Genotype Representations: Allele, Carrier, and Diplotype Coding

Why Genotype Representation Matters

A genetic result is not itself a population PK model covariate. Before estimating an effect, the analyst must decide how to represent the genotype: as the number of copies of a designated allele, as an indicator of carrying at least one copy, or as a category for each diplotype. These choices encode different assumptions about how genotype relates to a PK parameter. They can therefore lead to different estimates and interpretations, even when they use the same participants and the same genetic data.

The examples below use clearance, \(CL\), but the same coding logic applies to other positive PK parameters, such as volume or an absorption parameter. The genotype effects described are conditional associations in the specified model. Coding alone does not establish a biological mechanism or a causal effect.

Three Ways to Represent a Biallelic Variant

Allele dose keeps the distinction between one and two variant copies but represents genotype with a single ordered number. Carrier status is binary and combines the two genotypes with at least one variant copy. Diplotype coding retains all three genotype categories as distinct levels. The labels \(A\) and \(a\) are simply a way to define the coding; whichever allele is counted must be stated so that the direction of an estimated effect is interpretable.

A standard way to connect any of these covariates to a positive typical population parameter is a log-linear model. Let \(\theta_{CL}\) be typical clearance for the reference genotype, and let \(\eta_{CL,i}\) represent an individual’s random effect on clearance. Other model terms, such as dose or body size effects, are omitted here to focus on genotype.

The exponential form keeps \(CL_i\) positive. For interpreting the genotype effect, set \(\eta_{CL,i}=0\) and hold other modeled covariates fixed. The resulting contrasts describe changes in typical clearance, not necessarily every individual’s clearance. The usual interpretation also presumes that the chosen functional form is appropriate and that the genotype effect is distinguishable from other model effects in the available data.

Allele-Dose Coding: A Per-Copy Effect

With allele-dose coding, the genotype contribution is \(\beta_g g_i\), where \(\beta_g\) is the change in log typical clearance for each additional copy of \(a\). Thus the model is

For the typical parameter, each extra copy multiplies clearance by \(\exp(\beta_g)\). The model therefore imposes equal spacing of the genotype groups on the log-clearance scale: the log contrast from \(AA\) to \(Aa\) equals the log contrast from \(Aa\) to \(aa\). On the clearance scale, the corresponding changes are multiplicative, not fixed additive increments.

This interpretation depends on the log-linear per-copy assumption. It does not follow merely from observing a numerical allele count. If the heterozygote and homozygote effects do not follow the assumed spacing, the single coefficient can be a poor summary of their differences.

Carrier-Status Coding: One Contrast for All Carriers

With carrier coding, the genotype contribution is \(\beta_C C_i\):

Here \(\theta_{CL}\) is typical clearance among noncarriers, and \(\exp(\beta_C)\) is the ratio of typical clearance for carriers to typical clearance for noncarriers. Because both \(Aa\) and \(aa\) have \(C_i=1\), this encoding assumes they have the same genotype-associated parameter value, after accounting for other model terms.

Carrier coding may be suitable when the scientific question is specifically about carrying any copy or when the data cannot support separate estimates for heterozygotes and homozygotes. Its simplicity comes with a substantive restriction: it cannot represent a dose gradient or a distinct effect in \(aa\) individuals.

Diplotype Coding: Separate Genotype Contrasts

Diplotype coding represents each genotype category separately. Taking \(AA\) as the reference, define indicators \(I_{Aa,i}\) and \(I_{aa,i}\), each equal to 1 for the named genotype and 0 otherwise. A model for clearance is

The \(AA\) category has both indicators equal to zero. The ratios \(\exp(\beta_{Aa})\) and \(\exp(\beta_{aa})\) compare typical clearance for \(Aa\) and \(aa\), respectively, with typical clearance for \(AA\). This coding does not impose equal per-copy effects or equal effects for all carriers.

How the Encodings Relate

The distinctions can be seen by writing the expected typical clearance in each genotype group. Let \(m_{AA}\), \(m_{Aa}\), and \(m_{aa}\) denote those group values with individual random effects set to zero. Allele-dose coding requires equal adjacent log contrasts; carrier coding requires equality of the two carrier-group values; diplotype coding places no such restriction on these three means.

The allele-dose restriction follows directly from the model. Under that model, \(m_{AA}=\theta_{CL}\), \(m_{Aa}=\theta_{CL}\exp(\beta_g)\), and \(m_{aa}=\theta_{CL}\exp(2\beta_g)\). Therefore,

This proves the equal-spacing condition on the log scale. In contrast, carrier coding uses \(C_i=1\) for both \(Aa\) and \(aa\), so the model gives each the same typical value, \(\theta_{CL}\exp(\beta_C)\). Diplotype coding estimates both contrasts separately and permits the two conditions to fail.

Choosing a Representation and Checking Its Fit

The representation should follow the scientific question and the amount of information the data can support. Allele dose is compact and directly answers a per-copy question, but it is appropriate only when the equal log-scale spacing assumption is defensible. Carrier status answers a carrier-versus-noncarrier question and uses fewer distinctions, but merges heterozygotes with variant homozygotes. Diplotype coding is more flexible, but requires enough information in each genotype group to estimate separate contrasts with useful precision.

A practical check is to compare the fitted model’s implications with genotype-specific parameter estimates or displays, while recognizing that estimates for small groups can be unstable. Look for systematic discrepancies—for example, an allele-dose model that consistently overpredicts one genotype group’s typical parameter—or uncertainty so large that the apparent pattern is not informative. Also check that the reference genotype and counted allele are documented, that the estimated direction matches the coding, and that the model’s other covariates and random effects have been handled consistently across comparisons.

When comparing encodings, use the same PK structure, participants, and other covariate terms as far as possible. Otherwise, a difference in the genotype estimate may reflect a changed analysis rather than the coding choice. A more flexible diplotype model can describe more patterns, but its additional parameters do not guarantee a better-supported or more useful scientific conclusion. Conversely, a simpler coding should not be selected solely because it produces a clearer-looking result.

Common Pitfall

Another interpretive boundary matters: a genotype coefficient is an association conditional on the included model terms. It is not, by itself, proof that the variant directly changes clearance. The coding determines the contrast being estimated; it does not establish the mechanism behind that contrast.