Defining Rare Variants With Allele Frequency

Why “Rare” Needs a Definition

A variant can be called rare in one data set and not rare in another. The label depends not only on the variant, but also on the frequency measure, the threshold, and the people whose genotypes were counted. In genetic studies, the basic quantity is usually the proportion of observed allele copies at a site that carry a specified allele.

That proportion is not the proportion of people who carry the allele. A person with two copies contributes two allele copies; a heterozygous person contributes one. Keeping the unit of counting clear is essential when defining frequency, identifying a singleton, or applying a threshold.

Counting Allele Copies

For \(N\) diploid individuals with complete genotype calls at a biallelic site, each person contributes two chromosome copies. If \(k\) of the \(2N\) copies carry the alternate allele, its observed frequency is \(k/(2N)\). For example, a heterozygous genotype contributes one alternate copy, while a homozygous-alternate genotype contributes two. The reference-allele frequency is \(1-p_{\mathrm{alt}}\), and the MAF is the smaller of those two frequencies.

The denominator should match the data actually used. If some individuals have no usable genotype at the site, their chromosome copies are not observed and should not be included in the denominator. More generally, if the called individuals have different ploidies, the denominator is the total number of observed chromosome copies, not automatically twice the number of individuals. This tutorial uses diploid examples unless stated otherwise.

At a multiallelic site, there are more than two alleles, so the simple biallelic definition \( \min(p_{\mathrm{alt}},1-p_{\mathrm{alt}}) \) does not apply to an individual alternate allele. The frequency of each allele can be reported separately. If a study uses a summary called “minor-allele frequency” for a multiallelic site, its convention should be stated; the label alone does not specify which frequency is being summarized.

Singletons and Frequency Thresholds

A singleton is an allele observed exactly once in the sample being described. In a diploid sample, that is one alternate chromosome copy, not necessarily one heterozygous individual in every possible data structure. Under complete diploid genotype calls, a single alternate copy occurs in one heterozygote. The term is sample-relative: it describes the observed count in a specified sample, not a claim that the allele occurs only once in a wider population.

Different studies use different cutoffs, and the inequality matters. “Less than 1%” excludes a frequency exactly equal to 1%, whereas “at most 1%” includes it. A useful report identifies the frequency measure, cutoff, inequality, and sample in which frequency was calculated. Without these details, “rare” is underspecified.

From a Frequency Cutoff to an Allele-Count Rule

For a complete diploid sample of \(N\) individuals, a frequency threshold can be translated into a maximum allele count. This makes the role of sample size explicit. Let \(k\) be the count of the allele of interest and let \(t\) be a frequency cutoff. For the strict rule \(k/(2N)<t\), multiplying by the positive number \(2N\) gives \(k<2Nt\). Since \(k\) must be an integer, the largest qualifying count is \(\lceil 2Nt\rceil-1\), where \(\lceil x\rceil\) denotes the smallest integer greater than or equal to \(x\).

For an inclusive rule \(k/(2N)\leq t\), the largest qualifying count is instead \(\lfloor 2Nt\rfloor\), where \(\lfloor x\rfloor\) is the greatest integer less than or equal to \(x\). These formulas assume the denominator is \(2N\); with missing calls or variable ploidy, use the actual number of observed chromosome copies in its place.

How the Sample and Study Design Affect the Label

A sample frequency describes the sampled chromosome copies. Which individuals are recruited therefore matters. A study restricted to people with a particular disease, a specific ancestry background, or membership in a selected family is not a random miniature of every population. Its allele counts and frequency may differ from those in a broader target population. A case-control study can also have a case fraction chosen by design rather than by disease prevalence; a frequency calculated by pooling cases and controls then describes that pooled study sample, not automatically the population from which the cases arose.

Sample size matters in a separate but related way. At a fixed frequency, a larger sample will generally contain more copies of the allele than a smaller sample. Thus an observed count alone does not describe rarity: one copy among 200 chromosome copies is 0.5%, while one copy among 20,000 is 0.005%. The count must be interpreted with its denominator.

Common Mistakes and Careful Reporting

• Confusing allele frequency with carrier proportion. Three alternate copies among 800 chromosomes give an allele frequency of \(3/800\), not a carrier proportion of \(3/800\). Carriers are people; allele frequency counts chromosome copies.
• Assuming “alternate” means “minor.” Alternate is a label relative to a reference representation. Compute the two allele frequencies before identifying the minor allele.
• Calling a singleton universally rare. A singleton is observed once in a specified sample. State that sample and avoid extending the count to unsampled populations.
• Reporting a rarity label without its rule. A statement such as “this is rare” omits the measure, threshold, inequality, and sample. Report those details so the classification can be interpreted and reproduced.
• Interpreting a study-sample frequency as a population frequency. Recruitment and case-control sampling can shape the observed sample. Describe what was measured before making a broader claim.