Calculating Pharmacogenetic Phenotype Frequencies

From Genetic Frequencies to Phenotype Frequencies

A PBPK cohort may need a specified proportion of poor, intermediate, normal, rapid, or ultrarapid metabolizers. Allele frequencies alone do not give those proportions directly: they first imply diplotype frequencies under a stated pairing model, and each diplotype must then be assigned a phenotype using explicit gene-specific rules. The calculation is therefore a two-stage translation, not a relabeling of allele frequencies.

The earlier material on Hardy–Weinberg equilibrium gives the standard random-pairing model for predicting genotype frequencies from allele frequencies. Here, the key additional operation is grouping diplotypes by phenotype. If diplotype frequencies have been measured directly, they can instead be grouped without assuming Hardy–Weinberg equilibrium.

In a diploid locus under Hardy–Weinberg equilibrium, the two alleles are paired at random from the same allele-frequency distribution. Thus a homozygous diplotype \(i/i\) has predicted frequency \(f_i^2\), while a heterozygous diplotype \(i/j\), for \(i\ne j\), has predicted frequency \(2f_if_j\). The factor of 2 accounts for the two possible allele orders, \(i\) from one parent and \(j\) from the other, or vice versa.

Here \(g(i/j)\) denotes the specified rule that maps diplotype \(i/j\) to phenotype \(m\). The order restriction \(i\leq j\) means that each unordered diplotype is counted once. If all possible diplotypes are included, their predicted frequencies sum to one because \((\sum_i f_i)^2=1\).

Make the Genotype-to-Phenotype Rules Explicit

Phenotype categories are interpretations of genetic function, not direct measurements of drug exposure. The rules depend on the gene and the functional classification of its alleles. For a calculation to be reproducible, state both the allele function assumptions and the rule used to classify each diplotype.

For the simplified CYP2C19 examples below, *1 is treated as normal function, *2 as no function, and *17 as increased function. The following commonly used assignments are assumed: *1/*1 is normal; *1/*2 and *2/*17 are intermediate; *2/*2 is poor; *1/*17 is rapid; and *17/*17 is ultrarapid. The *2/*17 assignment reflects the convention that a no-function allele paired with *17 is classified as intermediate in this simplified rule set; it should not be inferred by adding allele labels or treating increased function as a universal offset.

For CYP2D6, a common approach assigns an activity value to each allele, sums the two values to obtain an activity score, and applies phenotype thresholds. In the simplified examples here, *1 has value 1, *10 has value 0.25, and *4 has value 0. The assumed categories are poor metabolizer (score 0), intermediate metabolizer (score greater than 0 and less than 1.25), normal metabolizer (score from 1.25 through 2.25), and ultrarapid metabolizer (score greater than 2.25). This example does not include copy-number variation, hybrid alleles, or other CYP2D6 complexities.

Using CYP2D6 Activity Scores

For an activity-score method, the phenotype mapping happens after diplotype frequencies are calculated. Each diplotype receives the sum of its two allele activity values; the score is then placed in the stated phenotype interval. This order prevents an easy but consequential error: categorizing individual alleles as phenotypes before combining the two alleles.

Direct Diplotype Frequencies and a Short Justification

If representative diplotype frequencies are available, direct aggregation is often preferable to reconstructing diplotypes from allele frequencies. This approach retains the observed pairing pattern, including departures from random pairing. It still requires correct diplotype identification and a declared genotype-to-phenotype mapping.

The aggregation step follows directly from the law of total probability. The diplotype categories are mutually exclusive and, if exhaustive, partition the population. For a phenotype \(m\), the event “phenotype \(m\)” is the union of the diplotype events assigned to \(m\). Since those events are disjoint, the probability of their union is the sum of their probabilities:

This also explains why omitted diplotypes create a problem: the sum is a population phenotype proportion only when the diplotype set is sufficiently complete, or when omitted cases are explicitly handled.

Assumptions, Diagnostics, and Alternatives

Before using allele frequencies to predict phenotype proportions, check the conditions behind the calculation. The allele categories must be mutually exclusive and collectively cover the relevant alleles; their frequencies must sum to one. The Hardy–Weinberg prediction assumes random pairing for the population being represented and a diploid locus with the modeled allele system. The phenotype map must be specified for every diplotype that can occur. If haplotypes or linked variants affect the functional interpretation, they must be represented at the haplotype or diplotype level rather than collapsed into an inadequate single-variant allele list.

A practical diagnostic is to calculate all diplotype frequencies before grouping them. Confirm that none are negative, that every possible diplotype has a stated assignment, and that the diplotype frequencies sum to one. Then check that phenotype frequencies also sum to one. If they do not, look for an omitted diplotype, double counting of heterozygotes, inconsistent allele frequencies, or an unclassified phenotype. For observed counts, the denominator should be the number of individuals with interpretable diplotypes; if some are missing, report that denominator and do not silently treat missing cases as a phenotype.

These methods answer related but different questions. Hardy–Weinberg calculations provide a prediction from allele frequencies under an explicit pairing assumption. Direct diplotype aggregation describes the diplotype distribution that was observed. If the observed distribution departs from Hardy–Weinberg expectations, that difference is not repaired by substituting predicted frequencies for the observed ones; first determine which distribution is relevant to the intended cohort.

Common Pitfalls and Limits

• Using allele frequencies as phenotype frequencies. An allele frequency is not the proportion of people with that allele, and neither is generally the proportion with a phenotype. Form diplotypes and apply the mapping first.
• Forgetting the heterozygote factor of 2. Under random pairing, \(i/j\) has frequency \(2f_if_j\), not \(f_if_j\), when \(i\ne j\).
• Applying a rule without stating it. Phenotype categories depend on allele-function assignments and thresholds. A reported proportion is not reproducible unless these are clear.
• Treating CYP2D6 as an uncomplicated two-copy locus in every dataset. Copy-number variation and complex alleles can alter both diplotype representation and activity score. Use suitable copy-number-aware diplotypes or observed phenotype-relevant genotypes rather than forcing such data into a three-allele diploid calculation.
• Equating genetic phenotype proportions with drug response proportions. These calculations assign genotype-based metabolizer categories. They do not account for environmental effects, interacting medicines, disease, or other causes of altered enzyme activity.

The main limitation is that the result is only as reliable as its allele-frequency source, pairing model, and genotype-to-phenotype classification. It is a useful way to create or describe genetic strata, but it does not by itself establish how much exposure differs between strata or how a dose should change.