How do you calculate carrier risk in an X-linked (X-chromosome linked) pedigree?

Calculating Carrier Risk in X-Linked Pedigrees

Carrier risk calculation in X-linked pedigrees requires Bayesian analysis that incorporates prior probability (based on pedigree position), conditional probability (based on number of unaffected sons), and posterior probability (final carrier risk after considering all evidence).

Core Principles of X-Linked Inheritance

• Females can be carriers or affected depending on penetrance and X-inactivation patterns, while males are either affected or unaffected (hemizygous state) 1
• The traditional "X-linked recessive" versus "X-linked dominant" classification is outdated because most X-linked disorders show variable penetrance in females (28% high, 31% intermediate, 40% low penetrance), making simple dominant/recessive categorization inadequate 1
• Carrier females typically show skewed X-inactivation in relevant cell lineages, which can be used diagnostically (>95% skewing in B lymphocytes for X-linked agammaglobulinemia carriers) 2

Bayesian Calculation Framework

The calculation involves three sequential steps that can be programmed into calculators or performed manually 3:

Step 1: Establish Prior Probability

• Obligate carriers (mothers of affected males with affected male relatives, or daughters of affected males): Prior probability = 1 (100%) 2
• Possible carriers (mothers of isolated affected males, sisters of affected males, daughters of carriers): Prior probability depends on pedigree position
  • Sister of affected male with carrier mother: 1/2 (50%)
  • Daughter of carrier female: 1/2 (50%)
  • Mother of isolated affected male with no family history: 1/2 (50%, accounting for new mutation possibility)

Step 2: Calculate Conditional Probability

• For each unaffected son, the conditional probability is modified 3:
  • If carrier: probability of having unaffected son = 1/2
  • If non-carrier: probability of having unaffected son = 1
• Multiple unaffected sons reduce carrier probability exponentially: Each additional unaffected son multiplies the "carrier" conditional probability by 1/2 3

Step 3: Compute Posterior Probability

Use Bayes' theorem: Posterior probability = (Prior × Conditional for carrier) / [(Prior × Conditional for carrier) + ((1-Prior) × Conditional for non-carrier)] 3

Practical Example Calculation

For a woman who is the sister of an affected male (prior = 1/2) with 2 unaffected sons:

• Prior probability of being carrier: 1/2
• Conditional probability if carrier: (1/2)² = 1/4 (for 2 unaffected sons)
• Conditional probability if non-carrier: 1
• Posterior probability = (1/2 × 1/4) / [(1/2 × 1/4) + (1/2 × 1)] = 1/8 ÷ 5/8 = 1/5 or 20% 3

Molecular Testing Considerations

When Mutation is Known

• Direct mutation testing provides definitive carrier status when the familial mutation is identified 2
• Linkage analysis using flanking markers (RFLPs or microsatellite markers) can be used when direct testing is unavailable, with recombination fractions affecting accuracy 4, 2

Genetic Heterogeneity Impact

• Some X-linked conditions show linkage heterogeneity (e.g., Fragile X syndrome with F9 probe showing tight linkage in some families, loose in others, P<0.0005) 4
• Penetrance varies by linkage type: Families with tight linkage may show different expression patterns than those with loose linkage 4
• Approximately 20% of males and 44% of females with Fragile X are non-penetrant for mental impairment, complicating risk assessment 4

Critical Pitfalls to Avoid

• Do not assume all X-linked disorders follow simple recessive patterns: Variable expressivity and penetrance in females is the rule, not the exception 1
• Account for new mutations: In isolated cases with no family history, approximately 50% represent new mutations, affecting the mother's prior probability 2
• Consider X-inactivation skewing: Carrier testing using X-inactivation patterns in relevant cell types (CD19+ cells for XLA) provides >95% accuracy in obligate carriers 2
• Recognize that non-penetrant transmitting males occur in both tight and loose linkage families, so their presence does not indicate heterogeneity type 4

Population-Based Carrier Frequencies

When no family history exists, population carrier frequencies guide screening recommendations 5:

• Screening threshold: American College of Medical Genetics recommends carrier screening for conditions with carrier frequency ≥1/200 5
• 324 genes meet this threshold in at least one ancestry group based on gnomAD v4.0 data 5
• Ancestry-specific calculations are essential: At-risk couple frequencies vary significantly (Ashkenazi Jewish 6.11% highest) 5