Comparing mutation frequency between a case and a pool of controls I"m working in genomics and trying to come up with the appropriate statistical test for my question.
To call mutations in a tumor's DNA, we use sequencing that samples from the total population of cells in a tumor. For each genomic position, we then get two numbers: The number of reads that support a mutation and the number of reads that support the wildtype sequence (and summing those gives the total number of reads).
If I want to identify mutations that are unique to the tumor sample (as compared to the normal control), I can set up a contingency table and use Fisher's exact test.  (e.g. Is 21/100 mutation-supporting reads at this site significantly different from 2/98 in the control?)
What comparable test is appropriate when I have a pool of several normal samples? I want to test whether the frequency of mutation at a particular site in my tumor sample is significantly higher than it is across 10 normal samples.  So I'm comparing one case (21/100) to many controls: (1/94, 3/85, 0/100 ... ).  The null hypothesis is that there is no difference between case and control.
 A: Logistic regression with samples as the independent variable would be a useful way to proceed. Reshape the data so that there is one row per read, with a 0 value for wild type and 1 for mutant in the first column, and a second column identifying the sample. Your null hypothesis then is a particular pre-specified contrast of the tumor sample against the mean of the controls, avoiding multiple-comparison issues.
This has some advantages: it reduces to chi-square when there is only 1 tumor and 1 control, it takes differences in total counts among samples into account, it generalizes to multinomial regression if you want to consider all 4 bases at the position instead of just mutant/wild-type, and it allows for testing differences among the controls. See this page for further discussion of this approach.
That said, I'm still concerned about biological interpretation of the results if you don't have a normal-DNA match for the tumor.
A: My answer seems like more than a comment but not quite an answer. Sorry if I'm posting in the wrong format.
I'll take the other side of "how do you know it's somatic?" If you want to use normal samples to estimate context-specific technical error rates, do you risk (and/or do you care about) low-frequency residual clones confounding that estimate? I suppose it depends on whether or not you can assume non-zero residual disease can exist in these normal samples at a frequency in the ballpark of your error rate (~0.1-1%). Are your normal samples from the same tissue type? If you have on the order of 10 I'm assuming these are all hematological. Ideally, I'd consider estimating these error rates from completely independent tissues, or, more practically, from different patients (samples processed in the same way, but from individuals who never had evidence of harboring the variant in question). Just an opinion.
Regarding the actual statistical approach, I wonder if a likelihood framework would be useful here. Your data are generated by a binomial process, where the number of non-reference reads, X, out of n sequencing reads is given by X~Bin(n,p). Here p is a reflection the the true variant allele frequency/fraction (VAF) and your technical error rate:
p=P(true non-reference)(1-error rate) + P(true reference)(error rate)
So the assumption that VAF=0 in control samples reduces to p=(1)(error rate).
Your tumor sample and N control samples are N+1 independent experiments:
X[i]~Bin(n[i],p[i])
Your null hypothesis is that p[i] is the same for all samples (estimate for p comes from pooling all tumor and control samples). Your alternative is that p[i] is different for the tumor sample versus your control samples (maximum likelihood estimate for tumor p[i] is derived from the tumor sample, estimate for control p[i] is derived from pooled control samples). Your likelihood statistic is then:
D=-2ln(p(observed non-reference counts X[1], X[2], ..., X[N+1] | jointly estimated p)) + 2ln(p(observed non-reference counts X[1], X[2], ..., X[N+1] | p estimated independently for tumor vs. control samples))
You can then calculate a p-value for this test statistic either empirically or using a chi-square distribution with 1 degree of freedom.
