1.  Introduction

This is implementation of the fixed threshold collapsing methods for both disease and quantitative traits. Collapsing method for rare variants treats a genetic region as a test unit; based on observed genotype it assigns a numeric coding to the region {$X$}:{$$X = I_{(0,N)}(\sum_i^N X_i)$$} i.e., the observed genotype will be coded as {$1$} if there exists at least one mutation, and {$0$} otherwise. This coding theme has been used in Li and Leal 20081 and Bhatia et al 20102.

Advantages in using collapsing methods instead of aggregation methods is in its robustness to LD of multiple rare variants in the region under investigation, which would potentially inflate type I error. However under additive assumptions of genetic effects, collapsing methods may be less powerful than aggregation methods.

Our program implements the collapsing coding in a logistic regression framework for disease traits analysis (case control data) as CollapseBt method, and a linear regression framework for quantitative traits analysis as CollapseQt method. {$p$} value for collapsing 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

If the pattern of missing genotypes is not random in sample (e.g., missing ratio in cases is different from in controls), then type I error can be inflated. For small proportion of missing data, this issue can be alleviated using methods proposed by Auer et al 20133, which is implemented as an option --NA_adjust.

2.  Details

2.1  Command interface

% vtools show test CollapseBt
Name:          CollapseBt
Description:   Collapsing method for disease traits, Li & Leal 2008
usage: vtools associate --method CollapseBt [-h] [--name NAME]
                                            [--mafupper MAFUPPER]
                                            [--alternative TAILED]
                                            [--NA_adjust]
                                            [--moi {additive,dominant,recessive}]

Fixed threshold collapsing method for disease traits (Li & Leal 2008). p-value
is based on the significance level of the regression coefficient for
genotypes. If --group_by option is specified, variants within a group will be
collapsed into a single binary coding using an indicator function (coding will
be "1" if ANY locus in the group has the alternative allele, "0" otherwise)

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 CollapseQt
Name:          CollapseQt
Description:   Collapsing method for quantitative traits, Li & Leal 2008
usage: vtools associate --method CollapseQt [-h] [--name NAME]
                                            [--mafupper MAFUPPER]
                                            [--alternative TAILED]
                                            [--NA_adjust]
                                            [--moi {additive,dominant,recessive}]

Fixed threshold collapsing method for quantitative traits (Li & Leal 2008).
p-value is based on the significance level of the regression coefficient for
genotypes. If --group_by option is specified, variants within a group will be
collapsed into a single binary coding using an indicator function (coding will
be "1" if ANY locus in the group has the alternative allele, "0" otherwise)

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

# create a project and download sample project
% vtools init asso --parent vt_ExomeAssociation
% vtools associate rare status --covariates age gender bmi exposure -m "CollapseBt --name Col\
lapseBt --alternative 2" --group_by name2 --to_db collapseBt -j8 > collapseBt.txt
INFO: 3180 samples are found
INFO: 2632 groups are found
INFO: Starting 8 processes to load genotypes
Loading genotypes: 100% [=============================] 3,180 32.8/s in 00:01:36
Testing for association: 100% [=====================] 2,632/147 5.7/s in 00:07:37
INFO: Association tests on 2632 groups have completed. 147 failed.
INFO: Using annotation DB collapseBt in project test.
INFO: Annotation database used to record results of association tests. Created on Wed, 30 Jan 2013 23:10:09
% vtools show fields | grep collapseBt
collapseBt.name2             name2
collapseBt.sample_size_CollapseBt sample size
collapseBt.num_variants_CollapseBt number of variants in each group (adjusted for specified MAF
collapseBt.total_mac_CollapseBt total minor allele counts in a group (adjusted for MOI)
collapseBt.beta_x_CollapseBt test statistic. In the context of regression this is estimate of
collapseBt.pvalue_CollapseBt p-value
collapseBt.wald_x_CollapseBt Wald statistic for x (beta_x/SE(beta_x))
collapseBt.beta_2_CollapseBt estimate of beta for covariate 2
collapseBt.beta_2_pvalue_CollapseBt p-value for covariate 2
collapseBt.wald_2_CollapseBt Wald statistic for covariate 2
collapseBt.beta_3_CollapseBt estimate of beta for covariate 3
collapseBt.beta_3_pvalue_CollapseBt p-value for covariate 3
collapseBt.wald_3_CollapseBt Wald statistic for covariate 3
collapseBt.beta_4_CollapseBt estimate of beta for covariate 4
collapseBt.beta_4_pvalue_CollapseBt p-value for covariate 4
collapseBt.wald_4_CollapseBt Wald statistic for covariate 4
collapseBt.beta_5_CollapseBt estimate of beta for covariate 5
collapseBt.beta_5_pvalue_CollapseBt p-value for covariate 5
collapseBt.wald_5_CollapseBt Wald statistic for covariate 5
% head collapseBt.txt
name2   sample_size_CollapseBt  num_variants_CollapseBt total_mac_CollapseBt    beta_x_CollapseBt       pvalue_CollapseBt       wald_x_CollapseBt       beta_2_CollapseBt    beta_2_pvalue_CollapseBt        wald_2_CollapseBt       beta_3_CollapseBt       beta_3_pvalue_CollapseBt        wald_3_CollapseBt       beta_4_CollapseBt    beta_4_pvalue_CollapseBt        wald_4_CollapseBt       beta_5_CollapseBt       beta_5_pvalue_CollapseBt        wald_5_CollapseBt
AADACL4 3180    5       138     -0.2941 0.368956        -0.89843        0.0312903       4.30942E-09     5.87186 -0.296598       0.0154271       -2.42219    0.129942 1.83369E-40     13.3174 0.437372        0.00133613      3.2081
AAMP    3180    3       35      0.00135633      0.997852        0.0026919       0.0312624       4.39097E-09     5.86875 -0.298944       0.0146254       -2.44152     0.130231        1.24946E-40     13.346  0.43547 0.00139464      3.19576
ABCB10  3180    6       122     0.333178        0.219379        1.22818 0.0312644       4.40563E-09     5.8682  -0.301597       0.013796        -2.46253    0.130493 9.8029E-41      13.3641 0.431826        0.00154525      3.16605
ABCG8   3180    12      152     -0.432823       0.171192        -1.36838        0.0314772       3.67916E-09     5.89801 -0.295762       0.0157794       -2.41398     0.130108        1.52929E-40     13.331  0.440976        0.001228        3.2323
ABCB6   3180    7       151     -0.0619203      0.825828        -0.220056       0.0312972       4.27575E-09     5.87316 -0.299244       0.0145216       -2.4441      0.130203        1.22141E-40     13.3477 0.435756        0.00138398      3.19797
ABHD1   3180    5       29      -0.129748       0.840786        -0.200889       0.0312418       4.49451E-09     5.86488 -0.298341       0.0148474       -2.43608     0.130264        1.16331E-40     13.3513 0.43624 0.00137271      3.20033
ABCG5   3180    6       87      0.35312 0.287604        1.06339 0.0312942       4.1554E-09      5.87789 -0.298364       0.0148076       -2.43705        0.130389     9.49319E-41     13.3665 0.440212        0.00124756      3.22778
ABCD3   3180    3       42      -0.255649       0.662305        -0.436732       0.0312799       4.33855E-09     5.87074 -0.301233       0.0139678       -2.45809     0.130221        1.02858E-40     13.3605 0.436902        0.00134823      3.20551
ABCA4   3180    43      492     -0.00909763     0.95585 -0.0553619      0.0312634       4.37388E-09     5.8694  -0.298919       0.0146254       -2.44153    0.130239 1.15466E-40     13.3519 0.435484        0.00139409      3.19587

QQ-plot

% vtools associate rare bmi --covariates age gender exposure -m "CollapseQt --name CollapseQt\
 --alternative 2" --group_by name2 --to_db collapseQt -j8 > collapseQt.txt
INFO: 3180 samples are found
INFO: 2632 groups are found
INFO: Starting 8 processes to load genotypes
Loading genotypes: 100% [=======================] 3,180 33.4/s in 00:01:35
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 collapseQt in project test.
INFO: Annotation database used to record results of association tests. Created on Thu, 31 Jan 2013 03:48:21
% vtools show fields | grep collapseQt
collapseQt.name2             name2
collapseQt.sample_size_CollapseQt sample size
collapseQt.num_variants_CollapseQt number of variants in each group (adjusted for specified MAF
collapseQt.total_mac_CollapseQt total minor allele counts in a group (adjusted for MOI)
collapseQt.beta_x_CollapseQt test statistic. In the context of regression this is estimate of
collapseQt.pvalue_CollapseQt p-value
collapseQt.wald_x_CollapseQt Wald statistic for x (beta_x/SE(beta_x))
collapseQt.beta_2_CollapseQt estimate of beta for covariate 2
collapseQt.beta_2_pvalue_CollapseQt p-value for covariate 2
collapseQt.wald_2_CollapseQt Wald statistic for covariate 2
collapseQt.beta_3_CollapseQt estimate of beta for covariate 3
collapseQt.beta_3_pvalue_CollapseQt p-value for covariate 3
collapseQt.wald_3_CollapseQt Wald statistic for covariate 3
collapseQt.beta_4_CollapseQt estimate of beta for covariate 4
collapseQt.beta_4_pvalue_CollapseQt p-value for covariate 4
collapseQt.wald_4_CollapseQt Wald statistic for covariate 4
% head collapseQt.txt
name2   sample_size_CollapseQt  num_variants_CollapseQt total_mac_CollapseQt    beta_x_CollapseQt       pvalue_CollapseQt       wald_x_CollapseQt       beta_2_CollapseQt    beta_2_pvalue_CollapseQt        wald_2_CollapseQt       beta_3_CollapseQt       beta_3_pvalue_CollapseQt        wald_3_CollapseQt       beta_4_CollapseQt    beta_4_pvalue_CollapseQt        wald_4_CollapseQt
ABCD3   3180    3       42      -0.487474       0.571152        -0.566415       0.0149956       0.0588415       1.89006 -0.0808192      0.693535        -0.394098    -0.941867       2.64731E-05     -4.20804
ABCB6   3180    7       151     -0.532616       0.24625 -1.15972        0.0151515       0.056238        1.90989 -0.0810239      0.692719        -0.395204   -0.944219        2.5176E-05      -4.21945
ABHD1   3180    5       29      0.18344 0.859929        0.176479        0.0150381       0.0581416       1.89531 -0.0794273      0.698569        -0.387288   -0.94411 2.54398E-05     -4.21708
ABCA12  3180    28      312     -0.415972       0.211796        -1.24889        0.0151627       0.0560493       1.91135 -0.0789784      0.700073        -0.385257    -0.937093       2.90651E-05     -4.18676
ABCG8   3180    12      152     -0.56687        0.212912        -1.24585        0.0151496       0.0562578       1.90973 -0.0744998      0.716361        -0.363359    -0.939062       2.78992E-05     -4.1961
ABCA4   3180    43      492     0.0984281       0.721612        0.356337        0.0150102       0.0586022       1.89185 -0.0792212      0.699266        -0.386347    -0.942427       2.61944E-05     -4.21045
ABI2    3180    1       25      1.19633 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      -0.613866       0.475633        -0.713429       0.0150498       0.0579226       1.89697 -0.0781101      0.703263        -0.380954    -0.945432       2.46814E-05     -4.22394
ACADL   3180    5       65      1.33815 0.0528276       1.93705 0.0150444       0.0578831       1.89727 -0.082882       0.685934        -0.404416       -0.941384    2.64356E-05     -4.20836

QQ-plot

 

1 Bingshan Li and Suzanne M. Leal (2008) Methods for Detecting Associations with Rare Variants for Common Diseases: Application to Analysis of Sequence Data. The American Journal of Human Genetics doi:10.1016/j.ajhg.2008.06.024. http://linkinghub.elsevier.com/retrieve/pii/S0002929708004084

2 Gaurav Bhatia, Vikas Bansal, Olivier Harismendy, Nicholas J. Schork, Eric J. Topol, Kelly Frazer and Vineet Bafna (2010) A Covering Method for Detecting Genetic Associations between Rare Variants and Common Phenotypes. PLoS Computational Biology doi:10.1371/journal.pcbi.1000954. http://dx.plos.org/10.1371/journal.pcbi.1000954

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