 0.2327604 -0.1280109 13.3330204 0.6368838 -1.8504154
iteration = 23
Step:
[1] -2.147584e-05 -1.782139e-04 -2.820838e-06 -4.448776e-03 2.300308e-03
Parameter:
[1] 0.11700323 1.23392481 -0.01704179 0.01611603 0.56486241
Function Value
[1] 85.97232
Gradient:
[1] 0.0407797 -0.2296893 3.2202396 0.1065418 -0.3775389
iteration = 24
Step:
[1] 2.100106e-04 1.011371e-03 -1.666699e-05 -8.021938e-04 5.843177e-04
Parameter:
[1] 0.11721324 1.23493618 -0.01705846 0.01531384 0.56544673
Function Value
[1] 85.97201
Gradient:
[1] 0.0251049244 -0.0547675061 0.2311979017 0.0002037837 -0.0090097529
iteration = 25
Step:
[1] 4.934181e-05 2.424817e-04 -3.728102e-06 1.111069e-05 2.115294e-05
Parameter:
[1] 0.11726258 1.23517866 -0.01706219 0.01532495 0.56546788
Function Value
[1] 85.97201
Gradient:
[1] 0.0301315310 -0.0095977850 -0.0054372435 -0.0009220997 0.0042019792
iteration = 26
Step:
[1] -1.141559e-05 -5.365086e-05 1.183770e-06 4.993538e-06 -6.702999e-06
Parameter:
[1] 0.11725117 1.23512501 -0.01706100 0.01532994 0.56546118
Function Value
[1] 85.97201
Gradient:
[1] 0.0414433963 -0.0122687862 -0.2509527523 0.0001301730 -0.0003211782
iteration = 27
Step:
[1] -9.104591e-07 -1.711337e-06 1.550256e-07 2.007738e-07 -4.050822e-08
Parameter:
[1] 0.11725026 1.23512330 -0.01706085 0.01533014 0.56546114
Function Value
[1] 85.97201
Gradient:
[1] 0.0457206828 -0.0100074515 -0.0153045217 0.0001630244 -0.0003469030
iteration = 28
Step:
[1] -1.227432e-06 6.804299e-07 1.296649e-07 -2.454676e-07 3.630021e-07
Parameter:
[1] 0.11724903 1.23512398 -0.01706072 0.01532990 0.56546150
Function Value
[1] 85.97201
Gradient:
[1] 0.0498894327 -0.0073959214 0.2111691386 0.0001190067 -0.0001191921
iteration = 29
Step:
[1] -3.737215e-06 1.884942e-06 2.183423e-07 -4.706268e-07 6.454854e-07
Parameter:
[1] 0.11724529 1.23512586 -0.01706050 0.01532943 0.56546215
Function Value
[1] 85.97201
Gradient:
[1] 5.603347e-02 -3.407595e-03 5.475658e-01 3.281798e-05 2.858548e-04
iteration = 30
Step:
[1] -1.142010e-05 4.254433e-06 4.423371e-07 -7.359192e-07 1.085509e-06
Parameter:
[1] 0.11723387 1.23513012 -0.01706006 0.01532869 0.56546323
Function Value
[1] 85.97201
Gradient:
[1] 0.0659069509 0.0031735540 1.0975789171 -0.0001141005 0.0009671048
iteration = 31
Step:
[1] -3.151371e-05 9.369947e-06 9.103723e-07 -9.702077e-07 1.694285e-06
Parameter:
[1] 0.11720236 1.23513949 -0.01705915 0.01532772 0.56546493
Function Value
[1] 85.97201
Gradient:
[1] 0.0807429653 0.0134705386 1.9494695627 -0.0003447373 0.0020305705
iteration = 32
Step:
[1] -8.254308e-05 2.101176e-05 1.931148e-06 -9.686785e-07 2.517150e-06
Parameter:
[1] 0.11711981 1.23516050 -0.01705722 0.01532675 0.56546744
Function Value
[1] 85.97201
Gradient:
[1] 0.101439009 0.028920694 3.206312792 -0.000690120 0.003610907
iteration = 33
Step:
[1] -1.953935e-04 4.457181e-05 3.909832e-06 9.470495e-09 3.151548e-06
Parameter:
[1] 0.11692442 1.23520507 -0.01705331 0.01532676 0.56547060
Function Value
[1] 85.972
Gradient:
[1] 0.123920837 0.048677577 4.759249822 -0.001129683 0.005590399
iteration = 34
Step:
[1] -3.794344e-04 7.943713e-05 6.681595e-06 3.201200e-06 2.254270e-06
Parameter:
[1] 0.11654499 1.23528451 -0.01704662 0.01532996 0.56547285
Function Value
[1] 85.97199
Gradient:
[1] 0.131075232 0.063887065 5.816506478 -0.001462763 0.007008171
iteration = 35
Step:
[1] -4.824975e-04 9.252834e-05 7.410266e-06 7.891759e-06 -1.741882e-06
Parameter:
[1] 0.11606249 1.23537703 -0.01703921 0.01533785 0.56547111
Function Value
[1] 85.97198
Gradient:
[1] 0.096645259 0.055615324 4.825691273 -0.001262813 0.005918292
iteration = 36
Step:
[1] -2.633445e-04 4.238559e-05 3.005662e-06 7.967450e-06 -5.356862e-06
Parameter:
[1] 0.11579915 1.23541942 -0.01703621 0.01534582 0.56546575
Function Value
[1] 85.97198
Gradient:
[1] 0.0362227937 0.0246916262 2.0514463507 -0.0005533286 0.0025591554
iteration = 37
Step:
[1] 1.243395e-05 -8.808387e-06 -1.012929e-06 2.657355e-06 -3.444412e-06
Parameter:
[1] 0.11581158 1.23541061 -0.01703722 0.01534848 0.56546231
Function Value
[1] 85.97198
Gradient:
[1] 4.168421e-03 4.007759e-03 3.096829e-01 -8.701605e-05 4.005280e-04
iteration = 38
Step:
[1] 4.059390e-05 -9.229106e-06 -8.082137e-07 -3.551224e-08 -6.428609e-07
Parameter:
[1] 0.11585217 1.23540138 -0.01703803 0.01534844 0.56546166
Function Value
[1] 85.97198
Gradient:
[1] -3.397523e-04 6.336557e-06 -4.224546e-03 1.159606e-07 -1.382148e-06
iteration = 39
Step:
[1] 7.529060e-06 -1.495965e-06 -1.223247e-07 -1.000007e-07 -3.802770e-09
Parameter:
[1] 0.11585970 1.23539989 -0.01703815 0.01534834 0.56546166
Function Value
[1] 85.97198
Gradient:
[1] -7.058532e-05 -3.463151e-05 -3.147052e-03 7.305090e-07 -3.529266e-06
iteration = 40
Step:
[1] 3.606942e-07 -6.094939e-08 -4.488056e-09 -9.051264e-09 5.355309e-09
Parameter:
[1] 0.11586006 1.23539983 -0.01703816 0.01534833 0.56546167
Function Value
[1] 85.97198
Gradient:
[1] -2.702336e-06 -1.717634e-06 -1.453417e-04 3.289813e-08 -1.588774e-07
iteration = 41
Parameter:
[1] 0.11586006 1.23539983 -0.01703816 0.01534833 0.56546167
Function Value
[1] 85.97198
Gradient:
[1] -2.529532e-08 -2.151069e-08 -1.737135e-06 1.421085e-10 -8.526513e-10
Successive iterates within tolerance.
Current iterate is probably solution.
difFGLS:
[1] 2.119508e-10 4.683787e-11 4.283435e-12
******************************************
*** GOOD convergence indicated by FGLS ***
******************************************
Warning message:
In polygenic(height ~ sex + age, kin = gkin, ge03d2.clean) :
some eigenvalues close/less than 1e-8, setting them to 1e-8
you can also try option llfun='polylik' instead
[1] 0.01534833
$estimate
[1] 1.060492
$se
[1] 0.001515374
$estimate
[1] 1.060492
$se
[1] 0.001515374
$estimate
[1] 1.061001
$se
[1] 0.001538555
$estimate
[1] 1.061001
$se
[1] 0.001538555
$estimate
[1] 1.054117
$se
[1] 0.001528574
$estimate
[1] 1.054117
$se
[1] 0.001528574
Summary for top 10 results, sorted by P1df
Chromosome Position Strand A1 A2 N effB se_effB chi2.1df
rs70099 2 8857747 + C A 196 -6.500045 1.1978528 29.44597
rs3436694 2 8921418 - C G 196 -5.590550 1.1629543 23.10914
rs3074653 2 8915495 - G C 199 -4.722629 0.9913521 22.69404
rs5036749 2 8609623 + T G 199 -4.180553 1.0202037 16.79166
rs1351516 2 8602074 + G A 199 -3.970576 1.0530589 14.21680
rs1801282 2 8931192 + C T 198 -3.973233 1.0614569 14.01146
rs6392986 2 8935924 + A T 197 3.000714 0.8241997 13.25514
rs7217010 1 2495320 + C A 199 7.234709 1.9919199 13.19163
rs3815984 1 1265810 - A G 199 2.744970 0.7763617 12.50106
rs4295994 1 1259891 - C A 198 4.514403 1.2999348 12.06029
P1df Pc1df effAB effBB chi2.2df P2df
rs70099 5.749745e-08 1.368882e-07 NA NA 0 NA
rs3436694 1.530611e-06 3.040293e-06 NA NA 0 NA
rs3074653 1.899560e-06 3.728614e-06 NA NA 0 NA
rs5036749 4.171617e-05 6.915462e-05 NA NA 0 NA
rs1351516 1.629099e-04 2.508411e-04 NA NA 0 NA
rs1801282 1.816998e-04 2.781292e-04 NA NA 0 NA
rs6392986 2.718329e-04 4.071593e-04 NA NA 0 NA
rs7217010 2.812024e-04 4.204256e-04 NA NA 0 NA
rs3815984 4.067203e-04 5.961429e-04 NA NA 0 NA
rs4295994 5.150741e-04 7.454562e-04 NA NA 0 NA
Summary for top 10 results, sorted by P1df
Chromosome Position Strand A1 A2 N effB se_effB chi2.1df
rs70099 2 8857747 + C A 196 -6.508972 1.1940149 29.71703
rs3436694 2 8921418 - C G 196 -5.601744 1.1569093 23.44487
rs3074653 2 8915495 - G C 199 -4.726256 0.9938815 22.61337
rs5036749 2 8609623 + T G 199 -4.192524 1.0240754 16.76051
rs1351516 2 8602074 + G A 199 -3.969659 1.0536795 14.19350
rs1801282 2 8931192 + C T 198 -3.984373 1.0666498 13.95328
rs6392986 2 8935924 + A T 197 3.011420 0.8242173 13.34932
rs7217010 1 2495320 + C A 199 7.237399 1.9971163 13.13283
rs3815984 1 1265810 - A G 199 2.745335 0.7766189 12.49611
rs4295994 1 1259891 - C A 198 4.521877 1.2966720 12.16122
P1df effAB effBB chi2.2df P2df Pc1df
rs70099 4.999376e-08 NA NA NA NA 1.207842e-07
rs3436694 1.285448e-06 NA NA NA NA 2.592216e-06
rs3074653 1.981016e-06 NA NA NA NA 3.900271e-06
rs5036749 4.240669e-05 NA NA NA NA 7.051826e-05
rs1351516 1.649397e-04 NA NA NA NA 2.546661e-04
rs1801282 1.874107e-04 NA NA NA NA 2.873575e-04
rs6392986 2.585160e-04 NA NA NA NA 3.895164e-04
rs7217010 2.901660e-04 NA NA NA NA 4.344736e-04
rs3815984 4.078006e-04 NA NA NA NA 5.994567e-04
rs4295994 4.879335e-04 NA NA NA NA 7.103254e-04
Summary for top 10 results, sorted by P1df
Chromosome Position Strand A1 A2 N effB se_effB chi2.1df
rs70099 2 8857747 + C A 196 -6.368126 1.1719856 29.52424
rs3436694 2 8921418 - C G 196 -5.480529 1.1355646 23.29277
rs3074653 2 8915495 - G C 199 -4.623985 0.9755446 22.46666
rs5036749 2 8609623 + T G 199 -4.101803 1.0051815 16.65178
rs1351516 2 8602074 + G A 199 -3.883760 1.0342393 14.10141
rs1801282 2 8931192 + C T 198 -3.898155 1.0469704 13.86275
rs6392986 2 8935924 + A T 197 2.946256 0.8090106 13.26272
rs7217010 1 2495320 + C A 199 7.080790 1.9602699 13.04763
rs3815984 1 1265810 - A G 199 2.685929 0.7622904 12.41504
rs4295994 1 1259891 - C A 198 4.424029 1.2727487 12.08233
P1df effAB effBB chi2.2df P2df Pc1df
rs70099 5.522180e-08 NA NA NA NA 1.207842e-07
rs3436694 1.391217e-06 NA NA NA NA 2.592216e-06
rs3074653 2.138226e-06 NA NA NA NA 3.900271e-06
rs5036749 4.490822e-05 NA NA NA NA 7.051826e-05
rs1351516 1.732135e-04 NA NA NA NA 2.546661e-04
rs1801282 1.966575e-04 NA NA NA NA 2.873575e-04
rs6392986 2.707368e-04 NA NA NA NA 3.895164e-04
rs7217010 3.036682e-04 NA NA NA NA 4.344736e-04
rs3815984 4.258900e-04 NA NA NA NA 5.994567e-04
rs4295994 5.090201e-04 NA NA NA NA 7.103254e-04
GenABEL documentation built on May 30, 2017, 3:36 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
Fast approximate test for association between a trait and genetic polymorphisms, in samples with genetic sub-structure (e.g. relatives). The function implements several varieties of GRAMMAR ('gamma','gc', and 'raw').
Usage
1 2 |
Arguments
polyObject |
object returned by
|
data |
object of |
method |
to be used, one of 'gamma','gc', or 'raw' |
propPs |
proportion of non-corrected P-values used
to estimate the inflation factor Lambda, passed directly
to the |
... |
arguments passed to the function used for
computations, ( |
Details
With 'raw' argument, the original GRAMMAR (Aulchenko et al., 2007) is implemented. This method is conservative and generates biased estimates of regression coefficients.
With 'gc' argument, the GRAMMAR-GC (Amin et al., 2007) is implemented. This method solves the conservativity of the test, but the Genomic Control (GC) lambda is by definition "1" and can not serve as an indicator of goodness of the model; also, the estimates of regression coefficients are biased (the same as in 'raw' GRAMMAR).
GRAMMAR-Gamma (default 'gamma' argument) solves these problems, producing a correct distribution of the test statistic, interpretable value of GC Lambda, and unbiased estimates of the regression coefficients. All together, the default 'gamma' method is recommended for use.
Value
Object of scan.gwaa-class
Author(s)
Gulnara Svischeva, Yurii Aulchenko
References
GRAMMAR-Raw: Aulchenko YS, de Koning DJ, Haley C. Genomewide rapid association using mixed model and regression: a fast and simple method for genomewide pedigree-based quantitative trait loci association analysis. Genetics. 2007 Sep;177(1):577-85.
GRAMMAR-GC: Amin N, van Duijn CM, Aulchenko YS. A genomic background based method for association analysis in related individuals. PLoS One. 2007 Dec 5;2(12):e1274.
GRAMMAR-Gamma: Svischeva G, Axenovich TI, Belonogova NM, van Duijn CM, Aulchenko YS. Rapid variance components-based method for whole-genome association analysis. Nature Genetics. 2012 44:1166-1170. doi:10.1038/ng.2410
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | # Using clean ge03d2 data
require(GenABEL.data)
data(ge03d2.clean)
# take only a small piece for speed
ge03d2.clean <- ge03d2.clean[1:200,]
# estimate genomic kinship
gkin <- ibs(ge03d2.clean[,sample(autosomal(ge03d2.clean),1000)], w="freq")
# perform polygenic analysis
h2ht <- polygenic(height ~ sex + age, kin=gkin, ge03d2.clean)
h2ht$est
# compute mmscore stats
mm <- mmscore(h2ht, data=ge03d2.clean)
# compute grammar-gc
grGc <- grammar(h2ht, data=ge03d2.clean, method="gc")
# compute grammar-gamma
grGamma <- grammar(h2ht, data=ge03d2.clean, method="gamma")
# compare lambdas
lambda(mm)
estlambda(mm[,"chi2.1df"])
lambda(grGamma)
estlambda(grGamma[,"chi2.1df"])
lambda(grGc)
estlambda(grGc[,"chi2.1df"])
# compare top results
summary(mm)
summary(grGamma)
summary(grGc)
|
Example output
Loading required package: MASS
Loading required package: GenABEL.data
LM estimates of fixed parameters:
desmat(Intercept) desmatsex desmatage
0.11651925 1.23453121 -0.01704133
iteration = 0
Step:
[1] 0 0 0 0 0
Parameter:
[1] 0.11651925 1.23453121 -0.01704133 0.30000000 0.56832793
Function Value
[1] 89.87921
Gradient:
[1] -1.061380 -4.246806 -5.815243 26.732438 -13.566868
iteration = 1
Step:
[1] 1.075834e-05 4.304638e-05 5.894433e-05 -2.709647e-04 1.375162e-04
Parameter:
[1] 0.11653001 1.23457426 -0.01698238 0.29972904 0.56846544
Function Value
[1] 89.87432
Gradient:
[1] 1.979885 -2.394381 155.957289 26.694853 -13.454761
iteration = 2
Step:
[1] 2.628014e-04 1.155500e-03 -2.265721e-05 -7.390687e-03 3.749879e-03
Parameter:
[1] 0.11679281 1.23572976 -0.01700504 0.29233835 0.57221532
Function Value
[1] 89.63131
Gradient:
[1] 1.797861 -2.170466 141.325218 25.576060 -10.239625
iteration = 3
Step:
[1] 0.0029385946 0.0129220964 -0.0002451896 -0.0828199740 0.0416949746
Parameter:
[1] 0.11973141 1.24865185 -0.01725023 0.20951837 0.61391030
Function Value
[1] 88.16933
Gradient:
[1] 0.4232801 0.3662474 19.7069061 15.1389873 19.3499897
iteration = 4
Step:
[1] 6.139895e-04 2.700878e-03 -4.932103e-05 -1.750270e-02 8.488991e-03
Parameter:
[1] 0.12034540 1.25135273 -0.01729955 0.19201568 0.62239929
Function Value
[1] 88.10673
Gradient:
[1] 0.2623950 0.8999993 2.4421952 13.3512515 24.2057816
iteration = 5
Step:
[1] 2.177535e-04 9.586542e-04 -1.697442e-05 -6.425734e-03 2.774330e-03
Parameter:
[1] 0.12056315 1.25231139 -0.01731653 0.18558994 0.62517362
Function Value
[1] 88.09325
Gradient:
[1] 0.2291314 1.1010952 -2.3436799 12.7406456 25.7517118
iteration = 6
Step:
[1] 2.497896e-04 1.101197e-03 -1.915382e-05 -7.796971e-03 2.725423e-03
Parameter:
[1] 0.12081294 1.25341258 -0.01733568 0.17779297 0.62789904
Function Value
[1] 88.07044
Gradient:
[1] 0.2060923 1.3433700 -7.0447692 12.0488119 27.3051850
iteration = 7
Step:
[1] 4.738517e-04 2.092856e-03 -3.591166e-05 -1.589951e-02 3.988192e-03
Parameter:
[1] 0.12128679 1.25550544 -0.01737159 0.16189346 0.63188723
Function Value
[1] 88.00679
Gradient:
[1] 0.184047 1.822799 -14.828292 10.751654 29.699901
iteration = 8
Step:
[1] 7.718745e-04 3.417875e-03 -5.773777e-05 -2.845054e-02 3.794478e-03
Parameter:
[1] 0.12205866 1.25892331 -0.01742933 0.13344292 0.63568171
Function Value
[1] 87.8579
Gradient:
[1] 0.1851475 2.6427793 -25.4501919 8.6367267 32.3593859
iteration = 9
Step:
[1] 1.217179e-03 5.408498e-03 -8.951109e-05 -5.056697e-02 -1.688116e-05
Parameter:
[1] 0.12327584 1.26433181 -0.01751884 0.08287595 0.63566483
Function Value
[1] 87.53159
Gradient:
[1] 0.2497556 4.0251007 -38.2882063 5.0435165 33.8085009
iteration = 10
Step:
[1] 1.318754e-03 5.895294e-03 -9.431383e-05 -6.625823e-02 -1.202102e-02
Parameter:
[1] 0.12459460 1.27022711 -0.01761315 0.01661773 0.62364381
Function Value
[1] 87.01577
Gradient:
[1] 0.4152722 5.7522646 -46.0170678 -0.3173002 29.7316738
iteration = 11
Step:
[1] 2.381536e-05 1.131750e-04 -1.285606e-06 -3.510845e-03 -2.631429e-03
Parameter:
[1] 0.12461841 1.27034028 -0.01761444 0.01310688 0.62101238
Function Value
[1] 86.94141
Gradient:
[1] 0.4382928 5.8385777 -45.3644019 -0.6494334 28.6226381
iteration = 12
Step:
[1] -1.467428e-04 -6.272553e-04 1.243517e-05 -2.755534e-03 -9.195834e-03
Parameter:
[1] 0.12447167 1.26971303 -0.01760200 0.01035135 0.61181655
Function Value
[1] 86.69443
Gradient:
[1] 0.5169688 5.8931143 -40.9548879 -0.9143002 24.5835931
iteration = 13
Step:
[1] -0.0014454485 -0.0062753561 0.0001180949 0.0050407505 -0.0567211402
Parameter:
[1] 0.12302622 1.26343767 -0.01748391 0.01539210 0.55509541
Function Value
[1] 86.09035
Gradient:
[1] 1.1153909 5.6572645 -1.8154223 -0.2558896 -6.8794239
iteration = 14
Step:
[1] 1.065194e-04 4.386146e-04 -7.663540e-06 6.058351e-03 1.129072e-02
Parameter:
[1] 0.12313274 1.26387628 -0.01749157 0.02145045 0.56638613
Function Value
[1] 86.0575
Gradient:
[1] 1.0778905 5.5525128 -3.3922638 0.4175381 0.4081793
iteration = 15
Step:
[1] -7.606184e-05 -3.388397e-04 6.463317e-06 1.312406e-03 -1.458151e-03
Parameter:
[1] 0.12305668 1.26353744 -0.01748511 0.02276286 0.56492798
Function Value
[1] 86.05625
Gradient:
[1] 1.1140196 5.5147359 -0.8338465 0.5774545 -0.5060683
iteration = 16
Step:
[1] -4.103823e-05 -1.889406e-04 3.515644e-06 6.210880e-04 -3.817184e-04
Parameter:
[1] 0.12301564 1.26334850 -0.01748159 0.02338394 0.56454626
Function Value
[1] 86.05578
Gradient:
[1] 1.1311945 5.4891718 0.4742630 0.6521680 -0.7474911
iteration = 17
Step:
[1] -1.589290e-04 -7.459876e-04 1.319486e-05 1.672453e-03 -9.648692e-04
Parameter:
[1] 0.1228567 1.2626025 -0.0174684 0.0250564 0.5635814
Function Value
[1] 86.05384
Gradient:
[1] 1.1754009 5.3768328 4.3962897 0.8557264 -1.3593902
iteration = 18
Step:
[1] -3.169631e-04 -1.510996e-03 2.529739e-05 2.003729e-03 -1.199914e-03
Parameter:
[1] 0.12253975 1.26109152 -0.01744310 0.02706012 0.56238148
Function Value
[1] 86.04973
Gradient:
[1] 1.215000 5.125732 9.681021 1.106875 -2.122185
iteration = 19
Step:
[1] -7.655672e-04 -3.689513e-03 5.910652e-05 2.496814e-03 -1.684974e-03
Parameter:
[1] 0.12177418 1.25740201 -0.01738400 0.02955694 0.56069650
Function Value
[1] 86.03951
Gradient:
[1] 1.217237 4.466678 17.548818 1.441639 -3.193369
iteration = 20
Step:
[1] -0.0014535945 -0.0070654690 0.0001090949 0.0011786754 -0.0013891727
Parameter:
[1] 0.12032059 1.25033654 -0.01727490 0.03073561 0.55930733
Function Value
[1] 86.02005
Gradient:
[1] 1.074382 3.133432 24.746057 1.662613 -4.060041
iteration = 21
Step:
[1] -0.002012655 -0.009862492 0.000146854 -0.003143938 0.000458561
Parameter:
[1] 0.11830793 1.24047405 -0.01712805 0.02759168 0.55976589
Function Value
[1] 85.99382
Gradient:
[1] 0.682195 1.191626 24.349985 1.404159 -3.700420
iteration = 22
Step:
[1] -1.283226e-03 -6.371026e-03 8.907643e-05 -7.026871e-03 2.796214e-03
Parameter:
[1] 0.11702471 1.23410302 -0.01703897 0.02056481 0.56256210
Function Value
[1] 85.97652
Gradient:
[1] 0.2327604 -0.1280109 13.3330204 0.6368838 -1.8504154
iteration = 23
Step:
[1] -2.147584e-05 -1.782139e-04 -2.820838e-06 -4.448776e-03 2.300308e-03
Parameter:
[1] 0.11700323 1.23392481 -0.01704179 0.01611603 0.56486241
Function Value
[1] 85.97232
Gradient:
[1] 0.0407797 -0.2296893 3.2202396 0.1065418 -0.3775389
iteration = 24
Step:
[1] 2.100106e-04 1.011371e-03 -1.666699e-05 -8.021938e-04 5.843177e-04
Parameter:
[1] 0.11721324 1.23493618 -0.01705846 0.01531384 0.56544673
Function Value
[1] 85.97201
Gradient:
[1] 0.0251049244 -0.0547675061 0.2311979017 0.0002037837 -0.0090097529
iteration = 25
Step:
[1] 4.934181e-05 2.424817e-04 -3.728102e-06 1.111069e-05 2.115294e-05
Parameter:
[1] 0.11726258 1.23517866 -0.01706219 0.01532495 0.56546788
Function Value
[1] 85.97201
Gradient:
[1] 0.0301315310 -0.0095977850 -0.0054372435 -0.0009220997 0.0042019792
iteration = 26
Step:
[1] -1.141559e-05 -5.365086e-05 1.183770e-06 4.993538e-06 -6.702999e-06
Parameter:
[1] 0.11725117 1.23512501 -0.01706100 0.01532994 0.56546118
Function Value
[1] 85.97201
Gradient:
[1] 0.0414433963 -0.0122687862 -0.2509527523 0.0001301730 -0.0003211782
iteration = 27
Step:
[1] -9.104591e-07 -1.711337e-06 1.550256e-07 2.007738e-07 -4.050822e-08
Parameter:
[1] 0.11725026 1.23512330 -0.01706085 0.01533014 0.56546114
Function Value
[1] 85.97201
Gradient:
[1] 0.0457206828 -0.0100074515 -0.0153045217 0.0001630244 -0.0003469030
iteration = 28
Step:
[1] -1.227432e-06 6.804299e-07 1.296649e-07 -2.454676e-07 3.630021e-07
Parameter:
[1] 0.11724903 1.23512398 -0.01706072 0.01532990 0.56546150
Function Value
[1] 85.97201
Gradient:
[1] 0.0498894327 -0.0073959214 0.2111691386 0.0001190067 -0.0001191921
iteration = 29
Step:
[1] -3.737215e-06 1.884942e-06 2.183423e-07 -4.706268e-07 6.454854e-07
Parameter:
[1] 0.11724529 1.23512586 -0.01706050 0.01532943 0.56546215
Function Value
[1] 85.97201
Gradient:
[1] 5.603347e-02 -3.407595e-03 5.475658e-01 3.281798e-05 2.858548e-04
iteration = 30
Step:
[1] -1.142010e-05 4.254433e-06 4.423371e-07 -7.359192e-07 1.085509e-06
Parameter:
[1] 0.11723387 1.23513012 -0.01706006 0.01532869 0.56546323
Function Value
[1] 85.97201
Gradient:
[1] 0.0659069509 0.0031735540 1.0975789171 -0.0001141005 0.0009671048
iteration = 31
Step:
[1] -3.151371e-05 9.369947e-06 9.103723e-07 -9.702077e-07 1.694285e-06
Parameter:
[1] 0.11720236 1.23513949 -0.01705915 0.01532772 0.56546493
Function Value
[1] 85.97201
Gradient:
[1] 0.0807429653 0.0134705386 1.9494695627 -0.0003447373 0.0020305705
iteration = 32
Step:
[1] -8.254308e-05 2.101176e-05 1.931148e-06 -9.686785e-07 2.517150e-06
Parameter:
[1] 0.11711981 1.23516050 -0.01705722 0.01532675 0.56546744
Function Value
[1] 85.97201
Gradient:
[1] 0.101439009 0.028920694 3.206312792 -0.000690120 0.003610907
iteration = 33
Step:
[1] -1.953935e-04 4.457181e-05 3.909832e-06 9.470495e-09 3.151548e-06
Parameter:
[1] 0.11692442 1.23520507 -0.01705331 0.01532676 0.56547060
Function Value
[1] 85.972
Gradient:
[1] 0.123920837 0.048677577 4.759249822 -0.001129683 0.005590399
iteration = 34
Step:
[1] -3.794344e-04 7.943713e-05 6.681595e-06 3.201200e-06 2.254270e-06
Parameter:
[1] 0.11654499 1.23528451 -0.01704662 0.01532996 0.56547285
Function Value
[1] 85.97199
Gradient:
[1] 0.131075232 0.063887065 5.816506478 -0.001462763 0.007008171
iteration = 35
Step:
[1] -4.824975e-04 9.252834e-05 7.410266e-06 7.891759e-06 -1.741882e-06
Parameter:
[1] 0.11606249 1.23537703 -0.01703921 0.01533785 0.56547111
Function Value
[1] 85.97198
Gradient:
[1] 0.096645259 0.055615324 4.825691273 -0.001262813 0.005918292
iteration = 36
Step:
[1] -2.633445e-04 4.238559e-05 3.005662e-06 7.967450e-06 -5.356862e-06
Parameter:
[1] 0.11579915 1.23541942 -0.01703621 0.01534582 0.56546575
Function Value
[1] 85.97198
Gradient:
[1] 0.0362227937 0.0246916262 2.0514463507 -0.0005533286 0.0025591554
iteration = 37
Step:
[1] 1.243395e-05 -8.808387e-06 -1.012929e-06 2.657355e-06 -3.444412e-06
Parameter:
[1] 0.11581158 1.23541061 -0.01703722 0.01534848 0.56546231
Function Value
[1] 85.97198
Gradient:
[1] 4.168421e-03 4.007759e-03 3.096829e-01 -8.701605e-05 4.005280e-04
iteration = 38
Step:
[1] 4.059390e-05 -9.229106e-06 -8.082137e-07 -3.551224e-08 -6.428609e-07
Parameter:
[1] 0.11585217 1.23540138 -0.01703803 0.01534844 0.56546166
Function Value
[1] 85.97198
Gradient:
[1] -3.397523e-04 6.336557e-06 -4.224546e-03 1.159606e-07 -1.382148e-06
iteration = 39
Step:
[1] 7.529060e-06 -1.495965e-06 -1.223247e-07 -1.000007e-07 -3.802770e-09
Parameter:
[1] 0.11585970 1.23539989 -0.01703815 0.01534834 0.56546166
Function Value
[1] 85.97198
Gradient:
[1] -7.058532e-05 -3.463151e-05 -3.147052e-03 7.305090e-07 -3.529266e-06
iteration = 40
Step:
[1] 3.606942e-07 -6.094939e-08 -4.488056e-09 -9.051264e-09 5.355309e-09
Parameter:
[1] 0.11586006 1.23539983 -0.01703816 0.01534833 0.56546167
Function Value
[1] 85.97198
Gradient:
[1] -2.702336e-06 -1.717634e-06 -1.453417e-04 3.289813e-08 -1.588774e-07
iteration = 41
Parameter:
[1] 0.11586006 1.23539983 -0.01703816 0.01534833 0.56546167
Function Value
[1] 85.97198
Gradient:
[1] -2.529532e-08 -2.151069e-08 -1.737135e-06 1.421085e-10 -8.526513e-10
Successive iterates within tolerance.
Current iterate is probably solution.
difFGLS:
[1] 2.119508e-10 4.683787e-11 4.283435e-12
******************************************
*** GOOD convergence indicated by FGLS ***
******************************************
Warning message:
In polygenic(height ~ sex + age, kin = gkin, ge03d2.clean) :
some eigenvalues close/less than 1e-8, setting them to 1e-8
you can also try option llfun='polylik' instead
[1] 0.01534833
$estimate
[1] 1.060492
$se
[1] 0.001515374
$estimate
[1] 1.060492
$se
[1] 0.001515374
$estimate
[1] 1.061001
$se
[1] 0.001538555
$estimate
[1] 1.061001
$se
[1] 0.001538555
$estimate
[1] 1.054117
$se
[1] 0.001528574
$estimate
[1] 1.054117
$se
[1] 0.001528574
Summary for top 10 results, sorted by P1df
Chromosome Position Strand A1 A2 N effB se_effB chi2.1df
rs70099 2 8857747 + C A 196 -6.500045 1.1978528 29.44597
rs3436694 2 8921418 - C G 196 -5.590550 1.1629543 23.10914
rs3074653 2 8915495 - G C 199 -4.722629 0.9913521 22.69404
rs5036749 2 8609623 + T G 199 -4.180553 1.0202037 16.79166
rs1351516 2 8602074 + G A 199 -3.970576 1.0530589 14.21680
rs1801282 2 8931192 + C T 198 -3.973233 1.0614569 14.01146
rs6392986 2 8935924 + A T 197 3.000714 0.8241997 13.25514
rs7217010 1 2495320 + C A 199 7.234709 1.9919199 13.19163
rs3815984 1 1265810 - A G 199 2.744970 0.7763617 12.50106
rs4295994 1 1259891 - C A 198 4.514403 1.2999348 12.06029
P1df Pc1df effAB effBB chi2.2df P2df
rs70099 5.749745e-08 1.368882e-07 NA NA 0 NA
rs3436694 1.530611e-06 3.040293e-06 NA NA 0 NA
rs3074653 1.899560e-06 3.728614e-06 NA NA 0 NA
rs5036749 4.171617e-05 6.915462e-05 NA NA 0 NA
rs1351516 1.629099e-04 2.508411e-04 NA NA 0 NA
rs1801282 1.816998e-04 2.781292e-04 NA NA 0 NA
rs6392986 2.718329e-04 4.071593e-04 NA NA 0 NA
rs7217010 2.812024e-04 4.204256e-04 NA NA 0 NA
rs3815984 4.067203e-04 5.961429e-04 NA NA 0 NA
rs4295994 5.150741e-04 7.454562e-04 NA NA 0 NA
Summary for top 10 results, sorted by P1df
Chromosome Position Strand A1 A2 N effB se_effB chi2.1df
rs70099 2 8857747 + C A 196 -6.508972 1.1940149 29.71703
rs3436694 2 8921418 - C G 196 -5.601744 1.1569093 23.44487
rs3074653 2 8915495 - G C 199 -4.726256 0.9938815 22.61337
rs5036749 2 8609623 + T G 199 -4.192524 1.0240754 16.76051
rs1351516 2 8602074 + G A 199 -3.969659 1.0536795 14.19350
rs1801282 2 8931192 + C T 198 -3.984373 1.0666498 13.95328
rs6392986 2 8935924 + A T 197 3.011420 0.8242173 13.34932
rs7217010 1 2495320 + C A 199 7.237399 1.9971163 13.13283
rs3815984 1 1265810 - A G 199 2.745335 0.7766189 12.49611
rs4295994 1 1259891 - C A 198 4.521877 1.2966720 12.16122
P1df effAB effBB chi2.2df P2df Pc1df
rs70099 4.999376e-08 NA NA NA NA 1.207842e-07
rs3436694 1.285448e-06 NA NA NA NA 2.592216e-06
rs3074653 1.981016e-06 NA NA NA NA 3.900271e-06
rs5036749 4.240669e-05 NA NA NA NA 7.051826e-05
rs1351516 1.649397e-04 NA NA NA NA 2.546661e-04
rs1801282 1.874107e-04 NA NA NA NA 2.873575e-04
rs6392986 2.585160e-04 NA NA NA NA 3.895164e-04
rs7217010 2.901660e-04 NA NA NA NA 4.344736e-04
rs3815984 4.078006e-04 NA NA NA NA 5.994567e-04
rs4295994 4.879335e-04 NA NA NA NA 7.103254e-04
Summary for top 10 results, sorted by P1df
Chromosome Position Strand A1 A2 N effB se_effB chi2.1df
rs70099 2 8857747 + C A 196 -6.368126 1.1719856 29.52424
rs3436694 2 8921418 - C G 196 -5.480529 1.1355646 23.29277
rs3074653 2 8915495 - G C 199 -4.623985 0.9755446 22.46666
rs5036749 2 8609623 + T G 199 -4.101803 1.0051815 16.65178
rs1351516 2 8602074 + G A 199 -3.883760 1.0342393 14.10141
rs1801282 2 8931192 + C T 198 -3.898155 1.0469704 13.86275
rs6392986 2 8935924 + A T 197 2.946256 0.8090106 13.26272
rs7217010 1 2495320 + C A 199 7.080790 1.9602699 13.04763
rs3815984 1 1265810 - A G 199 2.685929 0.7622904 12.41504
rs4295994 1 1259891 - C A 198 4.424029 1.2727487 12.08233
P1df effAB effBB chi2.2df P2df Pc1df
rs70099 5.522180e-08 NA NA NA NA 1.207842e-07
rs3436694 1.391217e-06 NA NA NA NA 2.592216e-06
rs3074653 2.138226e-06 NA NA NA NA 3.900271e-06
rs5036749 4.490822e-05 NA NA NA NA 7.051826e-05
rs1351516 1.732135e-04 NA NA NA NA 2.546661e-04
rs1801282 1.966575e-04 NA NA NA NA 2.873575e-04
rs6392986 2.707368e-04 NA NA NA NA 3.895164e-04
rs7217010 3.036682e-04 NA NA NA NA 4.344736e-04
rs3815984 4.258900e-04 NA NA NA NA 5.994567e-04
rs4295994 5.090201e-04 NA NA NA NA 7.103254e-04
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