### Description

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)