Verifying Sample Identities - Implementation

Principle

We should be able to verify that the right sample has been sequenced by comparing base calls in a read to known genotypes for a sample. If the sample has been sequenced correctly, the base calls should match previously known genotypes. If the wrong sample has been sequenced, we will see quite a bit more mismatches.

Mathematical Details

For each sample, we would like to calculate the likelihood of a set of reads assuming that we sequenced the correct sample, assuming we sequenced a sample related to the correct sample, or assuming we sequenced an incorrect sample. We would then like to flag samples where it appears likely that the wrong sample has been sequenced.

If we have a list of bases that overlap a known genotype, we can will describe the probability of a matching of mismatching base using the following notation:

Notation

Variable	Definition
A/A	Previously known genotype; we only consider homozygous sites.
PA	Frequency of allele A in the population
Pibd	Probability that the sequenced sample and the target sample share a chromosome. This should be 1.0 when we have sequenced the correct sample and 0.0 if we sequence an unrelated sample. If we sequence a related sample (e.g. a parent or sibling of the target sample), we will see intermediate values.
$\epsilon$	Estimate error rate for the current base in the sequence data.

Then, the probabilities of interest are:

$P(match)=P_{ibd}(1-\epsilon )+(1-P_{ibd})\epsilon P(nomatch)=P_{ibd}\epsilon +(1-P_{ibd})\epsilon$