Start With the Study Structure
A family-based test is not chosen by asking which method is most familiar. The choice depends first on what was measured, then on which relatives were recruited and genotyped, and finally on whether the observed family information supports a valid comparison. A binary disease studied in complete parent–offspring trios calls for a different design choice than a quantitative trait measured in siblings whose parents are unavailable.
The methods considered here share a broad aim: test whether genetic variation is associated with a phenotype using comparisons within families. Their handling of phenotype type, missing genotypes, and dependence differs. A method that can use a particular pedigree is not automatically valid for every way that pedigree was selected or every pattern of missingness.
A practical selection sequence is: specify whether the phenotype is binary or quantitative; map which relatives are available and genotyped; identify which allele transmissions or within-family contrasts are actually informative; and verify that the proposed method accommodates the pedigree and recruitment scheme. Genotyping quality control comes before this sequence: Mendelian inconsistencies or allele-calling errors can distort the very transmissions being tested.
What Each Design Is Suited to
| Available design and phenotype | Natural candidate | Key qualification |
|---|---|---|
| One affected child and both genotyped parents; binary phenotype | Trio transmission disequilibrium test (TDT) | Requires informative transmissions and valid conditional transmission assumptions. |
| Quantitative phenotype with informative parental or family genotypes | Quantitative-trait FBAT | Uses a trait-weighted conditional score; trait centering and variance calibration must suit the design. |
| Genotyped siblings but one or both parents unavailable | Sibling-based test | Must use the sibling structure and account for relatedness; informativeness depends on the siblings’ genotypes and phenotypes. |
| Incomplete trio with enough observed genotype information | Pseudocontrol approach | Use only when the method can construct or properly account for the relevant untransmitted-genotype comparator. |
| Several genotyped relatives across a larger pedigree | Extended-pedigree FBAT or another suitable pedigree-based method | Must preserve the dependence structure and use the pedigree information correctly. |
The table is a starting point, not an automatic decision rule. A complete trio is not required for every family-based analysis, and a missing parent does not by itself make a family unusable. Conversely, a large pedigree does not guarantee more useful information: relatives may be uninformative at the variant, have missing phenotypes, or contribute highly dependent observations.
Why the Trio TDT Fits Complete Case–Parent Trios
The trio TDT is a natural candidate when a study has a binary phenotype, typically one affected child per family, and genotypes for that child and both biological parents. It tests whether an allele is transmitted to affected offspring more often than expected under the null of no association, conditional on the parental genotypes. A parent heterozygous at a biallelic marker provides an informative transmission; a homozygous parent does not distinguish which allele was transmitted.
The conditional null has a simple Mendelian basis. Under the null, for a heterozygous parent and a randomly transmitted allele, each allele has transmission probability one half. If \(T\) indicates transmission of the allele being tested, then
Thus the centered transmission \(T-\frac{1}{2}\) has conditional expectation zero. Summing such centered contributions gives the basic logic of the TDT. The comparison uses transmissions within families, rather than treating the affected children as an ordinary case sample and comparing them with unrelated controls.
Worked Example: Complete Trios With a Binary Phenotype
Suppose a hypothetical study has 28 nuclear families, each with one affected child and both parents genotyped at a biallelic marker. Across the families, there are 56 informative transmissions from heterozygous parents: the allele of interest was transmitted 34 times and not transmitted 22 times. The study question concerns association with disease status.
Choose the method. These are complete case–parent trios with a binary phenotype, so the trio TDT is a direct candidate. This choice presumes correct parent–child relationships, reliable genotypes, valid Mendelian transmission, and a recruitment scheme for which the conditional test is appropriate. The 56 transmissions are informative because each came from a heterozygous parent.
Check the conditional score. Under the null, the expected number of transmissions is \(56(0.5)=28\). The observed excess is \(34-28=6\), or equivalently \(34-22=12\) more transmissions than nontransmissions. Using the usual one-degree-of-freedom TDT statistic based on transmitted versus untransmitted counts,
For a chi-square distribution with \(df=1\), this gives approximately \(p=0.109\). At \(\alpha=0.05\), this result does not provide evidence against the conditional null. It does not establish that the allele has no effect; it indicates that these data do not show a statistically significant transmission imbalance at that threshold. The computation illustrates the test choice and its conditional comparison, not a substitute for checking model assumptions or study quality.
Quantitative Traits and Quantitative-Trait FBAT
When the phenotype is quantitative—for example, a measured biomarker or blood pressure—a binary-disease TDT is not the right formulation simply because parents and offspring are genotyped. A quantitative-trait FBAT combines a centered genetic transmission score with a centered trait value. In a simplified single-offspring setting, the contribution can be written as
where \(X_i\) is the offspring’s allele count, \(\mathcal{F}_i\) denotes the observed family genotype information used for conditioning, \(Y_i\) is the quantitative trait, and \(\mu\) is the trait center specified under the null. The total score sums family contributions. The precise score and variance calculation depend on the chosen FBAT specification and family design. The important selection point is that the trait contributes through its deviation from the specified center, while the genotype is centered on its conditional expectation.
Worked Example: A Quantitative Trait in Genotyped Parent–Child Families
Consider four hypothetical, unrelated nuclear families. In each, both parents are heterozygous at a biallelic marker, so the child’s allele count \(X_i\) has conditional expectation 1. The children’s biomarker values are 12, 9, 11, and 8 mg/dL, and the null trait center is set to \(\mu=10\) mg/dL. Their allele counts are 2, 1, 0, and 1, respectively.
A quantitative-trait FBAT is a suitable candidate because the outcome is quantitative and the parental genotypes provide the conditional transmission expectation. The centered allele counts are \(1,0,-1,0\), and the centered traits are \(2,-1,1,-2\) mg/dL. The score contributions and total score are
The score is in allele-copy–mg/dL units under this simplified representation. A positive score indicates that, in these data, higher-than-centered allele counts tend to pair with higher-than-centered trait values, but the score alone is not an inferential conclusion. With only four families, a large-sample normal approximation would be questionable; the test’s conditional variance and an appropriate small-sample calibration must be used before making a significance claim. The choice of quantitative FBAT is justified by the outcome and available family information, not by this uncalibrated score.
When Parents Are Missing: Siblings and Pseudocontrols
If parents are unavailable but siblings are genotyped, sibling-based tests can use within-family information rather than requiring a complete trio. For example, discordant affected and unaffected siblings may provide a contrast for a binary phenotype. These methods must account for the fact that siblings share genes and environment; they are not independent case and control observations. Their usefulness depends on the siblings’ phenotype pattern, genotypes, and the test’s assumptions about how the families entered the study.
Pseudocontrol methods offer another route for some incomplete trios. The idea is to compare an affected child with a constructed, untransmitted-genotype comparator, while retaining a within-family comparison. This is not equivalent to filling in a missing parental genotype with a guessed value. The observed genotypes must permit the method to construct or correctly represent the comparator, including uncertainty where appropriate. If the missing parent’s genotype makes the relevant comparison unidentified, the family cannot be treated as if it supplied a fully observed pseudocontrol.
Worked Example: Choosing Between a Sibling Test and Pseudocontrols
A hypothetical study recruits 60 families through a child with a binary disease. In 24 families, the affected child and both parents are genotyped. In 20 more, the affected child and an unaffected sibling are genotyped, but neither parent is available. In the remaining 16, only the affected child and one parent are genotyped.
Complete trios. The 24 complete case–parent families are candidates for a trio TDT, subject to informative transmissions and the TDT assumptions.
Genotyped siblings. The 20 families with an affected child and an unaffected genotyped sibling are candidates for a sibling-based approach. The siblings’ relationship and joint recruitment must be represented in the analysis; their genotypes cannot be treated as independent observations.
One-parent families. The final 16 families are not complete trios. A pseudocontrol approach is a candidate only if the observed parent–child genotypes and the method’s rules provide an identifiable or properly uncertainty-adjusted untransmitted comparator. If they do not, those families do not supply the required pseudocontrol comparison. They should not be forced into a complete-trio TDT by imputing the absent parent without a justified model.
The result is a design-specific plan: use each method only for the family subset it can validly analyze, and report the subsets and eligibility rules. Combining the families into one analysis requires a method that explicitly handles the different structures; the three subsets are not automatically interchangeable.
Extended Pedigrees and Dependence
When a study includes several related individuals across an extended pedigree, an extended-pedigree FBAT or another pedigree-based family method may use information beyond a single parent–child trio. The method must condition on or otherwise model the relevant pedigree structure. Multiple affected relatives, siblings, or descendants can contribute information, but their scores may be dependent because they share ancestors and transmissions.
This is why a larger family is not simply equivalent to a larger number of independent trios. A suitable method must use the observed relationships and an appropriate variance calculation. A test that assumes independence can give incorrect standard errors and p-values if related contributions are treated as independent. The earlier material on dependence and variance in family-based scores is directly relevant when deciding whether a particular extended-pedigree implementation is appropriate.
Worked Example: Several Affected Relatives in a Pedigree
Suppose a hypothetical study has 18 pedigrees, each containing an affected grandparent, two affected adult siblings, and several genotyped offspring. Genotypes are available for many, but not all, relatives. The phenotype is binary, and the study aims to test association at one marker.
A trio TDT could be applied to an eligible subset only if the analysis is defined around complete, informative parent–offspring trios and does not ignore dependence between overlapping trios. Because the study’s principal structure is a multigenerational pedigree with related affected members, an extended-pedigree family-based method is the more natural candidate.
Before analysis, the researcher must verify that pedigree relationships are specified, identify which genotyped relatives contribute informative transmissions, and use a test whose score and variance accommodate their dependence and the actual missing-genotype pattern. If a particular method requires genotypes that are absent, the pedigree cannot be analyzed by that method as though those genotypes had been observed. The method choice is therefore extended-pedigree analysis, conditional on those design and data checks—not simply “use every relative.”
Assumptions and a Practical Decision Sequence
Family-based designs can reduce sensitivity to population stratification because their comparisons are made within families, but this does not remove every threat to validity. Correct genotypes and relationships, appropriate handling of phenotype ascertainment, suitable treatment of missing data, and a valid variance calculation remain necessary. In particular, the conditional null is meaningful only for the family information and sampling scheme assumed by the selected test.
Use a binary-phenotype transmission design for disease status and a quantitative-trait FBAT formulation for a measured continuous outcome, unless the analysis explicitly defines another appropriate model.
Record which parents, offspring, siblings, and other relatives are observed and genotyped. Separate complete trios from incomplete trios, sibships, and extended pedigrees.
Check whether observed genotypes support a transmission, sibling contrast, pseudocontrol, or pedigree score. A family with no informative genetic contrast may add no information to that test.
Check genotyping quality, ascertainment, dependence, missingness, and the test’s variance or small-sample calibration before interpreting a statistic or p-value.
Common Mistakes
- Using TDT for any family sample. The TDT is designed for a suitable case–parent transmission structure; genotyped siblings without parents do not become complete trios.
- Treating missing genotypes as known. A pseudocontrol is a method-defined comparator, not an arbitrary replacement for an absent parent.
- Ignoring the phenotype scale. A quantitative trait requires a quantitative-trait score and an appropriate trait center; it should not be converted to a binary outcome without a scientific reason.
- Counting relatives as independent. Overlapping trios or multiple relatives in a pedigree can have dependent scores, so the analysis must use an appropriate variance.
- Assuming family-based means assumption-free. These methods still require valid genotypes, relationships, ascertainment handling, and a test calibrated for the observed design.
Check Your Understanding
For each scenario, identify a candidate method and one important validity check.
- A binary disease study has one affected child and both genotyped parents per family. What method is a natural candidate, and what makes a parental transmission informative?
- A biomarker is measured in children with both parents genotyped. Why is a quantitative-trait FBAT more suitable than a binary-disease TDT formulation?
- Parents are unavailable, but affected and unaffected siblings are genotyped. What kind of family-based comparison could be considered, and why must sibling dependence be handled?
- In what sense is a pseudocontrol different from imputing a missing parent’s genotype?
- A pedigree contains several related affected relatives and overlapping parent–offspring pairs. Why may an extended-pedigree method be preferable to treating every pair as an independent trio?