Why Genotyping Errors Matter in Family-Based Tests
A transmission test compares alleles passed from parents to affected offspring with alleles that could have been passed but were not. This within-family comparison can protect against some forms of population stratification, but it does not protect against inaccurate genotypes. An error can make an impossible parent–child combination appear, change which parents count as informative, or reverse the inferred direction of a transmission. The resulting statistic may be biased, and the direction of that bias is not predictable in general.
Genotyping-error diagnosis therefore combines evidence: inheritance checks, the pattern of transmission counts, replicate samples, and laboratory quality-control measures. No single check identifies every error. In particular, a genotype can be wrong yet remain compatible with Mendelian inheritance, so absence of inconsistencies is not proof that the genotypes are correct.
Mendelian Compatibility as a Diagnostic Check
Consider a diploid autosomal locus with two alleles, \(A\) and \(a\). Assume the recorded parents are the biological parents, each person has two copies of the locus, and inheritance follows ordinary Mendelian transmission. Also assume no new mutation, copy-number change, or other biological event that would alter the expected genotype. Under this model, a child receives one allele from each parent. These assumptions define the compatibility check; if they do not apply, a mismatch needs a different interpretation.
For a trio, a basic check asks whether at least one allele in the child can be inherited from each parent. If the mother is \(Aa\), the father is \(aa\), and the child is recorded as \(AA\), the child cannot have received an \(A\) allele from the father under the model. That trio is incompatible. By contrast, a recorded child genotype \(Aa\) or \(aa\) is compatible with those parents.
A practical Mendelian inconsistency rate needs a denominator that reflects the opportunities for checking. One useful definition is the number of incompatible, scorable trio-locus checks divided by the number of scorable trio-locus checks. “Scorable” means the required genotypes are present and interpretable. The rate is not the proportion of all calls that are wrong: one incompatibility may involve an error in a parent, a child, sample identity, or pedigree information, and errors that preserve compatibility will not be counted.
Worked Example: Checking a Trio for Compatibility
In a hypothetical quality-control review, the mother is called \(Aa\), the father \(aa\), and the child \(AA\) at a biallelic autosomal marker. Assume the trio relationship is correct and the simple inheritance model applies. Is this trio compatible?
The mother can pass either \(A\) or \(a\). The father can pass only \(a\). Thus the child can be \(Aa\) if the mother passes \(A\), or \(aa\) if she passes \(a\). The recorded child genotype \(AA\) requires an \(A\) allele from the father, which the recorded father does not carry. The trio is therefore incompatible under the stated model.
This check identifies the locus and trio for review, not the erroneous call. The father could have been miscalled, the child's call could be wrong, or a sample or pedigree issue could be involved. Re-genotyping the trio and checking sample identity are more informative than changing one call solely to make the transmission possible.
Transmission Counts as a Diagnostic Signal
For a biallelic transmission disequilibrium test (TDT), let \(T\) be the number of transmissions of the allele being tested from informative heterozygous parents, and let \(U\) be the number of corresponding untransmitted copies. Under the conditional null of no preferential transmission, the tested allele is transmitted with probability \(1/2\) for each eligible heterozygous parent. With independent informative transmissions, the conventional score statistic is
This count-based statistic is useful for describing the association test, but a striking imbalance is not a genotyping-error diagnosis. It could reflect a genuine association, chance variation, or errors, among other possibilities. The diagnostic question is whether transmission counts or eligibility change when genotypes are checked against independent evidence. The simple statistic and its usual reference distribution also require an appropriate independence and calibration assumption; related or otherwise dependent observations may need a variance method that accounts for that dependence.
Genotype errors can affect the counts in several ways. An error in a child's genotype can change which parental allele appears transmitted. An error in a parent's genotype can turn a truly informative parent into one recorded as homozygous, or the reverse. An error can also create an apparent incompatibility and cause a family to be excluded. Consequently, errors may increase or decrease \(T-U\), alter \(T+U\), or change the set of families analyzed. Their net effect on the test statistic need not be toward or away from the null.
Worked Example: Recalculating Counts After a Genotype Audit
Suppose a hypothetical study has \(T=62\) and \(U=38\), giving 100 informative transmissions. Assume, for this illustration, that the transmissions can be treated as independent and that the usual asymptotic TDT calibration is appropriate. Eight transmissions are flagged for genotype review. Independent re-genotyping establishes that five originally counted as transmitted should instead be counted as untransmitted, one originally counted as untransmitted should instead be transmitted, and two originally counted as transmitted are no longer informative because the corrected parental genotype is homozygous.
Before the audit, the statistic is
With one degree of freedom, the chi-square tail probability is approximately \(0.0164\). Under the assumptions stated, this is evidence against equal transmission in the original recorded data; it is not evidence that the null hypothesis has a \(1.64\%\) probability of being true.
After the audit, the corrected counts are
The two observations removed from \(T\) are no longer informative, so the corrected total is 98. The recalculated statistic is
The one-degree-of-freedom chi-square tail probability is approximately \(0.1573\). In this hypothetical example, the reviewed genotype evidence changes both the counts and the strength of the statistical evidence. The audit does not establish that all real-world changes will weaken a result; different corrections can increase, decrease, or leave the imbalance similar.
Replicates and Laboratory Quality Control
Replicate genotyping gives a separate check on reproducibility. A duplicate specimen is tested again, ideally under conditions that make the second result an independent check rather than a repeat of the same systematic process. The replicate-discordance rate is the number of duplicate comparisons with different calls divided by the total number of comparisons with calls on both specimens. Its denominator, the comparison unit, and how missing calls are handled should be stated.
Worked Example: Interpreting Replicate Discordance
A hypothetical laboratory compares 200 pairs of duplicate genotype calls at one marker. Seven pairs have different calls. The observed replicate-discordance rate is
This means 3.5% of the paired comparisons disagreed; it does not mean that exactly 3.5% of all individual genotype calls are wrong. Without an independent truth standard, a discordant pair does not show which call, if either, is correct. The rate is a warning to examine the marker, samples, and assay, and to compare it with prespecified laboratory acceptance criteria.
A simple derivation illustrates why pair discordance is not the same as per-call error. In a deliberately simplified binary-call model, suppose each independent call has error probability \(e\), and every error switches the call to the other state. The pair disagrees if the first call is wrong and the second is correct, or vice versa. Therefore
Setting \(d=0.035\) gives \(e=(1-\sqrt{1-2d})/2\), the solution no greater than \(1/2\). Substitution yields
That is about 1.78% per call only under the toy model's assumptions. Real genotype calls usually have more than two possible states; errors need not be independent or symmetric, and duplicates can share systematic errors. The calculation is therefore not a general conversion from replicate discordance to genotype-error rate.
Other useful quality-control evidence includes missing-call rates, genotype cluster quality, allele balance where relevant, and whether error indicators concentrate in a sample, marker, plate, or laboratory batch. Concentration is often more informative than a single overall rate: a high inconsistency rate confined to one batch suggests a different investigation from a few scattered inconsistencies. Comparisons should use clear denominators and should not treat low call rate or unusual allele frequency as proof of error on its own.
Worked Example: Localizing an Elevated Inconsistency Rate
In a hypothetical data set, batch 1 has 9 incompatible checks among 500 scorable trio-locus checks. Batch 2 has 3 among 3,500. The batch-specific rates are
The overall rate is \(12/4000=0.003\), or \(0.300\%\). Reporting only that pooled rate would hide the much higher rate in batch 1: its observed rate is about \(1.80/0.0857\approx21.0\) times the batch 2 rate. This contrast motivates checking batch-specific procedures, sample labels, and marker performance. It does not, without further analysis, establish a cause or prove that every batch 1 call is unreliable.
A Disciplined Diagnostic Workflow
The purpose of these checks is to identify and resolve data-quality problems without choosing corrections to obtain a preferred association result. A defensible process keeps the diagnostic evidence distinct from the test result and records how each decision was made.
State the locus model, pedigree assumptions, and which family-locus records have enough calls to be checked. Count scorable checks separately from missing or uninformative records.
Report counts and rates, then inspect their distribution across samples, markers, and batches. Do not use an overall rate alone if it could conceal a localized problem.
Review duplicate genotypes, assay quality, sample identity, and any available re-genotyping. Where feasible, make these checks without using the direction or significance of the transmission result to decide which calls to change.
Correct a call only when the quality-control evidence supports the correction. If uncertainty remains, document the rule for flagging or excluding the record and assess how that rule affects the informative sample and transmission counts.
Recalculate the relevant counts and statistic using the resolved data, and report the original and reviewed results when informative. Interpret the result under the test's assumptions, including any dependence adjustment required by the family structure.
Common Pitfalls and Why the Checks Matter
- Treating every incompatibility as a proven genotype error. The check identifies a conflict with the assumed model. Sample swaps, incorrect relationships, or departures from the model can also explain it. Investigate before assigning blame to a particular call.
- Assuming compatibility guarantees accuracy. A wrong genotype can still permit a possible parent-to-child inheritance pattern. Mendelian checks detect some errors, not all errors.
- Reading a transmission imbalance as proof of error. A large \(T-U\) can be consistent with association under the test model. Error diagnosis needs independent evidence such as replicate or laboratory data.
- Assuming errors only dilute a true association. Errors can alter both transmission direction and eligibility. They may attenuate, exaggerate, or otherwise distort the statistic.
- Changing calls to improve the result. Selecting corrections based on whether they strengthen or weaken the association makes the analysis outcome-dependent. Use documented, independent quality-control criteria instead.
These distinctions matter because family-based inference conditions on observed family genotypes and transmissions. If those inputs are wrong, the protection against population stratification does not repair the measurement error. The useful conclusion from a diagnostic check is therefore appropriately limited: it identifies where the data warrant review, quantifies observed quality-control evidence, and shows how supported corrections affect the analysis.
Check Your Understanding
Use the assumptions and definitions in this tutorial to answer the following.
- Under the simple biallelic autosomal model, why is an \(AA\) child incompatible with two recorded \(aa\) parents?
- What does a Mendelian inconsistency rate measure, and why is it not automatically an estimate of the proportion of genotype calls that are wrong?
- Starting from \(T=45\) and \(U=35\), calculate the TDT score statistic. What assumptions are needed for its usual asymptotic interpretation?
- Why can a replicate-discordance rate not, by itself, identify which call in a discordant pair is correct?
- Name two ways that a genotype error can alter a transmission test, and explain why its effect on the test statistic has no fixed direction.