I'm working in bioinformatics and its been a long time since I dusted on my statistics. Basically I'm working on variant calling which amounts to sequencing a large number of sequence reads and analyzing them to see how they differ from a known sample. The same position in a genome will be covered many times like this:
AAAAAAAAAAAAAAAA - Reference sample AAAAAAAAAAAAAAAA - Sequenced read1 AAAAAAAAAAAAAAAA - Sequenced read2 AAAAAAATAAAAAAAA - Sequenced read3 AAAAAATAAAAAAAAA - Sequenced read4
The whole game is to figure out when the reads represent a sample that differs from the reference. In the example above there is a single position where half of the reads suggest there is a variant of A to T near the middle.
One way to associate a p-value with the likelihood that the middle position is in fact different from the reference sample is to compute, or collect a sequence error rate, E, and use the total depth and depth of just the T's in a binomial test to see if we have a significant non-reference signal that is higher than expected given the error rate.
I'm working on a new method for this where I am trying to combine multiple types of sequence error. Basically, for any position in my sample I have a list like:
The likelihood of seeing an A to T error in position 8 in a read (E1) The likelihood of seeing an A to T error in position 7 in a read (E2) ...
and so on where I am calculating many types of error metrics, and they're not completely independent of each other.
Now in a real world example I have maybe 100 sequence reads covering a position and for each read that covers it I have an error probability of seeing that base substitution due to sequence error as a function of the within-read position.
Can you point in the right direction to figure out how to combine a list of error likelihoods into a p-value?
One basic thing I can think of is to just multiply my error likelihoods to get the overall likelihood that these sequence reads reported a sequence at a position by chance after which I can apply a threshold to the final likelihoods to float my putative true-positives to the top of the heap, but I feel as though there must be a better way to think about this.