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# AS_StrandOddsRatio

Allele-specific strand bias estimated by the symmetric odds ratio test (AS_SOR)

## Overview

Allele-specific strand bias estimated by the Symmetric Odds Ratio test

Strand bias is a type of sequencing bias in which one DNA strand is favored over the other, which can result in incorrect evaluation of the amount of evidence observed for one allele vs. the other. The AS_StrandOddsRatio annotation is one of several methods that aims to evaluate whether there is strand bias in the data. It is an updated form of the Fisher Strand Test that is better at taking into account large amounts of data in high coverage situations. It is used to determine if there is strand bias between forward and reverse strands for the reference or alternate allele. It does so separately for each allele. The reported value is ln-scaled.

### Statistical notes

The following 2x2 contingency table gives the notation for allele support and strand orientation.

+ strand   - strand
REF   X[0][0]X[0][1]
ALT   X[1][0]X[1][1]

We can then represent the Odds Ratios with the equation:

$R = \frac{X[0][0] * X[1][1]}{X[0][1] * X[1][0]}$

and its inverse:

$\frac{1}{R} = \frac{X[0][1] * X[1][0]}{X[0][0] * X[1][1]}$

The sum R + 1/R is used to detect a difference in strand bias for REF and for ALT. The sum makes it symmetric. A high value is indicative of large difference where one entry is very small compared to the others. A scale factor of refRatio/altRatio where

$refRatio = \frac{min(X[0][0], X[0][1])}{max(X[0][0], X[0][1])}$

and

$altRatio = \frac{min(X[1][0], X[1][1])}{max(X[1][0], X[1][1])}$

ensures that the annotation value is large only. The final SOR annotation is given in natural log space.

See the method document on statistical tests for a more detailed explanation of this statistical test, and see StrandOddsRatio documentation for an example calculation.

### Caveat

The name AS_StrandOddsRatio is not entirely appropriate because the implementation was changed somewhere between the start of development and release of this annotation. Now SOR isn't really an odds ratio anymore. The goal was to separate certain cases of data without penalizing variants that occur at the ends of exons because they tend to only be covered by reads in one direction (depending on which end of the exon they're on), so if a variant has 10 ref reads in the + direction, 1 ref read in the - direction, 9 alt reads in the + direction and 2 alt reads in the - direction, it's actually not strand biased, but the FS score is pretty bad. The implementation that resulted derived in part from empirically testing some read count tables of various sizes with various ratios and deciding from there.

### Related annotations

• AS_FisherStrand uses Fisher's Exact Test to evaluate strand bias.
• StrandOddsRatio outputs a version of this annotation that includes all alternate alleles in a single calculation.
• StrandBiasBySample outputs counts of read depth per allele for each strand orientation.