A paternity DNA test has two possible outcomes: 

1.  The tested man is not the father.  The report will say that the alleged father is not the biological father (excluded) of the tested child.  The paternity test report will show a minimum of two exclusions.

 2.  The tested man is the father.  If the report says that the tested man is not excluded as the biological father of the tested child, the results will be reported as a statistic known as the Combined Paternity Index.  A Combined Paternity Index of 100 or greater is the accepted standard to establish parental rights in most States.

The father of the child can be confirmed by identifying genetic markers.  These markers (alleles) occur in pairs and are passed from each parent to the child.  For each pair of markers, one comes from the mother (the maternal marker or allele) and the other comes from the father (the paternal marker or allele).  The true biological father is expected to share the paternal allele with the child for each allele tested (see Table 1). If the tested man shares one allele with the child at each location he cannot be excluded as the biological father of the child in question. When the alleged father shares the parental allele with the child a paternity index number is calculated for each location there is a match.  Table 1. Inclusion (non-exclusion) In this example the paternal allele is colored red.   Allele Child Alleged Father Parental Allele Click on the image below to view a typical report. CSF1PO 12, 13 12, 14 12 D3S1358 17, 19 14, 19 19 FGA 22, 27 24, 27 27 TH01 8, 9 7, 9 9
The paternity index (PI) is a likelihood ratio.  Paternity index summarizes information provided by genetic testing.  It basically states how many more times likely the person was to inherit the allele versus the chance of the same allele existing in the random population.  Look at table 2 and the allele CSF1P0, in the example the child is 4.182 more times likely to inherit the 12 allele.  For FGA the child is 19.231 more times likely to inherit the 19 allele.  The real strength of the DNA test resides in the combined paternity index.

Combined Paternity Index (CPI) is the biostatistic that completely evaluates the genetic information.  The CPI is a measure of the strength of the genetic evidence.  It indicates whether the evidence fits better with the hypothesis that the tested man is the father or with the hypothesis that someone else is the father.  It is a ratio (a CPI of 100 means 100 to 1) which expresses the relative "fit" of the genetic data to the alternate hypotheses of paternity and non-paternity.  The CPI is a simple odds ratio.  Because of the increased accuracy possible with DNA testing, the generally accepted minimum standard for an inclusionary result has risen to a CPI of 100.  Because each of the alleles tested are on different chromosome they are considered independent events, because they are independent events we can use the Product Rule to calculated the CPI.  The Product Rule allows us to multiply all the paternity index numbers together to generate the CPI.  The CPI is calculated by multiplying all the paternity index numbers together (4.182 x 19.231 x 19.231 x 2.029=3,138.122).  In this example the CPI is 3,138.1219.

Probability of Paternity is a mathematically rigorous way expressing and understanding the significance of the genetic results.  Probability of paternity has the same meaning as more commonly experienced probabilities. A probability of rain of 99% means that, of 100 such predictions one expects that only one will be followed by clear skies.  It follows that a probability of paternity depends on an evaluation of the other evidence presented, as well as the genetic evidence.  The prior probability of paternity (p) is the strength of one's belief that the tested man is the father based only on the non-genetic evidence. The other (non-genetic) evidence is summarized by p, the prior probability of paternity.  p=0 means that the other evidence indicates that paternity is impossible, while p=100% means that the other evidence indicates that paternity is certain.  Of course, we have no certainty, so that in each paternity case, p is larger than 0, but less than 100%.  In the United States the court system has made the assumption that the prior probability that the prior probability of paternity is equal to 50% (p=0.5).  The argument for using p=50% that is that the tested man is either the true father or he is not.  It is a neutral number.  In the absence of any knowledge about which was the case, it is reasonable to give these two possibilities equal prior probabilities.  In this example, the probability of paternity takes the simple form: probability of paternity = (CPI)/(CPI+1) *100.  In this example the CPI= 3,138.122 and the CPI+1= 3,139.122 therefore, the probability of paternity is  99.9681

Exclusion Example:  The father or the mother of the child can be confirmed or ruled out by identifying genetic markers.  These markers occur in pairs and are passed from each parent to the child.  For each pair of markers, one comes from the mother (the maternal marker or allele) and the other comes from the father (the paternal marker or allele).  The father is expected to share the paternal marker with the child for each allele tested. This rule of inheritance is very reliable, mismatch (exclusion) between the tested man and the child, typically found in two or more alleles, results in exclusion of the tested man.  In this example, at the loci CSF1PO, D3S1358 and THO1, you can see that the child does not share an allele with the father.

Allele Child Father Paternity Index Click on the image below to view a typical report. CSF1PO 12, 14 11, 13 Exclusion D3S1358 13, 15 14, 16 Exclusion TH01 6, 10 7, 9.3 Exclusion The Father and Child do not share genetic markers in the following systems, CSF1PO, D3S1358 and THO1. Based on these results, the Father is excluded as the biological father. The probability of paternity is 0%