Combining quality scores when aligning/assembling

Question

[earonesty]

Suppose I have 2 reads, and I align them as a part of a joining program or an assembly:

AATGCGTTTGA
   GCGTTAGATGCTGA
________^

Then I output one combined read:

AATGCGTTTGATGCTGA

How do I combine the associated (phred scaled) quality scores in the overlapped region?

If the two bases match, and say one is q20 and the other q20 is then the likelihood of correctness is probably higher than q20.

It's clear that if the two bases don't match, and say one is q20 and the other q20 is then the likelihood of correctness is 50% (phred quality score of 3).

If the two bases don't match, and one is q40 and the other q3, and I choose the q40 base, then the correctness likelihood is probably still really near around q40. That q3 base shouldn't pull down the q40 that much.

Is there a "correct" formula for:

• combining quality scores when bases match in an overlapped region
• combining quality scores when don't match in an overlapped region

[earonesty]

Note: When the bases match, it's a much easier problem. With an assumption of independence, you can simple add the q scores. But that this assumption is fundamentally flawed. For Illumina I use max(a,b)+min(4,min(a,b)) ... when they match. It's the mismatches that are harder.

[earonesty]

For mismatches.... min(a,b,max(abs(a-b),3))? That seems a close approximation. At least it seems to make sense to me when they are the same (3), and when they are far apart.

Answer 1

[earonesty]

I spoke to a statistician here. I think a correct'ish answer for ambiguous bases is (after taking the better quality base):

E = max(3,((1-e2/2) * e1) / ((1-e1) * e2/2 + (1-e2/2) * e1))

Where e2 is the lower score.

And that this algorithm can be used to approximate it without needing to convert to/from phredspace

min(max(q1,q2),max(abs(q1-q2),3))

[Ashutosh Pandey]

I am not sure about the solution but +1 for taking an effort to ask others and posting the answer.

Answer 2

[mikhail.shugay]

It would be very rare case when your bases don't match and have the same quality. Also note that Phred score is in log scale, so the difference between 20 and 25 is quite high. Therefore I usually do the following (quite extreme) thing:

1. if there are two ambiguous bases, take the one with highest quality
2. when bases match output the highest quality

I've implemented it in demultiplexing/overlapping util called Checkout here

Anyway I believe the answer to your question could have only some heuristic behind it.