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