Accuracy vs. Probability in Paternity Testing

How can a paternity test be 100% accurate, yet the probability of paternity only be 99.99%?

Paternity Test

Accuracy of DNA testing refers to the quality of the testing procedures used by the laboratory only. It does not mean a guarantee of any given response on paternity results. Dr. Donna Housley, Identigene’s assistant laboratory director, walks us through how it works.

The definition of the word “accurate” in reference to DNA testing means the process being described is free from mistakes, this exemption arising from carefulness; exact conformity to truth, or to a rule or model; exactness; nicety; correctness.

For instance, in paternity testing, according to the genetic systems analyzed, there is 100% accuracy that the calculation of the probability of paternity results is 99.99%. This is based on the accuracy of our genetic testing, sample handling, and reporting procedures, which involve utilizing complex computer systems and accurate data to generate the Combined Paternity Index and Probability of Paternity.

Why will paternity results never result in a 100% probability of paternity?

The probability of paternity is a result of using Bayes’ Theorem. This theorem is based on the prior probability. In a paternity test, we assume in most cases, that the prior probability that the alleged father is the biological father of the child is 50%. That means the calculations are not based on accusations (“He said” vs. “She said”).  This is a standard prior probability to use in the paternity DNA testing industry because we, as a laboratory, have no prior information regarding the case. Therefore both paternity and non-paternity must have equal weight.

The probability statement in a paternity test is calculated based on the Combined Parentage Index (CPI), which is a likelihood ratio that measures the likelihood that the shared alleles (or markers) between the child and the tested man occur because he is the biological father, vs. if a random untested man were the biological father. It is a measure of the strength of the genetic evidence presented on the report. This is described elsewhere in detail.

This CPI in a paternity test is then used to calculate the probability that this man is the actual father of the child by using Bayes’ Theorem, which, as stated above, assumes a prior probability of 50%.

The equation shortens to CPI /(CPI + 1)

Because the denominator is always larger than the numerator, the Probability of Paternity on a paternity test can never reach 100%.

A more mathematical approach:

  • P(A) is the prior probability or marginal probability of A. It is “prior” in the sense that it does not take into account any information about B.
  • P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.
  • P(B|A) is the conditional probability of B given A. It is also called the likelihood.
  • P(B) is the prior or marginal probability of B, and acts as a normalizing constant.

In paternity terms:

P(A|B): The probability that the tested man is the father of the child, given the genetic data (posterior probability). POP (probability of paternity)

P(A): Prior probability that the tested man is the father: equal to 50% or 0.5 (The tested man is the father or he is not: equally weighted) Does not take into account the genetic data.

P(B|A) the likelihood that the data we see is due to the fact that the tested man is the father. (conditional probability)

P(B) the probability that the data we see is from a randomly selected man regardless of any other information

The probability that someone else is the father is also 50% (or 0.5).

POP = P(B|A) * P(A) / P(B)

For a CPI of 1000 to 1

X = 1000

Y = 1

POP = 1000 * (0.5) / 1000 * (0.5) + 1 * (1 – 0.5) = 1000 / (1000 + 1) = 0.999 = 99.90%

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  1. I got a letter saying father name cannot be excluded as father the probability of paternity is 99.99℅ and the prior probability is .5 what’s that mean

    • Hi Cassandra,

      If the results say that he is “not excluded” or cannot be excluded as the father and the probability of paternity is 99.99%, we consider him to be the father. If you have any other questions regarding your test results, our friendly client support team can help. You can reach them at 1-888-404-4363.

  2. My boyfriend tested both my child and another recently born. Our child results came out stronger than the other, but was both determined to be his. How accurate does the test need to be to be considered a positive result?

    • Hello LC,

      IDENTIGENE is a highly accredited labhttp://www.dnatesting.com/dna-laboratory/dna-testing-laboratory-accreditations and implements several controls to ensure the highest level of accuracy and quality in our testing.

      In order for us to give a yes (“not excluded”) or no (“excluded”) to your paternity test, we need to know for a certainty that our answer is accurate. If we are unable to determine the paternity, your test results would come back inconclusive. If you received an answer of “not excluded” or “excluded” it is likely that the probability of paternity is near 100% for “not excluded” and for “excluded” near 0% probability.

      If you would like more detailed information regarding your specific test, you’ll need to contact our friendly client support staff and they would be happy to help you understand how accurate your result is. Their phone number is 1-888-404-4363. Best to you!

  3. My husband dna test for himself and my step son cam back 98%…The child looks nothing like my husband or any of the other children. NOW we are in the state of Texas in which paternity requires 99% probability. He already pays child support and the rest we got was not court admissable test. Would you REtest? (if possibility is there that 98 does NOT prove paternity) Or leave it as is and assume he is the father?

  4. my brother passed away and now there is a child that could be his — can i be tested to determine paternity if it is my deceased brother