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# StrandOddsRatio

Strand bias estimated by the symmetric odds ratio test (SOR)

## Overview

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 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(s).

### 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.

### Example calculation

Here is a variant record where SOR is 0.592.

     AC=78;AF=2.92135e-02;AN=2670;DP=31492;FS=48.628;MQ=58.02;MQRankSum=-2.02400e+00;MQ_DP=3209;QD=3.03; \


Read support shows some strand bias for the reference allele but not the alternate allele. The SB_TABLE annotation (a non-GATK annotation) indicates 1450 reference alleles on the forward strand, 345 reference alleles on the reverse strand, 160 alternate alleles on the forward strand and 212 alternate alleles on the reverse strand. The tool uses these counts towards calculating SOR. To avoid multiplying or dividing by zero values, the tool adds one to each count.

 refFw = 1450 + 1 = 1451
refRv = 345 + 1 = 346
altFw = 160 + 1 = 161
altRv = 212 + 1 = 213


Calculate SOR with the following.

$SOR = ln(symmetricalRatio) + ln(refRatio) - ln(altRatio)$

where

$symmetricalRatio = R + \frac{1}{R}$

$R = \frac{(\frac{refFw}{refRv})}{(\frac{altFw}{altRv})} = \frac{(refFw*altRv)}{(altFw*refRv)}$

$refRatio = \frac{(smaller\;of\;refFw\;and\;refRv)}{(larger\;of\;refFw\;and\;refRv)}$

and

$altRatio = \frac{(smaller\;of\;altFw\;and\;altRv)}{(larger\;of\;altFw\;and\;altRv)}$

Fill out the component equations with the example counts to calculate SOR.

 symmetricalRatio  = (1451*213)/(161*346) + (161*346)/(1451*213) = 5.7284
refRatio = 346/1451 = 0.2385
altRatio = 161/213 = 0.7559
SOR = ln(5.7284) + ln(0.2385) - ln(0.7559) = 1.7454427755 + (-1.433) - (-0.2798) = 0.592


### Related annotations

• AS_StrandOddsRatio allele-specific strand bias estimated by the symmetric odds ratio test.
• StrandBiasBySample outputs counts of read depth per allele for each strand orientation.
• FisherStrand uses Fisher's Exact Test to evaluate strand bias.