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

## 1. Introduction

This implements the variable thresholds version of aggregation methods. Similar to the VT method, the `VariableThresholdsBt`

and `VariableThresholdsQt`

tests use a variable thresholds definition for the rare variants being considered such that multiple test statistics are calculated for an aggregation unit. The final statistic is taken as the one that gives the best result. Type I error is controlled due to the use of permutation testing.

Results from variable thresholds methods have one additional column, i.e., an MAF column reporting the statistic of VT at which it is derived.

## 2. Details

### 2.1 Command interface

vtools show test VariableThresholdsBt

Name: VariableThresholdsBt Description: Variable thresholds method for disease traits, in the spirit of Price et al 2010 usage: vtools associate --method VariableThresholdsBt [-h] [--name NAME] [-q1 MAFUPPER] [-q2 MAFLOWER] [--alternative TAILED] [-p N] [--permute_by XY] [--adaptive C] [--NA_adjust] [--moi {additive,dominant,recessive}] Variable thresholds in burden test for disease traits (in the spirit of Price et al 2010). The burden test statistic of a group of variants will be maximized over subsets of variants defined by applying different minor allele frequency thresholds. Significance of the statistic obtained is evaluated via permutation 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. -q1 MAFUPPER, --mafupper MAFUPPER Minor allele frequency upper limit. All variants having sample MAF<=m1 will be included in analysis. Default set to 1.0 -q2 MAFLOWER, --maflower MAFLOWER Minor allele frequency lower limit. All variants having sample MAF>m2 will be included in analysis. Default set to 0.0 --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 --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 VariableThresholdsQt

Name: VariableThresholdsQt Description: Variable thresholds method for quantitative traits, in the spirit of Price et al 2010 usage: vtools associate --method VariableThresholdsQt [-h] [--name NAME] [-q1 MAFUPPER] [-q2 MAFLOWER] [--alternative TAILED] [-p N] [--permute_by XY] [--adaptive C] [--NA_adjust] [--moi {additive,dominant,recessive}] Variable thresholds in burden test for quantitative traits (in the spirit of Price et al 2010). The burden test statistic of a group of variants will be maximized over subsets of variants defined by applying different minor allele frequency thresholds. Significance of the statistic obtained is evaluated via permutation 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. -q1 MAFUPPER, --mafupper MAFUPPER Minor allele frequency upper limit. All variants having sample MAF<=m1 will be included in analysis. Default set to 1.0 -q2 MAFLOWER, --maflower MAFLOWER Minor allele frequency lower limit. All variants having sample MAF>m2 will be included in analysis. Default set to 0.0 --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 --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`

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vtools associate rare status --covariates age gender bmi exposure -m "VariableThresholdsBt \ --name VariableThresholdsBt --alternative 2 -p 5000 --permute_by X --adaptive 0.05" --group\ _by name2 --to_db variablethresholdsBt -j8 > variablethresholdsBt.txt vtools show fields | grep variablethresholdsBt.txt head variablethresholdsBt.txt vtools associate rare bmi --covariates age gender exposure -m "VariableThresholdsQt --name \ VariableThresholdsQt --alternative 2 -p 5000 --permute_by X --adaptive 0.05" --group_by nam\ e2 --to_db variablethresholdsQt -j8 > variablethresholdsQt.txt INFO: 3180 samples are found INFO: 2632 groups are found INFO: Starting 8 processes to load genotypes Loading genotypes: 100% [=========================================================================================================================================] 3,180 34.2/s in 00:01:33 Testing for association: 100% [================================================================================================================================] 2,632/147 2.8/s in 00:15:35 INFO: Association tests on 2632 groups have completed. 147 failed. INFO: Using annotation DB variablethresholdsQt in project test. INFO: Annotation database used to record results of association tests. Created on Thu, 31 Jan 2013 22:54:27 vtools show fields | grep variablethresholdsQt.txt variablethresholdsQt.name2 name2 variablethresholdsQt.sample_size_VariableThresholdsQt sample size variablethresholdsQt.num_variants_VariableThresholdsQt number of variants in each group (adjusted for specified MAF upper/lower bounds) variablethresholdsQt.total_mac_VariableThresholdsQt total minor allele counts in a group (adjusted for MOI) variablethresholdsQt.beta_x_VariableThresholdsQt test statistic. In the context of regression this is estimate of effect size for x variablethresholdsQt.pvalue_VariableThresholdsQt p-value variablethresholdsQt.std_error_VariableThresholdsQt Empirical estimate of the standard deviation of statistic under the null variablethresholdsQt.num_permutations_VariableThresholdsQt number of permutations at which p-value is evaluated variablethresholdsQt.MAF_threshold_VariableThresholdsQt The minor allele frequency at which the test statistic is maximized head variablethresholdsQt.txt name2 sample_size_VariableThresholdsQt num_variants_VariableThresholdsQt total_mac_VariableThresholdsQt beta_x_VariableThresholdsQt pvalue_VariableThresholdsQt std_error_VariableThresholdsQt num_permutations_VariableThresholdsQt MAF_threshold_VariableThresholdsQt ABCB10 3180 6 122 5.93777 0.247752 3.68504 1000 0.000157233 ABCD3 3180 3 42 -1.48612 0.301698 0.740477 1000 0.00267296 AADACL4 3180 5 138 -1.70538 0.151848 0.927952 1000 0.00157233 AAMP 3180 3 35 2.352 0.0666445 0.923285 3000 0.00220126 ABCB6 3180 7 151 1.98423 0.655345 3.83344 1000 0.000157233 ABI2 3180 1 25 0 0.993007 0 1000 0.00393082 ABHD1 3180 5 29 -1.81424 0.257742 1.19045 1000 0.000314465 ABCG8 3180 12 152 -3.48381 0.143856 1.26176 1000 0.000786164 ACAP3 3180 3 17 2.70541 0.281718 2.01218 1000 0.000314465 |