Allele Counts, Carrier Indicators, And Dosage Burdens

Why the Form of a Burden Matters

A gene-level burden compresses genotype information across selected variants into a summary for each individual. That summary can count alternate-allele copies, count variant sites at which the individual is a carrier, or add genotype dosages. These options may sound interchangeable, but they answer different questions. Two alternate copies at one site count as two allele copies but only one carrier site; one alternate copy at each of two sites counts as two copies and two carrier sites.

The distinction matters before any statistical comparison is made. A burden is a constructed measurement, not a test result. Its meaning depends on the genotype coding, the selected variants, and whether each unit in the sum represents an allele copy, a site, or an expected number of copies.

Define the Variants and the Genotype Scale First

The set \(M\) determines which sites contribute. It might be a prespecified functional mask after quality and frequency filters have been applied. The calculations below do not choose that set or assign different weights to its variants: each included site contributes equally within each burden definition. A variant excluded from \(M\) contributes nothing, regardless of its genotype.

For a diploid autosomal biallelic site, the hard-call values have a direct interpretation: 0 alternate copies is reference homozygous, 1 is heterozygous, and 2 is alternate homozygous. A carrier indicator records whether the count is positive; it does not record whether the individual carries one or two copies. These definitions use diploid genotypes. Different ploidy, such as for some sex-chromosome genotypes, requires a coding appropriate to that ploidy rather than mechanically imposing a maximum of 2.

Dosage is a numerical estimate of alternate-allele copies. With uncertain genotype calls, it can be fractional. For example, a dosage of 0.7 represents an estimated 0.7 alternate copies in the sense of an expected allele count, not a literal fractional allele. A dosage alone does not specify a carrier indicator: deciding whether someone is a carrier requires genotype probabilities or a separately defined hard-call rule.

What Each Sum Counts

The allele-count burden gives one unit for every alternate copy at every included site. It therefore distinguishes a heterozygote from an alternate homozygote at the same site: that site contributes 1 for the former and 2 for the latter. A sum of 3 means three alternate copies across the included variants; it does not, by itself, say whether those copies occur at three sites, at two sites, or in some other distribution.

The carrier-site burden instead gives one unit to each site where the individual has at least one alternate allele. A heterozygote and an alternate homozygote each contribute 1 at that site. It records the number of included variant sites carried by that individual, not the number of allele copies. It can be useful when the intended summary is the breadth of sites at which an individual carries an alternate allele.

A different binary summary is whether an individual carries any included variant: \(I(C_i>0)\). This equals 0 or 1, whereas \(C_i\) can range from 0 to the number of variants in \(M\). Calling both quantities “carrier status” without specifying which is meant invites confusion. In this tutorial, \(C_i\) means the count of carrier sites.

For hard calls, the dosage burden and allele-count burden are identical because each dosage is exactly the corresponding alternate-copy count. When dosage estimates are fractional, the sum retains an expected-copy interpretation, but it need not be an integer. The distinction between a dosage burden and a carrier-site burden remains: a sum of dosages does not count the number of sites with a nonzero hard-call genotype.

Why Allele Counts and Carrier Sites Can Tell Different Stories

A single site can contribute at most 2 to an individual’s allele-count burden but at most 1 to the carrier-site burden. Consequently, an allele-count sum is sensitive to homozygosity at included sites, while a carrier-site sum deliberately discards that distinction. When variants have different allele counts across a sample, the two summaries can also rank individuals differently: the person with the most alternate copies need not be the person carrying the greatest number of distinct sites.

The difference also appears when variants have different allele counts in the study sample. An aggregate allele count across individuals is \(\sum_i\sum_{j\in M}G_{ij}\); an aggregate count of carrier sites is \(\sum_i\sum_{j\in M}I(G_{ij}>0)\). These sample totals answer different counting questions. For example, one alternate-homozygous individual at a site contributes two alternate copies but one carrier observation at that site. Aggregate totals should therefore be labelled with their unit, not reported simply as “the number of variants” or “the number of carriers.”

Dosage Burdens and Uncertain Genotypes

Sequencing data may not support a single confident genotype at every site. A dosage can summarize uncertainty by averaging the alternate-copy count over possible genotypes. If the probabilities of genotypes 0, 1, and 2 are \(p_0,p_1,p_2\), with \(p_0+p_1+p_2=1\), the expected alternate-copy dosage is \(d=p_1+2p_2\). For example, probabilities 0.2, 0.5, and 0.3 give dosage \(0.5+2(0.3)=1.1\).

Adding such values across included variants gives the expected total number of alternate copies represented by those genotype probabilities. It does not mean the person literally has a fractional number of alleles, and it is not a count of carrier sites. In the same example, the probability of carrying at least one alternate allele is \(p_1+p_2=0.8\), which is not the same quantity as dosage 1.1.

Practical Checks Before Using a Burden

A burden is meaningful only if its inputs and missing-data rules are clear. A missing genotype call is not evidence of a reference genotype. Coding a missing value as 0 can artificially reduce a person’s burden, especially if callability differs across individuals or variants. The earlier material on coverage and callability emphasizes why those differences need attention before interpreting variant summaries.

A defensible calculation should identify the included set \(M\), the genotype coding, and the treatment of missingness. For example, an analysis may restrict calculation to individuals with adequately observed genotypes across the selected sites, or use a documented procedure appropriate to uncertain calls. Whatever approach is used, a burden based on different observed site sets across individuals may not be directly comparable without accounting for that difference.

Common Mistakes and Why the Choice Matters

• Equating allele copies with carrier sites. The reasoning “two alternate alleles means two variants carried” is wrong if both copies occur at one site. Count sites with positive genotype counts to obtain \(C_i\).
• Calling every sum a carrier count. A dosage sum measures expected alternate copies, while \(C_i\) counts sites. State the unit explicitly.
• Treating dosage as a hard call. A dosage of 1.1 does not identify a definite genotype or determine carrier status. Interpret it as an expected allele count based on the genotype information used to compute it.
• Turning a burden into a causal conclusion. A larger burden is a larger value of the chosen genetic summary. On its own, it does not establish association with a trait or show that the variants cause a phenotype.
• Replacing missing calls with zero. Zero denotes an observed reference genotype, not an unavailable genotype. Treating missingness as zero can bias individual summaries downward.

These choices matter because a later analysis uses the burden as its input measurement. If the scientific question concerns accumulated alternate copies, collapsing each site to a carrier indicator discards copy-number information. If the intended question concerns the number of sites carried, counting copies gives extra contribution to alternate homozygotes. The burden definition should match the intended summary and be reported so that its interpretation is reproducible.