The probability that a D-positive father is heterozygous or homozygous for the D locus can be calculated based on the father's Rh phenotype, his race, and the D status of his offspring. This can be used in evaluating the risk of anti-D related Hemolytic Disease of the Newborn in a D-negative mother.
Probability of D Locus Status in Common Rh Phenotypes
|
Common Phenotype |
White
|
Black
|
||
|---|---|---|---|---|
|
|
Heterozygous |
Homozygous |
Heterozygous |
Homozygous |
|
CcDe |
0.90 |
0.10 |
0.41 |
0.59 |
|
CDe |
0.09 |
0.91 |
0.19 |
0.81 |
|
cDEe |
0.90 |
0.10 |
0.37 |
0.63 |
|
cDE |
0.13 |
0.87 |
0.01 |
0.99 |
|
CcDEe |
0.11 |
0.89 |
0.10 |
0.90 |
|
cDe |
0.94 |
0.06 |
0.54 |
0.46 |
If a D-positive father has had any D-negative offspring, then the probability that he is heterozygous for the D antigen is 1.0.
The probability that the father is heterozygous for the D locus given the Rh phenotype and the number of D-positive offspring is as follows:
Father is White
|
Phenotype |
n=0 |
n=1 |
n=2 |
n=3 |
n=4 |
n=5 |
|---|---|---|---|---|---|---|
|
CcDe |
0.90 |
0.82 |
0.69 |
0.53 |
0.36 |
0.22 |
|
CDe |
0.09 |
0.047 |
0.024 |
0.012 |
0.006 |
0.003 |
|
cDEe |
0.90 |
0.82 |
0.69 |
0.53 |
0.36 |
0.22 |
|
cDE |
0.13 |
0.070 |
0.036 |
0.018 |
0.009 |
0.005 |
|
CcDEe |
0.11 |
0.058 |
0.030 |
0.015 |
0.008 |
0.004 |
|
cDe |
0.94 |
0.89 |
0.80 |
0.66 |
0.49 |
0.33 |
Father is Black
|
Phenotype |
n=0 |
n=1 |
n=2 |
n=3 |
n=4 |
n=5 |
|---|---|---|---|---|---|---|
|
CcDe |
0.41 |
0.26 |
0.15 |
0.080 |
0.042 |
0.021 |
|
CDe |
0.19 |
0.10 |
0.055 |
0.028 |
0.014 |
0.007 |
|
cDEe |
0.37 |
0.23 |
0.13 |
0.068 |
0.035 |
0.018 |
|
cDE |
0.01 |
0.005 |
0.003 |
0.001 |
<0.001 |
<0.001 |
|
CcDEe |
0.10 |
0.053 |
0.027 |
0.014 |
0.0.007 |
0.003 |
|
cDe |
0.54 |
0.37 |
0.23 |
0.13 |
0.068 |
0.035 |
Calculating the Probability with Bayes Theorem
probability that the D-positive father with a given Rh phenotype is homozygous for D =
= A / (A + B)
probability that the D-positive father with a given Rh phenotype is heterozygous for D =
= 1 - (probability homozygous)
where:
• A = (probability homozygous for D with Rh phenotype)
• B = ((probability heterozygous for D with Rh phenotype) * ((0.5) ^ 2))
This is derived with Bayes theorem:
P(DD | i and n) =
= [P(DD|i) * P(n|DD)] / [P(DD|i) + {P(Dd|i) * P(n|Dd)}]
where:
• i = Rh phenotype
• n = number of D positive offspring
• P(n|DD) = 1
• P(n|Dd) = (0.5)^n
• P(DD|i) = (probability homozygous for D with Rh phenotype)
• P(Dd|i) = (probability heterozygous for D with Rh phenotype)
Specialty: Clinical Laboratory
ICD-10: ,
