Why the Source Matters
An allele frequency used to construct a PBPK cohort is not just a number retrieved from a database. It is an estimate obtained from particular people, using particular sampling and measurement procedures. If those people do not represent the intended cohort, or if the assay did not measure the intended variant reliably, a highly precise estimate can still be a poor input.
The practical task is therefore to match a reference estimate to the target cohort and the model question, then make the remaining uncertainty visible. The allele-frequency input may affect how often virtual subjects carry a variant and, through the genotype-to-activity assumptions already established, the distribution of a genotype-dependent model parameter. This tutorial focuses on choosing the frequency source, not on deriving genotype frequencies or translating genotypes into enzyme activity.
Start With the Target and the Variant
Before comparing sources, specify the target population for the virtual cohort: for example, adults treated in a particular clinical setting, or a population described using a stated ancestry definition. Also specify the exact variant and allele of interest. Variant identifiers, reference genome builds, and allele labels must align between the source and the model input. A frequency for a nearby marker or a different allele is not automatically interchangeable with the desired frequency.
For a biallelic autosomal variant, let \(n_0\), \(n_1\), and \(n_2\) be the numbers of sampled individuals with zero, one, and two copies of the designated allele, respectively. If all \(N=n_0+n_1+n_2\) individuals have valid genotype calls, the estimated frequency is
The numerator counts copies of the designated allele; the denominator counts all allele copies at that locus. If some individuals have missing calls, use the number with valid calls at that variant, not the study's total enrollment. Report both the estimate and the denominator so that the basis of the calculation is clear.
Worked Example: Calculating a Frequency From Genotype Counts
In a hypothetical reference sample, 270 unrelated participants have zero copies of an allele, 108 have one copy, and 22 have two copies. All 400 participants have valid calls for this autosomal variant.
The number of allele copies is \(108+2(22)=152\). The total number of copies is \(2(400)=800\). Therefore,
The estimated frequency is 0.190, or 19.0% of the counted allele copies in this sample. It is not the proportion of participants with at least one copy; that proportion is \((108+22)/400=0.325\), or 32.5%. These quantities answer different questions and should not be substituted for one another.
Assess Design Before Size
A large sample can reduce random sampling error, but it cannot by itself correct a mismatch between the sampled population and the target. Review how participants were recruited, which eligibility criteria were applied, whether sampling was population-based or clinic-based, and whether relatives or participants from a small number of families were included. A disease-specific clinical sample, for example, may not represent the broader population intended for a virtual cohort if the disease or recruitment pathway is related to who was sampled.
Also check the sampling unit. A study with many participants drawn from a few related families may contain less independent information about population frequency than its participant count suggests. Geographic or site clustering can have a similar effect. When sampling probabilities or survey weights are supplied, the unweighted proportion may not estimate the intended population quantity. For fully observed diploid genotypes with participant weights \(w_i\), a weighted estimate can be written as
where \(g_i\) is the number of designated allele copies for participant \(i\). This calculation is appropriate only when the weights and sampling design support the target-population estimate. Its uncertainty must also reflect the design; an ordinary binomial interval does not automatically do so.
Ancestry definitions are part of the sampling description, not a decorative label. Determine whether a source uses self-identified categories, geographic origin, genetic-ancestry methods, or a combination, and read the inclusion rules rather than relying on a category name alone. These definitions are not necessarily equivalent. Use a source whose definition can be related transparently to the intended cohort, and document that relationship. Do not treat a broad label as a precise biological boundary.
Worked Example: Choosing Between Two Reference Sources
A modeler needs an allele-frequency input for a hypothetical virtual cohort of adults treated at a regional clinic. Two sources report estimates for the same autosomal variant. Source A is a study of 400 unrelated adults recruited from clinics in the target region; its participant eligibility and ancestry definition are described, and the variant was directly genotyped. Source B is a biobank of 2,000 volunteers from a much wider area. It uses a broad self-identified category and reports a frequency based on an array marker used as a proxy for the target variant; the relationship between the proxy and target variant is not established in the supplied data.
For Source A, the genotype counts are 270 with zero copies, 108 with one copy, and 22 with two copies. Its estimate is \((108+2(22))/(2(400))=152/800=0.190\). For Source B, the counts are 1,280, 640, and 80, giving \((640+2(80))/(2(2{,}000))=800/4{,}000=0.200\).
Source B is larger, but its proxy measurement and broader population definition make its estimate less directly interpretable for this target. Source A is the more defensible primary input, provided its clinic recruitment does not create a material selection problem for the intended cohort. Source B can be retained as a sensitivity input, not treated as interchangeable evidence of the exact target-variant frequency. The choice rests on variant measurement and target relevance as well as sample size.
Check Assay Coverage and Data Quality
Confirm that the reported frequency pertains to the exact variant and allele used in the model. Inspect the assay method, genome build, variant identifier, strand or allele harmonization procedures, and whether calls were direct or inferred. For a panel, check whether the variant was included at all and whether the panel's design or quality filters could selectively exclude some samples. A frequency based on imputed calls may be useful, but its call quality and uncertainty should be reviewed; an indirect marker is not necessarily a reliable substitute.
Read variant-specific quality information where available: call rate, genotype quality, quality-control exclusions, and the number of successfully genotyped participants. Missingness matters because the relevant denominator is the successfully called sample at that locus. If missingness is related to genotype, ancestry, sample quality, or another characteristic connected to the target population, simply using the observed calls may introduce bias. When the source provides no information to judge this possibility, record it as a limitation rather than silently assuming complete measurement.
Quantify Sampling Uncertainty
A reported point estimate does not show how much it could vary under repeated sampling. For a simple illustrative interval, treat the \(m=2N\) allele copies as independent Bernoulli observations with common frequency \(p\). This approximation is most defensible for a random sample of unrelated individuals from a sufficiently homogeneous population under Hardy–Weinberg conditions, with valid calls and no unaccounted sampling design. Departures from those conditions, relatedness, clustering, weighting, or population mixture may require a design-based method, an individual-level resampling method, or another justified approach.
For a binomial count \(x\) out of \(m\), the Wilson interval is a useful alternative to the simple estimate plus-or-minus a normal standard error, particularly when the frequency is near zero or one. For a two-sided 95% interval, set \(z=1.96\). With \(\hat{p}=x/m\), the Wilson limits are
The interval describes uncertainty from sampling under the stated model; it does not cover every source of error. In particular, it does not correct an unrepresentative sample, allele-label mistakes, assay bias, or a mismatch between the source population and the target.
Worked Example: A Wilson Interval for an Allele Frequency
Suppose a hypothetical random sample contains 500 unrelated participants, all with valid calls for a biallelic autosomal variant. There are 120 designated allele copies among \(m=1{,}000\) total copies, so \(\hat{p}=120/1{,}000=0.120\). Assume for this calculation that allele copies are independent Bernoulli observations and that the sampling design supports this approximation.
Using \(z=1.96\), the Wilson denominator is \(1+1.96^2/1{,}000=1.003842\). The center numerator is \(0.120+1.96^2/(2{,}000)=0.121921\), and the margin numerator is \(1.96\sqrt{(0.120)(0.880)/1{,}000+1.96^2/(4{,}000{,}000)}=0.02023\).
The approximate 95% Wilson interval is 0.101 to 0.142, or 10.1% to 14.2%. In repeated sampling under the assumptions, intervals calculated this way would cover the population frequency about 95% of the time. This is not a statement that there is a 95% probability that the fixed population frequency lies in this particular interval.
Make a Defensible Input Decision
A practical comparison should keep separate the evidence for relevance, measurement, and precision. A short source audit makes the decision reproducible and helps distinguish a genuinely uncertain frequency from a precisely estimated but poorly matched one.
Write down the intended cohort, the allele, the exact variant, and the relevant population or ancestry definition.
Check variant identity, allele harmonization, assay coverage, genotype call quality, missingness, and the number successfully called.
Review recruitment, eligibility, relatedness, geographic or site clustering, weighting, and how closely the sample corresponds to the target.
Report the estimate, denominator, interval or justified alternative, and assumptions behind the uncertainty calculation.
Choose the best-supported source, state why it is suitable, and preserve plausible alternatives for sensitivity analysis when uncertainty remains material.
When sources disagree, do not automatically average them. First determine whether they measure the same variant and allele, whether their sampling frames target the same population, and whether differences could reflect assay or selection issues. Pooling can be justified only when the estimates are sufficiently comparable and the pooling method respects their designs and uncertainty. Otherwise, selecting a primary estimate and using credible alternatives in sensitivity analyses is more transparent.
The main alternatives are to use a directly measured, well-matched reference sample; use a larger but less directly matched database with explicit qualification; or use multiple compatible sources in a justified synthesis. No single option is always best. A smaller source with direct measurement and a relevant sampling frame may be preferable to a larger source with an uncertain proxy, while a small convenience sample may be too imprecise or biased to support a confident input.
Diagnostics, Limitations, and Common Pitfalls
- Using enrollment as the denominator. If only 900 of 1,000 participants have valid calls at the variant, the allele-frequency denominator is based on 900 diploid individuals, not 1,000.
- Confusing allele and carrier frequency. The allele frequency counts copies; carrier frequency counts people with one or more copies. The two can differ substantially.
- Assuming a large sample guarantees relevance. Sample size improves precision only under an appropriate sampling and measurement model; it cannot make a mismatched source representative.
- Treating an assay proxy as the target variant. A nearby marker or inferred call requires evidence that it supports the target estimate. Similar names or genomic proximity are not enough.
- Reporting a narrow interval as complete confidence. A sampling interval does not account for population mismatch, selection, measurement error, or uncertain ancestry definitions.
Diagnostics include checking whether genotype counts sum to the valid-call sample size, whether the allele count is between zero and \(2N\), and whether the reported frequency agrees with the count-based calculation. Large differences between sources should prompt investigation of variant harmonization, sampling frames, missingness, and assay methods before being treated as real population variation. A source audit cannot remove every limitation: reference samples may not match a future clinical population, ancestry categories may be broad, and uncertainty can remain even after careful quality review.
Check Your Understanding
Answer each question, then compare with the brief solutions.
- A sample has 180 participants with zero copies, 60 with one copy, and 10 with two copies of a designated allele. All calls are valid. What is the estimated allele frequency?
- A database reports an estimate from 5,000 people but gives no variant-specific call rate. What additional information is needed before using it?
- Why might a study of 300 unrelated participants be a more defensible source than a biobank of 3,000 participants?
- What does a 95% Wilson interval describe, and what important uncertainties does it not automatically include?
- A reported allele frequency uses a different allele label and genome build from the model input. What should be done before transferring the estimate?
Solutions: (1) The allele count is \(60+2(10)=80\), and the denominator is \(2(250)=500\), so \(\hat{p}=80/500=0.160\). (2) Seek the number successfully genotyped at that variant, call-rate and quality-control information, whether calls are direct or inferred, and the population and sampling definitions. (3) It may better match the target population and directly measure the variant, while the larger source may use a mismatched sampling frame or uncertain proxy; size alone does not determine suitability. (4) It describes repeated-sampling coverage under the interval's assumptions; it does not automatically include assay error, selection, population mismatch, or design effects. (5) Harmonize the variant identity, reference build, strand and allele coding, and confirm that the reported allele is the same one intended before using or converting the estimate.