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# Probability of Paternity

Sometimes a likelihood ratio is converted into a probability. This probability is known as the probability of paternity (POP).20 This formula tests the hypothesis that the alleged father is indeed 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), which represents the social evidence.20 Testing labs typically use a value of 0.5 for the PP on the basis that this is a neutral, unbiased value.16

Mathematically, POP = (100) (CPI) (PP) / [(CPI) (PP) + (1 – PP)]19

POP is not widely used in the United States. A more common approach, similar to the frequentist probability of exclusion, is the Random Man Not Excluded (RMNE) statistic. This is the proportion of the population that could contribute all of the obligate alleles and therefore could not be excluded, or would be falsely included.19 A single locus RMNE is calculated by 1-(1-p)2. Combining the RMNE statistics over all loci gives the combined RMNE (CRMNE), which is equivalent to the CPI. The value of the CRMNE is typically small (less than one), and is analogous to 1-CRMNE or exclusionary power (EP). EP represents the probability of excluding a falsely accused man.19

Although the previous terms and statistics are specific to parentage testing, similar methods are used to estimate the relatedness in other situations, such as identification of human remains and missing persons.

Watch a video on paternity indexes presented by Greggory LaBerge.