Paternity Indices - Dr. Ron Ostrowski, UNC Charlotte
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).
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. 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.
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. The potential of a randomly selected man to
pass the obligate gene is determined by using a database which lists the frequency distribution of
individual alleles within a given genetic system.
Combined Paternity Index
The combined paternity index (CPI) is determined by multiplying the individual PIs for each locus
tested. 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 based solely on genetic evidence.
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). This variable represents the social evidence. Testing labs typically use
a value of 0.5 for the PP assuming this is a neutral, unbiased value. The Baysian formula is CPI / CPI +
(1 - PP) x 100.
Elston, R.C. (1986). Probability and paternity testing. American Journal of Human Genetics. 39: 112-122.
Kaiser, L. and Sever, G. (1983). Paternity testing: I. Calculation of paternity indexes. American Journal of Medical Genetics. 15(2): 323-329.
Lee, C.L. (1979). Numerical expression of paternity test results using predetermined indexes. American Journal of Clinical Pathologists. 73(4).
Li, C.C. and Chakravarti, A. (1985). Basic fallacies in the formulation of the patrenity index. American Journal of Human Genetics. 37(4): 809-818.
Morris,J., Sandra, A.I., and Glassberg, J. (1989). Biostatistical evaluation of evidence from continuous allele frequency distribution deoxyribonucleic acid (DNA) probes in reference to disputed paternity and identity.
Journal of Forensic Sciences, JFSCA, 34(6): 1311-1317.
Morris,J. (1989). Experimental validation of paternity probability (to the editor).
Transfusion, 29(3): 281.
Morris,J. (1989). Limitations of paternity testing calculations revisited (to the editor).
Transfusion, 29(3): 280.
Thomson, J.A., Pilotti, V.,Stevens, P., Ayres, K.L.,
and Debenham, P.G. (1999).
Validation of short tandem repeat analysis for the
investigation of cases of disputed paternity. Forensic Science International. 100: 1–16.
Xiang, H.L., Tai, S.L., Karenda, F.N.N., and Wang, J. (2002). Deduction of paternity index from DNA mixture. Forensic Science International. 128: 105–107.
Zabell, S. (2003). A paternity paradox. Conference on Statistics and DNA Profiling, August 29-30, 2003.
Relevant Case Rulings
State of Wisconsin v. William Hartman. Supreme Court of Wisconsin. Argued April 26, 1988. Opinion filed July 19, 1988. Reconsideration denied September 13, 1988.
State of Connecticut v. Roy E. Skipper. Supreme Court of Connecticut. Argued September 23, 1993. Decided February 22, 1994.
State of New Jersey v. Joseph M. Spann. Supreme Court of New Jersey. Argued November 27, 1990. Decided January 5, 1993.
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