The sensitivity is then the probability of observing k or more reads given the allelic fraction and depth. The marginal distribution of the number of reads with the alternate allele, either originating from the alternate base or a misread reference base, follows a binomial distribution with a frequency that reflects the true underlying allelic fraction f and the probability of error e (note that here we take the worst case in which all misread bases convert to the same alternate allele). Therefore we can calculate the probability of having observed k or more reads as: ∑i=knbinom(i∣n,f(1-e)+(1-f)e)
