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

## 1. Introduction

This is implementation for the replication base test in Ionita-Laza et al 2011^{1}. The key of this method is *replication*, i.e., in the two-sided test of RBT it computes evidences to reject each of the two hypothesis

- Deleterious rare variants are enriched in cases
- Protective rare variants are enriched in controls

The final statistic is based on the stronger of the two evidences, adjusted for multiple testing. To increase the power of this approach a weighting theme is applied to variant counts in case or control group using a transformation of the probability of observing such counts under a Poisson model.

Implementation of RBT in this program has both one-sided and two-sided versions via the `--alternative`

parameter. The one-sided testing strategy tests for the presence of variants conferring risk to disease by focusing on variants that have higher observed frequency in cases compared with controls. Permutation procedure is used in both one-sided and two-sided tests to obtain valid {$p$} value.

## 2. Details

### 2.1 Command interface

vtools show test RBT

Name: RBT Description: Replication Based Test for protective and deleterious variants, Ionita-Laza et al 2011 usage: vtools associate --method RBT [-h] [--name NAME] [-q1 MAFUPPER] [-q2 MAFLOWER] [--alternative TAILED] [-p N] [--adaptive C] [--moi {additive,dominant,recessive}] Replication Based Test for protective and deleterious variants, Ionita-Laza et al 2011. Variant sites are scored based on -log transformation of probability of having more than observed variants in cases/ctrls; the RBT statistic is defined as sum of the variant sites scores. One-sided RBT is implemented in addition to the two-sided statistic described in the RBT paper. p-value is estimated via permutation test. 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 0.01 -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 --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 --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 "RBT --name RBT -p 5000" --group_by name2 --to_db rbt -j8 >\ rbt.txt INFO: 3180 samples are found INFO: 2632 groups are found INFO: Starting 8 processes to load genotypes Loading genotypes: 100% [===========================] 3,180 34.0/s in 00:01:33 Testing for association: 100% [===================================] 2,632/591 14.3/s in 00:03:03 INFO: Association tests on 2632 groups have completed. 591 failed. INFO: Using annotation DB rbt in project test. INFO: Annotation database used to record results of association tests. Created on Wed, 30 Jan 2013 05:32:45 vtools show fields | grep RBT rbt.sample_size_RBT sample size rbt.num_variants_RBT number of variants in each group (adjusted for specified MAF rbt.total_mac_RBT total minor allele counts in a group (adjusted for MOI) rbt.statistic_RBT test statistic. rbt.pvalue_RBT p-value rbt.std_error_RBT Empirical estimate of the standard deviation of statistic rbt.num_permutations_RBT number of permutations at which p-value is evaluated head rbt.txt name2 sample_size_RBT num_variants_RBT total_mac_RBT statistic_RBT pvalue_RBT std_error_RBT num_permutations_RBT AADACL4 3180 5 138 1.37261 0.898102 2.99763 1000 ABCB6 3180 7 151 4.94419 0.665335 3.29949 1000 ABCG5 3180 6 87 5.1935 0.413586 2.98032 1000 ABCG8 3180 12 152 4.96566 0.769231 4.03695 1000 ABL2 3180 4 41 2.67589 0.456543 2.29237 1000 ACADL 3180 5 65 2.18841 0.696304 2.64459 1000 ACADM 3180 4 103 2.04935 0.678322 2.58183 1000 ACAP3 3180 3 17 2.32431 0.422577 1.95933 1000 ABCD3 3180 3 42 1.10394 0.797203 2.16152 1000 |

^{1} Iuliana Ionita-Laza, Joseph D. Buxbaum, Nan M. Laird and Christoph Lange (2011) **A New Testing Strategy to Identify Rare Variants with Either Risk or Protective Effect on Disease**. *PLoS Genetics* doi:`10.1371/journal.pgen.1001289`

. http://dx.plos.org/10.1371/journal.pgen.1001289 ⇑