This is implementation of the fixed threshold aggregation methods for disease and quantitative traits. Originally described in (Morris and Zeggni, 2010) and known as Gene- or Region-based Analysis of Variants of Intermediate and Low frequency (GRANVIL), the Aggregation method for rare variants codes observed genotype of a genetic region the count of minor alleles: $$X = \sum_i^N X_i$$
Our program implements the aggregation methods in a logistic regression framework for disease traits analysis (case control data) as BurdenBt method, and a linear regression framework for quantitative traits analysis as BurdenQt method. \(p\) value for aggregation method is based on asymptotic normal distribution of the Wald statistic in generalized linear models. One could incorporate a number of phenotype covariates in collapsing tests and evaluate the significance of the genetics component.
The same --NA_adjust option is avaliable as with collapsing methods although they slightly differ in details, as described in (Auer et al, 2013).
vtools show test BurdenBt
Name: BurdenBt
Description: Burden test for disease traits, Morris & Zeggini 2009
usage: vtools associate --method BurdenBt [-h] [--name NAME]
[--mafupper MAFUPPER]
[--alternative TAILED] [--NA_adjust]
[--moi {additive,dominant,recessive}]
Fixed threshold burden test for disease traits (Morris & Zeggini 2009).
p-value is based on the significance level of the regression coefficient for
genotypes. If --group_by option is specified, the group of variants will be
coded using the counts of variants within the group.
optional arguments:
-h, --help show this help message and exit
--name NAME Name of the test that will be appended to names of
output fields, usually used to differentiate output of
different tests, or the same test with different
parameters.
--mafupper MAFUPPER Minor allele frequency upper limit. All variants
having sample MAF<=m1 will be included in analysis.
Default set to 0.01
--alternative TAILED Alternative hypothesis is one-sided ("1") or two-sided
("2"). Default set to 1
--NA_adjust This option, if evoked, will replace missing genotype
values with a score relative to sample allele
frequencies. The association test will be adjusted to
incorporate the information. This is an effective
approach to control for type I error due to
differential degrees of missing genotypes among
samples.
--moi {additive,dominant,recessive}
Mode of inheritance. Will code genotypes as 0/1/2/NA
for additive mode, 0/1/NA for dominant or recessive
model. Default set to additive
vtools show test BurdenQt
Name: BurdenQt
Description: Burden test for quantitative traits, Morris & Zeggini 2009
usage: vtools associate --method BurdenQt [-h] [--name NAME]
[--mafupper MAFUPPER]
[--alternative TAILED] [--NA_adjust]
[--moi {additive,dominant,recessive}]
Fixed threshold burden test for quantitative traits (Morris & Zeggini 2009).
p-value is based on the significance level of the regression coefficient for
genotypes. If --group_by option is specified, the group of variants will be
coded using the counts of variants within the group.
optional arguments:
-h, --help show this help message and exit
--name NAME Name of the test that will be appended to names of
output fields, usually used to differentiate output of
different tests, or the same test with different
parameters.
--mafupper MAFUPPER Minor allele frequency upper limit. All variants
having sample MAF<=m1 will be included in analysis.
Default set to 0.01
--alternative TAILED Alternative hypothesis is one-sided ("1") or two-sided
("2"). Default set to 1
--NA_adjust This option, if evoked, will replace missing genotype
values with a score relative to sample allele
frequencies. The association test will be adjusted to
incorporate the information. This is an effective
approach to control for type I error due to
differential degrees of missing genotypes among
samples.
--moi {additive,dominant,recessive}
Mode of inheritance. Will code genotypes as 0/1/2/NA
for additive mode, 0/1/NA for dominant or recessive
model. Default set to additive
vtools associate rare status --covariates gender age bmi exposure -m "BurdenBt --name Burde\
nBt --alternative 2" --group_by name2 --to_db burdenBt -j8 > burdenBt.txt
INFO: 3180 samples are found
INFO: 2632 groups are found
INFO: Starting 8 processes to load genotypes
Loading genotypes: 100% [========================================] 3,180 33.0/s in 00:01:36
Testing for association: 100% [=========================================] 2,632/147 25.3/s in 00:01:43
INFO: Association tests on 2632 groups have completed. 147 failed.
INFO: Using annotation DB burdenBt in project test.
INFO: Annotation database used to record results of association tests. Created on Wed, 30 Jan 2013 17:39:05
vtools show fields | grep burdenBt
burdenBt.name2 name2
burdenBt.sample_size_BurdenBt sample size
burdenBt.num_variants_BurdenBt number of variants in each group (adjusted for specified MAF
burdenBt.total_mac_BurdenBt total minor allele counts in a group (adjusted for MOI)
burdenBt.beta_x_BurdenBt test statistic. In the context of regression this is estimate of
burdenBt.pvalue_BurdenBt p-value
burdenBt.wald_x_BurdenBt Wald statistic for x (beta_x/SE(beta_x))
burdenBt.beta_2_BurdenBt estimate of beta for covariate 2
burdenBt.beta_2_pvalue_BurdenBt p-value for covariate 2
burdenBt.wald_2_BurdenBt Wald statistic for covariate 2
burdenBt.beta_3_BurdenBt estimate of beta for covariate 3
burdenBt.beta_3_pvalue_BurdenBt p-value for covariate 3
burdenBt.wald_3_BurdenBt Wald statistic for covariate 3
burdenBt.beta_4_BurdenBt estimate of beta for covariate 4
burdenBt.beta_4_pvalue_BurdenBt p-value for covariate 4
burdenBt.wald_4_BurdenBt Wald statistic for covariate 4
burdenBt.beta_5_BurdenBt estimate of beta for covariate 5
burdenBt.beta_5_pvalue_BurdenBt p-value for covariate 5
burdenBt.wald_5_BurdenBt Wald statistic for covariate 5
head burdenBt.txt
name2 sample_size_BurdenBt num_variants_BurdenBt total_mac_BurdenBt beta_x_BurdenBt pvalue_BurdenBt wald_x_BurdenBt beta_2_BurdenBt beta_2_pvalue_BurdenBt wald_2_BurdenBt beta_3_BurdenBt beta_3_pvalue_BurdenBt wald_3_BurdenBt beta_4_BurdenBt beta_4_pvalue_BurdenBt wald_4_BurdenBt beta_5_BurdenBt beta_5_pvalue_BurdenBt wald_5_BurdenBt
AADACL4 3180 5 138 -0.314582 0.321174 -0.992049 -0.295836 0.0157002 -2.41581 0.031285 4.33616E-09 5.87083 0.129902 1.92805E-40 13.3137 0.437291 0.00133887 3.20752
AAMP 3180 3 35 0.00135633 0.997852 0.0026919 -0.298944 0.0146254 -2.44152 0.0312624 4.39097E-09 5.86875 0.130231 1.24946E-40 13.346 0.43547 0.00139464 3.19576
ABCG8 3180 12 152 -0.432823 0.171192 -1.36838 -0.295762 0.0157794 -2.41398 0.0314772 3.67916E-09 5.89801 0.130108 1.52929E-40 13.331 0.440976 0.001228 3.2323
ABCG5 3180 6 87 0.324674 0.3172 1.00023 -0.2988 0.0146577 -2.44073 0.0312857 4.15942E-09 5.87773 0.130409 9.33403E-41 13.3677 0.439149 0.00127711 3.22107
ABCB10 3180 6 122 0.333178 0.219379 1.22818 -0.301597 0.013796 -2.46253 0.0312644 4.40563E-09 5.8682 0.130493 9.8029E-41 13.3641 0.431826 0.00154525 3.16605
ABHD1 3180 5 29 -0.149027 0.813232 -0.236258 -0.298211 0.0148918 -2.435 0.0312405 4.49306E-09 5.86494 0.130264 1.16337E-40 13.3513 0.436326 0.001369 3.20111
ABCB6 3180 7 151 -0.00762322 0.977401 -0.028327 -0.299001 0.0146089 -2.44193 0.0312671 4.42259E-09 5.86756 0.130228 1.17642E-40 13.3505 0.435506 0.00139372 3.19595
ABI2 3180 1 25 0.982737 0.0422609 2.03094 -0.30075 0.0140623 -2.45567 0.0311325 4.9292E-09 5.84954 0.129821 1.95802E-40 13.3125 0.436794 0.00135518 3.20403
ABL2 3180 4 41 0.192361 0.698251 0.387682 -0.298745 0.0146809 -2.44016 0.0312678 4.39516E-09 5.86859 0.130322 1.10243E-40 13.3553 0.436387 0.00136405 3.20215
QQ-plot
vtools associate rare bmi --covariates gender age exposure -m "BurdenQt --name BurdenQt --a\
lternative 2" --group_by name2 --to_db burdenQt -j8 > burdenQt.txt
INFO: 3180 samples are found
INFO: 2632 groups are found
INFO: Starting 8 processes to load genotypes
Loading genotypes: 100% [===========================] 3,180 33.7/s in 00:01:34
Testing for association: 100% [=========================] 2,632/147 26.2/s in 00:01:40
INFO: Association tests on 2632 groups have completed. 147 failed.
INFO: Using annotation DB burdenQt in project test.
INFO: Annotation database used to record results of association tests. Created on Wed, 30 Jan 2013 23:01:44
vtools show fields | grep burdenQt
burdenQt.name2 name2
burdenQt.sample_size_BurdenQt sample size
burdenQt.num_variants_BurdenQt number of variants in each group (adjusted for specified MAF
burdenQt.total_mac_BurdenQt total minor allele counts in a group (adjusted for MOI)
burdenQt.beta_x_BurdenQt test statistic. In the context of regression this is estimate of
burdenQt.pvalue_BurdenQt p-value
burdenQt.wald_x_BurdenQt Wald statistic for x (beta_x/SE(beta_x))
burdenQt.beta_2_BurdenQt estimate of beta for covariate 2
burdenQt.beta_2_pvalue_BurdenQt p-value for covariate 2
burdenQt.wald_2_BurdenQt Wald statistic for covariate 2
burdenQt.beta_3_BurdenQt estimate of beta for covariate 3
burdenQt.beta_3_pvalue_BurdenQt p-value for covariate 3
burdenQt.wald_3_BurdenQt Wald statistic for covariate 3
burdenQt.beta_4_BurdenQt estimate of beta for covariate 4
burdenQt.beta_4_pvalue_BurdenQt p-value for covariate 4
burdenQt.wald_4_BurdenQt Wald statistic for covariate 4
head burdenQt.txt
name2 sample_size_BurdenQt num_variants_BurdenQt total_mac_BurdenQt beta_x_BurdenQt pvalue_BurdenQt wald_x_BurdenQt beta_2_BurdenQt beta_2_pvalue_BurdenQt wald_2_BurdenQt beta_3_BurdenQt beta_3_pvalue_BurdenQt wald_3_BurdenQt beta_4_BurdenQt beta_4_pvalue_BurdenQt wald_4_BurdenQt
AADACL4 3180 5 138 -0.461457 0.308686 -1.01815 -0.0716573 0.726877 -0.349314 0.0150768 0.0574562 1.90051 -0.939843 2.75155E-05 -4.19925
ABCB10 3180 6 122 0.119 0.814045 0.23523 -0.0795874 0.697984 -0.388079 0.0150143 0.0585374 1.89233 -0.945568 2.50587E-05 -4.2205
ABHD1 3180 5 29 0.00268703 0.997829 0.00272057 -0.0787737 0.700934 -0.384095 0.0150272 0.0583193 1.89397 -0.943247 2.5858E-05 -4.21338
ABCA4 3180 43 492 0.0820913 0.74098 0.330584 -0.0787295 0.701037 -0.383955 0.0150093 0.0586193 1.89172 -0.942885 2.59414E-05 -4.21265
ABI2 3180 1 25 1.19633 0.276415 1.0886 -0.081478 0.691101 -0.397397 0.0150043 0.0586562 1.89144 -0.941765 2.64399E-05 -4.20833
ABL2 3180 4 41 -0.613866 0.475633 -0.713429 -0.0781101 0.703263 -0.380954 0.0150498 0.0579226 1.89697 -0.945432 2.46814E-05 -4.22394
ACADL 3180 5 65 1.30339 0.0536027 1.93075 -0.0819058 0.689433 -0.39966 0.0150828 0.0572499 1.90209 -0.940465 2.6925E-05 -4.20419
ACADM 3180 4 103 0.0561593 0.916101 0.105355 -0.0778643 0.704415 -0.379401 0.0150232 0.0583868 1.89347 -0.942722 2.61415E-05 -4.2109
ACAP3 3180 3 17 0.296682 0.823678 0.222835 -0.07936 0.698787 -0.386993 0.0150257 0.0583418 1.8938 -0.942487 2.61991E-05 -4.2104
QQ-plot
Andrew P. Morris and Eleftheria Zeggini (2010) An evaluation of statistical approaches to rare variant analysis in genetic association studies. Genetic Epidemiology doi:10.1002/gepi.20450. http://doi.wiley.com/10.1002/gepi.20450
Auer et al (2013) personal communication with Paul L. Auer at Fred Hutchinson Cancer Research Center