1.  Introduction

This is implementation of the fixed threshold aggregation methods for disease and quantitative traits. Originally described in Morris and Zeggni 20101 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.

1.1  Adjust for missing genotypes

The same --NA_adjust option is avaliable as with collapsing methods although they slightly differ in details, as described in Auer et al 20132.

2.  Details

2.1  Command interface

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

2.2  Application

Example using snapshot vt_ExomeAssociation

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

 

1 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

2 personal communication with Paul L. Auer at Fred Hutchinson Cancer Research Center