VAF Uncertainty Threshold

Screen a variant-frequency threshold using Wilson uncertainty bounds from read counts; reads are assumed independent and error-free.

Description

Calculate observed variant allele frequency and Wilson bounds, then compare the complete interval with a supplied frequency threshold.

Variant allele frequency, abbreviated VAF, is the fraction of reads at a site that support a specified alternate allele. Five alternate reads out of ten total reads gives VAF 0.5, or 50%. This observed fraction can vary from sample to sample, especially at low read depth, even when the underlying allele proportion is unchanged.

A Wilson interval estimates uncertainty in a binomial proportion using the success count, total count, and a normal critical value z. The critical value controls the nominal confidence level: about 1.96 corresponds to a conventional two-sided 95% interval. Wilson bounds remain within the possible proportion range and differ from simply adding and subtracting a normal standard error.^[1]

VAF Uncertainty Threshold returns the observed fraction, lower and upper Wilson bounds, and the label above, below, or uncertain relative to a threshold you choose. These labels describe the interval comparison under the read-count model.

When to compare a variant frequency with a threshold

Use the tool when the uncertainty around a read fraction matters more than the point estimate alone. Keep the read-filtering rules, z value, and frequency threshold consistent when comparing sites or samples.

Screen whether an interval supports a supplied minimum-frequency criterion.
See how limited read depth can leave a point estimate inconclusive.
Compare the uncertainty bounds with a threshold expressed as a fraction.

How to enter read counts and compute the threshold evidence

Enter nonnegative integer alternate reads and a positive integer total depth; alternate reads cannot exceed total reads.
Choose a positive Normal z value for the intended confidence convention. Enter z itself, such as 1.96, rather than a confidence percentage.
Enter Frequency threshold between 0 and 1; for example, 0.05 means 5%.
Run the tool and compare Observed vaf with both Wilson bounds and the Threshold evidence label.

p = alternateReads / totalReads; d = 1 + z²/n; center = (p + z²/(2n))/d; half = z × sqrt(p(1−p)/n + z²/(4n²))/d

Here n is total reads and z is Normal z. The implementation returns max(0, center − half) and min(1, center + half) as the bounds.

Condition checked in order	Threshold evidence
wilsonLower ≥ frequencyThreshold	above
Otherwise, wilsonUpper < frequencyThreshold	below
Otherwise	uncertain

Equality is asymmetric: a lower bound equal to the threshold qualifies as above, while an upper bound equal to the threshold remains uncertain. Thresholds 0 and 1 are accepted. The tool does not select z or the threshold automatically.

json

{
  "input": {
    "alternateReads": 5,
    "totalReads": 10,
    "normalZ": 1,
    "frequencyThreshold": 0.4
  },
  "output": {
    "observedVaf": 0.5,
    "wilsonLower": 0.34924432771111824,
    "wilsonUpper": 0.6507556722888818,
    "thresholdEvidence": "uncertain"
  }
}

Invalid counts, zero depth, nonpositive z, or a threshold outside the fraction range produce an input error rather than an uncertain result.

Limitations of the read-count uncertainty model

Reads are treated as independent binomial observations without sequencing error. PCR duplicates, strand bias, mapping errors, contamination, and overdispersion are not modeled.
No quality filtering, allele calling, biological interpretation, or multiple-testing correction is performed.
The interval summarizes sampling uncertainty under the supplied model. It does not give the probability that the threshold is true or confirm a clinically significant variant.
The user supplies the critical value and threshold; there is no confidence-level menu or automatic coverage check.

Alternative or Complementary proportion analyses

Review read quality and dependence before treating read depth as an effective sample size. For general binomial comparisons, use an interval method suited to the sample and report its name. The ordinary proportion interval tool uses a normal approximation rather than Wilson bounds, so its results can differ near zero or one.

References

NIST/SEMATECH e-Handbook: confidence intervals for a proportion — National Institute of Standards and Technology

Similar or alternative tools

Proportion Confidence Interval Calculator
Calculate a bounded normal-approximation interval for success counts at 90%, 95%, or 99%; this is a different method.
Allele Frequency From Counts
Calculate allele A frequency from AA, AB, and BB genotype counts rather than sequencing-read depth.