Paternity index

04/14/2023 saurabh bhargava 1

Types of Kinship Testing

• Paternal Testing

Know child’s genotype, try to determine father

• Reverse ParentageKnow parent’s genotypes, try to determine their child

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Random ManAlleged Mother

Missing ChildChild

Mother (known parent) Alleged Father Alleged Father


Genetic Markers

• Half of a child's genetic material (alleles) come from the mother, while the other half is contributed by the father.

• A series of genetic systems (loci) are analyzed in an attempt to ascertain the biological father of a child.

• Each genetic system in a person has two allele, these alleles are numerically labeled.

• In paternity testing, the alleles from the child are compared to those of the "parents" to determine if it is possible for either or both parents to have contributed the particular alleles present in the child.


How

• DNA (alleles) from the mother, child, and alleged father are extracted, amplified, and identified.

• A series of mathematical calculations are then used to either completely exonerate an accused man or provide an estimate of probability of his paternity (POP).


Rules of Inheritance

1)Child has two alleles for each autosomal marker (one from mother and one from biological father)

2)Child will have mother’s mitochondrial DNA haplotype (barring mutation)

3)Child, if a son, will have father’s Y-chromosome haplotype (barring mutation)

C, D

A, C

A, B


Conti..• For instance, assume that a child has a 10 and 11 allele for a particular

genetic system and the child's mother is known to possess a 10 and a 12 allele for this system.

• The mother must have contributed the 10 allele and the 11 allele must be paternal. In this example, any man who does not possess an 11 allele could not be the child's father (barring the possibility of mutation that converts one allele to another - something that is unlikely but can be taken into consideration if needed).

• In the event that a man is not excluded, the likelihood that a randomly chosen man might also be able to provide the allele in question to the child can be determined by examining the allelic frequencies from a relevant population database.


Obligate Paternal Allele

• The alleles the actual father MUST have• Compare the child to the mom; Whatever

allele the mom does not have is the obligate paternal allele

• If mom and dad share alleles there will be less information

• More markers you type –eventually you will find unique alleles



12, 14

12, 14

11, 12

8, 12

8, 14 8, 11

11, 14

OBLIGATE PATERNAL ALLELE 14 1114 1114



8, 12

12, 12

12, 12

11, 12

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8, 118, 12

Obligate Paternal Allele 12 EITHER

8 OR12111211

WHAT GENOTYPE MUST THE TRUE FATHER HAVE???IF THERE IS ONE FATHER FOR ALL THE CHILDREN THEN IT HAS TO BE 11, 12


Paternity Index

• The paternity index (PI) compares the likelihood that a genetic marker (allele) that the alleged father (AF) passed to the child to the probability that a randomly selected unrelated man of similar ethnic background could pass the allele to the child.

• This is presented in the formula X/Y, where X is the chance that the AF could transmit the obligate allele and Y is the chance that some other man of the same race could have transmitted the allele.

• X is assigned the value of 1 if the AF is homozygous for the allele of interest and 0.5 if the AF is heterozygous.


Conti.. • PI = paternity index

• Ratio of the two probabilities:

p(AF is the father) p(A random man is the father)

• Ratio then represents how much better the data (genotypes) fits with the hypothesis that the AF is the real father

• Larger ratio more evidence that this man is the real father


Two possible results

1.Inclusion:• Tested man, Alleged Father, could be this

child’s father

2. Exclusion:• There is no way that the AF could be this

child’s father


Combined Paternity Index

• When multiple genetic systems are tested, a PI is calculated for each system.

• The genetic systems are inherited independently, the Combined Paternity Index (CPI) is the product of system PIs.

or• The combined paternity index (CPI) is determined by

multiplying the individual PIs for each locus tested. • This value is referred to as system PI.


Combined Paternity Index• The CPI is an odds ratio that indicates how many times more likely it is

that the alleged father is the biological father than a randomly selected unrelated man of similar ethnic background.

• The CPI is a measure of the strength of the genetic evidence.

• The CPI is based solely on genetic evidence.

• Theoretically the range of CPI is 0- ∞ (zero to infinity)– CPI=1; no information

– CPI<1; the genetic evidence is more consistent with non-paternity than paternity

– CPI>1; the genetic evidence supports the assertion that the tested man is the father


Probability of Paternity

• The probability of paternity is the measure of strength of one’s belief in the hypothesis that the tested man is the father.

• The correct probability must be based on all the evidences of the case.

• The non-genetic evidence comes from the testimony of mother, tested man & other witnesses.

• The genetic evidence comes from DNA paternity tests



• The probability of paternity (W) is based upon Baye’s Theorem, which provides a method for determining a posterior probability based upon the genetic results of testing the mother, child and alleged father.

• In order to determine the probability of paternity, an assumption must be made (before testing) as to the prior probability that the tested man is the true biological father.

• The prior probability of paternity is the strength of one’s belief that the tested man is the father based only on the non-genetic evidences.


Probability of Paternity• To convert the genetic evidence to a probability of paternity (POP) it is necessary to

use the Baysian theorem.

• This is a formula that tests the hypothesis that the accused is the biological father of the child. – For example, a POP of 99% reflects a 99% probability that the hypothesis is correct and a

1% probability that it is not.

• The CPI is used in the Bayes formula along with another variable called a prior probability (PP). – Testing labs typically use a value of 0.5 for the PP assuming this is a neutral, unbiased value.

• The Baysian formula is

• CPI×PP{CPI×PP+(1-PP)}



• With a prior probability of 0.5, the– Probability of paternity(w) =

CPI X 0.5 {CPI X 0.5+(1-0.5)}

=CPI(CPI+1)


PRIOR PROBABILITY

• If we wishes to assume a prior probability of 50%, then the (posterior) probability will be “x” [whatever figure is given].

• On the other hand, if we feel that some other prior probability is appropriate, then the posterior probability will be somewhat different.

• NOTE: if the report gives a W value with no mention at all of a prior probability (which is the practice in most countries), then it is flat misleading.


PRIOR PROBABILITY

• But the effect of allowing “pp” to vary is often not material because using DNA tests (CPI) is usually very large.

• For example, suppose that CPI=100000. Then the paternity report will probably calculate W=100000/100001 and report W=99.999%, at 50% prior probability.


PRIOR PROBABILITY• Suppose that the defendant presents powerful testimony: the

woman is unreliable and has made many false accusations in the past; he is a prominent person, a likely target; she admits that full penetration did not occur and that he failed to ejaculate.

• Suppose that from all of this the judge is persuaded to estimate that if testimony like this were presented in 500 cases, only about once would the man be the father and 499 he would have been falsely accused. So pp=1/500.

• Applying the above formula, we get – W=99.5%, at 0.02% prior probability.

• The verdict is probably the same whether• W=99.5% or 99.99%.


PRIOR PROBABILITY

• So while the man is entitled by our system of jurisprudence to have his say in court, it is likely that nothing he can say will be significant compared to the force of the DNA evidence.

Education

Paternity index