2.2 Mendelian Risk Calculations

2.2 Mendelian Risk Calculations

Quick Answer: Use segregation math from the consultand's pedigree position: AD transmission ≈ 1/2 to each child of a heterozygous affected parent; AR recurrence ≈ 1/4 when both parents are carriers; unaffected sib of AR proband carrier risk = 2/3; XL carrier mother → 1/2 sons affected, 1/2 daughters carriers (absent mosaicism/de novo complications).

Domain 2A expects clean arithmetic and correct conditioning on affection status—especially the 2/3 carrier result that trips candidates who default to 1/2.

Why Simple Mendelian Math Still Dominates Exam Items

Many CGC items stop at Mendelian priors: no negative test, no age adjustment, no population frequency twist. If you mis-identify who is an obligate carrier or forget to condition on "unaffected," every downstream Bayes step fails.

Core Segregation Table

Always state assumptions: complete penetrance, correct diagnosis, true biologic relationships, and no germline mosaicism unless the stem introduces them.

Autosomal Dominant Transmission

If a parent is heterozygous for a pathogenic AD variant and penetrance is treated as complete for the exam item, each child has a 1/2 chance of inheriting the variant. With incomplete penetrance p, the chance a child is clinically affected is (1/2)×p, but the chance of inheriting the genotype remains 1/2.

Worked example (AD): A consultand has a parent with a known MSH2 pathogenic variant. Ignoring mosaicism and assuming the parent is heterozygous, the consultand's prior of inheriting the variant is 1/2. If the consultand already tested negative for the familial variant, Mendelian prior is replaced by the negative test result (residual risk approaches laboratory error / rare mosaicism discussions—not 1/2).

Siblings: Each full sibling of an AD consultand who inherited a parental variant also had an independent 1/2 prior at conception. Do not "share" the 1/2 across sibs.

Autosomal Recessive Risks After an Affected Child

When a child is diagnosed with a classic AR condition and parental genotypes are not yet known, counseling often treats both parents as obligate carriers for recurrence estimation if the diagnosis and inheritance are secure. Recurrence risk for each subsequent pregnancy is then 1/4 for an affected child.

Carrier Risk for Unaffected Siblings: Why 2/3

Parents Aa × Aa produce offspring ratios at conception:

• AA 1/4
• Aa 1/2
• aa 1/4

An unaffected sibling cannot be aa. Remaining probability mass is 1/4 + 1/2 = 3/4. Carrier probability among unaffected sibs:

(1/2) / (3/4) = 2/3

Non-carrier probability among unaffected sibs:

(1/4) / (3/4) = 1/3

Worked example (AR sib): A couple's first child has phenylketonuria (AR). An unaffected younger sister asks her carrier risk before partner testing. Prior carrier risk = 2/3. If she later partners with someone from a population with PKU carrier frequency 1/50, the couple's affected-child risk before any testing is (2/3)×(1/50)×(1/4) = 2/600 = 1/300 (order-of-magnitude teaching calc; use stem-specific frequencies on the exam).

Partner and Population Carrier Risks

For a consultand who is an obligate carrier (or 2/3 carrier), the partner's prior often comes from ethnicity-specific carrier frequency (or pan-ethnic screening panels). Couple risk ≈ (consultand carrier probability) × (partner carrier probability) × 1/4.

X-Linked Transmission Odds

Track the X chromosome path:

1. Carrier mother: Each son has 1/2 chance of being affected; each daughter has 1/2 chance of being a carrier (and may have mild manifestations depending on the condition).
2. Affected father (XL recessive paradigm): All daughters are obligate carriers; no sons inherit his pathogenic X.
3. Sister of affected male: If the mother is an obligate carrier (for example, two affected sons, or an affected brother and an affected son), the sister's carrier prior is 1/2 before Bayes. If the affected male is an isolated case, maternal carrier prior is <1 because of de novo / mosaicism possibilities—exam stems usually specify what to assume.

Worked example (XL): Mother is a known carrier of a pathogenic DMD variant. She is pregnant with a male fetus (sex known). Risk the boy is affected ≈ 1/2 before any prenatal genotype test. If she is pregnant with a female fetus, risk of affected disease is much lower than 1/2 for classic Duchenne (manifesting carriers exist, but "affected" thresholds differ); carrier probability for the daughter ≈ 1/2.

Combining Pedigree Position with Simple Multiplication

Multi-step AR example: Unaffected consultand is the sibling of a child with an AR disease (carrier risk 2/3). The consultand's partner is unrelated with population carrier risk 1/100. Without testing:

• Probability both are carriers: (2/3)×(1/100) = 2/300 = 1/150
• Probability next child affected: (1/150)×(1/4) = 1/600

State each factor; graders (and your own error-checking) need the chain.

Common Exam Traps

• Using 1/2 instead of 2/3 for unaffected AR sibs
• Giving an XL father-to-son transmission risk other than zero for the X-linked locus
• Applying 1/4 recurrence when only one parent is a known carrier and the partner is untested (must include partner prior)
• Confusing genotype probability with phenotype probability under incomplete penetrance
• Treating a de novo AD variant in the child as implying high parental recurrence without discussing germline mosaicism (recurrence is low but not absolute zero)

Bridge to Bayesian Analysis

Mendelian numbers are priors. Negative carrier screening, normal CK in an adult sister at risk for DMD carrier status, or multiple unaffected sons are conditional data. Section 2.3 shows how to convert prior → posterior with joint probabilities. If you cannot write the Mendelian prior cleanly, stop and fix pedigree position first.