DNA paternity testing is a scientific method used to establish a biological relationship between an alleged father and a child. This process relies on analyzing short segments of DNA known as Short Tandem Repeats (STRs), which are highly variable regions inherited from each parent. Accredited laboratories compare the specific patterns, or alleles, of these STR markers found in the DNA samples of the individuals involved. The result of this genetic comparison is a statistical measure called the Paternity Index, which requires careful mathematical interpretation to understand the strength of the evidence.
Understanding the Paternity Index
The Paternity Index (PI) is the first statistical value generated during DNA analysis and is calculated individually for each genetic marker (locus) tested. This index is expressed as a likelihood ratio that compares two opposing probabilities to determine the weight of the evidence. The numerator represents the probability that the alleged father passed on the necessary genetic marker to the child.
The denominator represents the probability that a random, unrelated man from the general population could have passed on that identical marker. The PI indicates how many times more likely the tested man is to be the biological father compared to an untested man selected at random. For instance, a PI of 100 for a single locus means the alleged father is 100 times more likely to be the source of that specific allele than a random man.
The PI is heavily influenced by the uniqueness of the alleles observed, as rare alleles contribute a much higher PI than common ones. If the alleged father could not have contributed the necessary allele to the child, the PI for that locus becomes zero, immediately excluding him from paternity. The PI must be calculated for every STR marker analyzed, as each provides an independent piece of statistical evidence.
Creating the Combined Paternity Index
The Combined Paternity Index (CPI) represents the total genetic evidence across all markers analyzed in the test. It is derived directly from the individual Paternity Indices calculated during the initial analysis. To create the CPI, the laboratory multiplies all the individual PI values from every locus tested.
Modern paternity tests typically analyze 16 to 24 separate STR markers to ensure high precision. Because the individual PIs are multiplied rather than added, the final CPI value grows exponentially, becoming an extremely large number. This multiplicative mechanism is based on the principle of statistical independence, meaning the result at one genetic marker does not influence the result at any other.
If a test includes 20 markers, and each contributes a PI of 10, the resulting CPI would be 1 followed by 20 zeros—a number in the quintillions. This massive figure represents the overwhelming statistical support for paternity when all markers match. The CPI is a powerful measure of the overall strength of the genetic match, summarizing the combined weight of evidence from the entire DNA profile.
Translating CPI into the Probability of Paternity
While the CPI is the raw statistical measure used by geneticists, the public typically receives the result as the Probability of Paternity (POP), expressed as a percentage. This percentage is calculated using a conversion formula derived from Bayes’ theorem, which translates the CPI into a more accessible figure. The standard formula used is POP = CPI / (CPI + 1).
This conversion requires the introduction of a “prior probability,” which is the chance that the alleged father is the biological father before any DNA testing. For a neutral, unbiased result, laboratories generally use a prior probability of 0.5, or 50%. This means that before the test, the man had an equal chance of being the father or not. When the CPI is extremely high, the POP rapidly approaches 100%.
For example, a CPI of 99 means the POP is \(99 / (99 + 1)\), or 99.0%, while a CPI of 999,999 translates to a POP of 99.9999%. The percentage can never truly reach 100% because the statistical calculation compares the tested man to a theoretical random man in the population, not to every male in the world. A result of 99.99% indicates that the evidence overwhelmingly supports paternity, making the possibility of a random man matching the profile incredibly remote.
Maximum Reporting Standards
The theoretical maximum Combined Paternity Index is essentially limitless, constrained only by the number of STR markers included in the test and the rarity of the alleles found. Since the CPI is a product of multiple independent indices, increasing the number of loci analyzed or finding rarer alleles results in a mathematically higher CPI. However, laboratories do not report these astronomical numbers to the public.
Instead, accredited laboratories adhere to strict quality assurance and reporting standards set by organizations like the American Association of Blood Banks (AABB). These standards mandate a minimum Probability of Paternity (POP) that must be reported to consider the tested man “not excluded” from paternity. The AABB requires a minimum POP of 99.0%, though certain legal or immigration cases may require a higher threshold, such as 99.5%.
In practice, laboratories establish an upper reporting limit for the POP, regardless of how high the calculated CPI might be. For instance, a lab may report the Probability of Paternity as “greater than 99.9999%” even if the CPI mathematically corresponds to a percentage with more decimal places. This practice ensures the result meets legal and scientific sufficiency standards while preventing the presentation of unnecessarily large, confusing numbers. The “highest combined paternity index” a consumer is likely to see is dictated by established reporting policies rather than the actual statistical maximum.