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  1. 1. Introduction
  2. 2. Details
    1. 2.1 Command interface
    2. 2.2 Application

1.  Introduction

This implements a collection of weighted aggregation tests. Different from plain aggregation methods which assumes equal contribution of each locus from the genetic region under investigation, the weighted methods assigns a "weight" to each variant site such that each site differs from another by the weight they are assigned, and these weights will contribute to the aggregated "burden", e.g., {$$X=\sum_i^N\omega_iX_i$$} where {$\omega_i$}'s are the weights. The weights often reflect the relative importance of a variant in terms of its contribution to phenotype.

The weighting approach was first proposed by Madsen and Browning 20101 with the assumption that "rarer" variants tend to be more important (the WSS statistic). This weighting theme is by far the most popular weights and has been adapted into a number of methods emerged later, such as Lin and Tang 20112 and Wu et al 20113. Other weighting themes such as KBAC and RBT weightings have different assumptions but they are also based solely on internal information from data. Price et al 20104 proposed the use of "external" weights, i.e., using functional annotation sources to calculate weight for rare variants. This weighting theme can also be naturally integrated into many rare variants methods.

Implementation of WeightedBurdenBt and WeightedBurdenQt are similar to aggregation methods but allows the use of the following weighting themes:

  • WSS weight, based on entire sample
  • WSS weight, based on controls or sample with above/below average phenotype values
  • RBT weight
  • KBAC weight
  • External weights from annotation

Permutation methods have to be used to obtain {$p$} value for WSS (control based), KBAC and RBT weighting themes.

2.  Details

2.1  Command interface

vtools show test WeightedBurdenBt
Name:          WeightedBurdenBt
Description:   Weighted genotype burden tests for disease traits, using one or many
               arbitrary external weights as well as one of 4 internal
               weighting themes
usage: vtools associate --method WeightedBurdenBt [-h] [--name NAME]
                                                  [--mafupper MAFUPPER]
                                                  [--alternative TAILED]
                                                  [-p N] [--permute_by XY]
                                                  [--adaptive C]
                                                  [--extern_weight [EXTERN_WEIGHT [EXTERN_WEIGHT ...]]]
                                                  [--weight {Browning_all,Browning,KBAC,RBT}]
                                                  [--NA_adjust]
                                                  [--moi {additive,dominant,recessive}]

Weighted genotype burden tests for disease traits, using one or many arbitrary
external weights as well as one of 4 internal weighting themes. External
weights (variant/genotype annotation field) are passed into the test by
--var_info and --geno_info options. Internal weighting themes are one of
"Browning_all", "Browning", "KBAC" or "RBT". p-value is based on logistic
regression analysis and permutation procedure has to be used for "Browning",
"KBAC" or "RBT" weights.

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
  -p N, --permutations N
                        Number of permutations
  --permute_by XY       Permute phenotypes ("Y") or genotypes ("X"). Default
                        is "Y"
  --adaptive C          Adaptive permutation using Edwin Wilson 95 percent
                        confidence interval for binomial distribution. The
                        program will compute a p-value every 1000 permutations
                        and compare the lower bound of the 95 percent CI of
                        p-value against "C", and quit permutations with the
                        p-value if it is larger than "C". It is recommended to
                        specify a "C" that is slightly larger than the
                        significance level for the study. To disable the
                        adaptive procedure, set C=1. Default is C=0.1
  --extern_weight [EXTERN_WEIGHT [EXTERN_WEIGHT ...]]
                        External weights that will be directly applied to
                        genotype coding. Names of these weights should be in
                        one of '--var_info' or '--geno_info'. If multiple
                        weights are specified, they will be applied to
                        genotypes sequentially. Note that all weights will be
                        masked if --use_indicator is evoked.
  --weight {Browning_all,Browning,KBAC,RBT}
                        Internal weighting themes inspired by various
                        association methods. Valid choices are:
                        'Browning_all', 'Browning', 'KBAC' and 'RBT'. Default
                        set to 'Browning_all'. Except for 'Browning_all'
                        weighting, tests using all other weighting themes has
                        to calculate p-value via permutation. For details of
                        the weighting themes, please refer to the online
                        documentation.
  --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 WeightedBurdenQt
Name:          WeightedBurdenQt
Description:   Weighted genotype burden tests for quantitative traits, using one or
               many arbitrary external weights as well as one of 4
               internal weighting themes
usage: vtools associate --method WeightedBurdenQt [-h] [--name NAME]
                                                  [--mafupper MAFUPPER]
                                                  [--alternative TAILED]
                                                  [-p N] [--permute_by XY]
                                                  [--adaptive C]
                                                  [--extern_weight [EXTERN_WEIGHT [EXTERN_WEIGHT ...]]]
                                                  [--weight {Browning_all,Browning,KBAC,RBT}]
                                                  [--NA_adjust]
                                                  [--moi {additive,dominant,recessive}]

Weighted genotype burden tests for quantitative traits, using one or many
arbitrary external weights as well as one of 4 internal weighting themes.
External weights (variant/genotype annotation field) are passed into the test
by --var_info and --geno_info options. Internal weighting themes are one of
"Browning_all", "Browning", "KBAC" or "RBT". p-value is based on linear
regression analysis and permutation procedure has to be used for "Browning",
"KBAC" or "RBT" weights.

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
  -p N, --permutations N
                        Number of permutations
  --permute_by XY       Permute phenotypes ("Y") or genotypes ("X"). Default
                        is "Y"
  --adaptive C          Adaptive permutation using Edwin Wilson 95 percent
                        confidence interval for binomial distribution. The
                        program will compute a p-value every 1000 permutations
                        and compare the lower bound of the 95 percent CI of
                        p-value against "C", and quit permutations with the
                        p-value if it is larger than "C". It is recommended to
                        specify a "C" that is slightly larger than the
                        significance level for the study. To disable the
                        adaptive procedure, set C=1. Default is C=0.1
  --extern_weight [EXTERN_WEIGHT [EXTERN_WEIGHT ...]]
                        External weights that will be directly applied to
                        genotype coding. Names of these weights should be in
                        one of '--var_info' or '--geno_info'. If multiple
                        weights are specified, they will be applied to
                        genotypes sequentially. Note that all weights will be
                        masked if --use_indicator is evoked.
  --weight {Browning_all,Browning,KBAC,RBT}
                        Internal weighting themes inspired by various
                        association methods. Valid choices are:
                        'Browning_all', 'Browning', 'KBAC' and 'RBT'. Default
                        set to 'Browning_all'. Except for 'Browning_all'
                        weighting, tests using all other weighting themes has
                        to calculate p-value via permutation. For details of
                        the weighting themes, please refer to the online
                        documentation.
  --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
                        mode. Default set to additive

2.2  Application

Example using snapshot vt_ExomeAssociation

vtools associate rare status --covariates age gender bmi exposure -m "WeightedBurdenBt --na\
me WeightedBurdenBt --alternative 2" --group_by name2 --to_db weightedburdenBt -j8 > weight\
edburdenBt.txt
INFO: 3180 samples are found
INFO: 2632 groups are found
INFO: Starting 8 processes to load genotypes
Loading genotypes: 100% [===============================================] 3,180 23.6/s in 00:02:15
Testing for association: 100% [=====================================================] 2,632/195 4.5/s in 00:09:48
INFO: Association tests on 2632 groups have completed. 195 failed.
INFO: Using annotation DB weightedburdenBt in project test.
INFO: Annotation database used to record results of association tests. Created on Thu, 31 Jan 2013 21:36:29
vtools show fields | grep weightedburdenBt
weightedburdenBt.name2       name2
weightedburdenBt.sample_size_WeightedBurdenBt sample size
weightedburdenBt.num_variants_WeightedBurdenBt number of variants in each group (adjusted for specified MAF
weightedburdenBt.total_mac_WeightedBurdenBt total minor allele counts in a group (adjusted for MOI)
weightedburdenBt.beta_x_WeightedBurdenBt test statistic. In the context of regression this is estimate of
weightedburdenBt.pvalue_WeightedBurdenBt p-value
weightedburdenBt.wald_x_WeightedBurdenBt Wald statistic for x (beta_x/SE(beta_x))
weightedburdenBt.beta_2_WeightedBurdenBt estimate of beta for covariate 2
weightedburdenBt.beta_2_pvalue_WeightedBurdenBt p-value for covariate 2
weightedburdenBt.wald_2_WeightedBurdenBt Wald statistic for covariate 2
weightedburdenBt.beta_3_WeightedBurdenBt estimate of beta for covariate 3
weightedburdenBt.beta_3_pvalue_WeightedBurdenBt p-value for covariate 3
weightedburdenBt.wald_3_WeightedBurdenBt Wald statistic for covariate 3
weightedburdenBt.beta_4_WeightedBurdenBt estimate of beta for covariate 4
weightedburdenBt.beta_4_pvalue_WeightedBurdenBt p-value for covariate 4
weightedburdenBt.wald_4_WeightedBurdenBt Wald statistic for covariate 4
weightedburdenBt.beta_5_WeightedBurdenBt estimate of beta for covariate 5
weightedburdenBt.beta_5_pvalue_WeightedBurdenBt p-value for covariate 5
weightedburdenBt.wald_5_WeightedBurdenBt Wald statistic for covariate 5
head weightedburdenBt.txt
name2	sample_size_WeightedBurdenBt	num_variants_WeightedBurdenBt	total_mac_WeightedBurdenBt	beta_x_WeightedBurdenBt	pvalue_WeightedBurdenBt	wald_x_WeightedBurdenBt	beta_2_WeightedBurdenBt	beta_2_pvalue_WeightedBurdenBt	wald_2_WeightedBurdenBt	beta_3_WeightedBurdenBt	beta_3_pvalue_WeightedBurdenBt	wald_3_WeightedBurdenBt	beta_4_WeightedBurdenBt	beta_4_pvalue_WeightedBurdenBt	wald_4_WeightedBurdenBt	beta_5_WeightedBurdenBt	beta_5_pvalue_WeightedBurdenBt	wald_5_WeightedBurdenBt
AAMP	3180	3	35	0.0449657	0.979459	0.0257468	0.0312612	4.39155E-09	5.86873	-0.298905	0.0146383	-2.44121	0.130226	1.2303E-40	13.3472	0.435497	0.00139398	3.19589
AADACL4	3180	5	138	-2.46402	0.191324	-1.30667	0.0313048	4.31926E-09	5.87148	-0.294729	0.0160925	-2.40681	0.129824	2.23801E-40	13.3025	0.437296	0.00134129	3.207
ABHD1	3180	5	29	-1.40549	0.502329	-0.67083	0.0312599	4.37216E-09	5.86946	-0.297393	0.0151487	-2.42881	0.13027	1.21612E-40	13.348	0.437962	0.00131275	3.21318
ABCG8	3180	12	152	-0.597925	0.598611	-0.526399	0.0313146	4.24769E-09	5.87425	-0.297519	0.0151294	-2.42927	0.130098	1.44734E-40	13.3351	0.436695	0.00135537	3.20399
ABI2	3180	1	25	4.90399	0.0422609	2.03094	0.0311325	4.9292E-09	5.84954	-0.30075	0.0140623	-2.45567	0.129821	1.95802E-40	13.3125	0.436794	0.00135518	3.20403
ABCA12	3180	28	312	-0.387274	0.567616	-0.571566	0.0312492	4.47694E-09	5.86553	-0.298553	0.0147626	-2.43815	0.13023	1.19773E-40	13.3492	0.437199	0.00134108	3.20704
ABCA4	3180	43	492	-0.0845646	0.866958	-0.167524	0.0312627	4.36946E-09	5.86956	-0.298887	0.0146353	-2.44128	0.130242	1.12648E-40	13.3537	0.435417	0.00139682	3.19531
ABCB6	3180	7	151	-0.349842	0.782487	-0.276079	0.0313125	4.21645E-09	5.87547	-0.299545	0.0144307	-2.44636	0.130211	1.1897E-40	13.3497	0.435621	0.00138786	3.19716
ABCD3	3180	3	42	-1.24687	0.595311	-0.531156	0.0312676	4.44499E-09	5.86672	-0.301058	0.0139996	-2.45727	0.130189	1.06821E-40	13.3577	0.436778	0.00135205	3.2047

QQ-plot

vtools associate rare bmi --covariates age gender exposure -m "WeightedBurdenQt --name Weig\
htedBurdenQt --alternative 2" --group_by name2 --to_db weightedburdenQt -j8 > weightedburde\
nQt.txt
INFO: 3180 samples are found
INFO: 2632 groups are found
Loading genotypes: 100% [===============================] 3,180 24.4/s in 00:02:10
Testing for association: 100% [===================================] 2,632/147 22.2/s in 00:01:58
INFO: Association tests on 2632 groups have completed. 147 failed.
INFO: Using annotation DB weightedburdenQt in project test.
INFO: Annotation database used to record results of association tests. Created on Thu, 31 Jan 2013 21:51:44
vtools show fields | grep weightedburdenQt
weightedburdenQt.name2       name2
weightedburdenQt.sample_size_WeightedBurdenQt sample size
weightedburdenQt.num_variants_WeightedBurdenQt number of variants in each group (adjusted for specified MAF
weightedburdenQt.total_mac_WeightedBurdenQt total minor allele counts in a group (adjusted for MOI)
weightedburdenQt.beta_x_WeightedBurdenQt test statistic. In the context of regression this is estimate of
weightedburdenQt.pvalue_WeightedBurdenQt p-value
weightedburdenQt.wald_x_WeightedBurdenQt Wald statistic for x (beta_x/SE(beta_x))
weightedburdenQt.beta_2_WeightedBurdenQt estimate of beta for covariate 2
weightedburdenQt.beta_2_pvalue_WeightedBurdenQt p-value for covariate 2
weightedburdenQt.wald_2_WeightedBurdenQt Wald statistic for covariate 2
weightedburdenQt.beta_3_WeightedBurdenQt estimate of beta for covariate 3
weightedburdenQt.beta_3_pvalue_WeightedBurdenQt p-value for covariate 3
weightedburdenQt.wald_3_WeightedBurdenQt Wald statistic for covariate 3
weightedburdenQt.beta_4_WeightedBurdenQt estimate of beta for covariate 4
weightedburdenQt.beta_4_pvalue_WeightedBurdenQt p-value for covariate 4
weightedburdenQt.wald_4_WeightedBurdenQt Wald statistic for covariate 4
head weightedburdenQt.txt
name2	sample_size_WeightedBurdenQt	num_variants_WeightedBurdenQt	total_mac_WeightedBurdenQt	beta_x_WeightedBurdenQt	pvalue_WeightedBurdenQt	wald_x_WeightedBurdenQt	beta_2_WeightedBurdenQt	beta_2_pvalue_WeightedBurdenQt	wald_2_WeightedBurdenQt	beta_3_WeightedBurdenQt	beta_3_pvalue_WeightedBurdenQt	wald_3_WeightedBurdenQt	beta_4_WeightedBurdenQt	beta_4_pvalue_WeightedBurdenQt	wald_4_WeightedBurdenQt
AADACL4	3180	5	138	-3.3906	0.159775	-1.40616	0.0150701	0.0575284	1.89996	-0.0698905	0.733286	-0.340787	-0.940103	2.72704E-05	-4.20129
AAMP	3180	3	35	5.33715	0.0927374	1.68164	0.0148223	0.0617461	1.86878	-0.0767246	0.708183	-0.374331	-0.939547	2.75008E-05	-4.19938
ABCB10	3180	6	122	0.652166	0.773271	0.288123	0.0150189	0.0584545	1.89296	-0.0795645	0.698049	-0.38799	-0.945327	2.49634E-05	-4.22137
ABCB6	3180	7	151	-0.938172	0.653007	-0.449631	0.0151034	0.0571025	1.90322	-0.0803477	0.695236	-0.391795	-0.943322	2.57074E-05	-4.21471
ABCG5	3180	6	87	-3.04695	0.171201	-1.36867	0.0147558	0.0630148	1.85974	-0.0732971	0.720746	-0.357493	-0.953839	2.10114E-05	-4.26027
ABHD1	3180	5	29	-1.47831	0.509375	-0.659886	0.0150935	0.05722	1.90232	-0.0777012	0.704752	-0.378948	-0.940358	2.73267E-05	-4.20082
ABCG8	3180	12	152	-2.29054	0.152981	-1.42942	0.0151166	0.0567651	1.90581	-0.0738058	0.71887	-0.360001	-0.940705	2.69354E-05	-4.2041
ABI2	3180	1	25	5.96983	0.276415	1.0886	0.0150043	0.0586562	1.89144	-0.081478	0.691101	-0.397397	-0.941765	2.64399E-05	-4.20833
ABL2	3180	4	41	-1.52705	0.578314	-0.555906	0.0150917	0.057261	1.902	-0.0773202	0.706151	-0.377064	-0.943905	2.54124E-05	-4.21733

QQ-plot

 

1 Bo Eskerod Madsen and Sharon R. Browning (2009) A Groupwise Association Test for Rare Mutations Using a Weighted Sum Statistic. PLoS Genetics doi:10.1371/journal.pgen.1000384. http://dx.plos.org/10.1371/journal.pgen.1000384

2 Dan-Yu Lin and Zheng-Zheng Tang (2011) A General Framework for Detecting Disease Associations with Rare Variants in Sequencing Studies. The American Journal of Human Genetics doi:10.1016/j.ajhg.2011.07.015. http://linkinghub.elsevier.com/retrieve/pii/S0002929711003090

3 MichaelC. Wu, Seunggeun Lee, Tianxi Cai, Yun Li, Michael Boehnke and Xihong Lin (2011) Rare-Variant Association Testing for Sequencing Data with the Sequence Kernel Association Test. The American Journal of Human Genetics doi:10.1016/j.ajhg.2011.05.029. http://linkinghub.elsevier.com/retrieve/pii/S0002929711002229

4 Alkes L. Price, Gregory V. Kryukov, Paul I.W. de Bakker, Shaun M. Purcell, Jeff Staples, Lee-Jen Wei and Shamil R. Sunyaev (2010) Pooled Association Tests for Rare Variants in Exon-Resequencing Studies. The American Journal of Human Genetics doi:10.1016/j.ajhg.2010.04.005. http://linkinghub.elsevier.com/retrieve/pii/S0002929710002077