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

## 1. Introduction

The variable thresholds method (VT, Price et al 2010^{1}) tests for association between phenotypic values (case control or quantitative traits) with individuals' genotype "score" subject to a variable MAF threshold. It assumes that there exists a fixed yet unknown MAF threshold on a given genetic region which is related to the cutoff for the causality of variants on that loci. In testing the association for the genetic region, for each possible MAF threshold a genotype score is computed based on given collapsing theme, and is tested for association between the phenotype of interest; the final MAF threshold is chosen such that the association signal is strongest. Permutation procedure has to be used to control for type I error due to multiple testing.

The VT strategy creates a very flexible framework that can be applied to many association tests, including the use of external information such as weight theme by annotation scores, as the VT paper suggested. The `VTtest`

method implements the test for case control phenotype using the CMC coding theme and Fisher's exact test, in addition to the original VT statistic. Permutation procedure is optimized due to the use of Fisher's exact test: the minimum {$p$} value resulted from Fisher's exact test on the original dataset have to exceed the expected significance level in order to enter the permutation test procedure; otherwise it will be reported as it is. This trick reduces the computation time the original VT test would require.

Please refer to `VariableThresholdsBt`

and `VariableThresholdsQt`

for more versatile versions of VT method, which tests for both case control and quantitative traits, with/without presence of phenotype co-variates, and is capable of incorporating functional information.

## 2. Details

### 2.1 Command interface

vtools show test VTtest

Name: VTtest Description: VT statistic for disease traits, Price et al 2010 usage: vtools associate --method VTtest [-h] [--name NAME] [-q1 MAFUPPER] [-q2 MAFLOWER] [--alternative TAILED] [-p N] [--adaptive C] [--cfisher] [--midp] [--moi {additive,dominant,recessive}] Variable thresholds test for disease traits, 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. This implementation provides two different statistics: the original VT statistics in Price et al 2010 (default) and an adaptive VT statistic combining the CFisher method (via "--cfisher" option). p-value is estimated by permutation test. The adaptive VT statistic will not generate uniformly distributed p-value. For a more generalized version of VT test, type "vtools show test VariableThresholdsBt / VariableThresholdsQt". 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"). Two sided test is only valid with "--cfisher" option evoked (please use "VariableThresholdsBt" otherwise). Default set to 1 -p N, --permutations N Number of permutations --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 --cfisher This option, if evoked, will use an adaptive VT test via Fisher's exact statistic. For more details, please refer to the online documentation. --midp This option, if evoked, will use mid-p value correction for one-sided Fisher's exact test. It is only applicatable to one sided test with "--cfisher" option. --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 -m "VTtest --name vt -p 5000" --group_by name2 --to_db vt -j8 \ > vt.txt INFO: 3180 samples are found INFO: 2632 groups are found INFO: Starting 8 processes to load genotypes Loading genotypes: 100% [=========================================================================================================================================] 3,180 14.6/s in 00:03:37 Testing for association: 100% [================================================================================================================================] 2,632/591 5.4/s in 00:08:04 INFO: Association tests on 2632 groups have completed. 591 failed. INFO: Using annotation DB vt in project test. INFO: Annotation database used to record results of association tests. Created on Thu, 31 Jan 2013 20:48:50 vtools show fields | grep vt vt.name2 name2 vt.sample_size_vt sample size vt.num_variants_vt number of variants in each group (adjusted for specified MAF vt.total_mac_vt total minor allele counts in a group (adjusted for MOI) vt.statistic_vt test statistic. vt.pvalue_vt p-value vt.std_error_vt Empirical estimate of the standard deviation of statistic vt.num_permutations_vt number of permutations at which p-value is evaluated head vt.txt name2 sample_size_vt num_variants_vt total_mac_vt statistic_vt pvalue_vt std_error_vt num_permutations_vt ABCD3 3180 3 42 -0.0717229 0.753247 0.316505 1000 ABCB10 3180 6 122 0.37788 0.396603 0.339246 1000 ABCG5 3180 6 87 0.204207 0.58042 0.337788 1000 ABCB6 3180 7 151 0.180786 0.609391 0.328099 1000 AADACL4 3180 5 138 -0.284233 0.986014 0.302561 1000 AAMP 3180 3 35 0.158666 0.474525 0.306232 1000 ABHD1 3180 5 29 -0.0677963 0.771229 0.343744 1000 ABL2 3180 4 41 0.0378648 0.593407 0.34231 1000 ABCG8 3180 12 152 0.187745 0.612388 0.310029 1000 vtools associate rare status -m "VTtest --name vtfisher --cfisher --midp -p 5000" --group_b\ y name2 --to_db vtfisher -j8 > vtfisher.txt vtools show fields | grep vtfisher head vtfisher.txt |

^{1} 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 ⇑