GENETIC EVIDENCE IN PATERNITY CASES: WHAT THE LAWYER MUST KNOW ERNEST P. CHIODO, M.D., J.D., M.P.H Genetic testing has been widely used in criminal cases as well as in cases involving establishment of paternity. Every legal practitioner dealing with genetic testing in either a criminal or paternity context should know how this testing can lead to drastically wrong conclusions. The statistical assumptions made during paternity testing can cause the results of testing to be misleading and unreliable. While the focus of this article is on a serious error in statistical methodology frequently occurring in paternity testing, the same error may occur in criminal DNA testing with dire consequences. An attorney practicing criminal or family law needs to understand the statistical assumptions that may cause the results of genetic testing to be misleading and unreliable. This understanding allows the knowledgeable advocate an opportunity to dispute testing results that are commonly and wrongly assumed to be infallible. While this article must by necessity discuss the use of a famous mathematical formula there is no need for the math phobic to fear. The mathematics in this article is limited to the application of a simple formula. In addition there is a great incentive to engage in the minor mental effort needed to understand this article since it provides the thoughtful attorney with an extremely powerful advocacy tool. The central issue is the common error called the "principle of indifference" may cause any genetic testing using Bayes formula to be misleading and unreliable. Thomas Bayes was an 18th century English clergyman 1,2 who devised a formula to give conditional probability. Conditional probability is the probability of an event occurring given the prior occurrence of another event. The following is an example of the use of Bayes formula and conditional probability in paternity testing.3 This example will demonstrate the dangers involving a common assumption concerning the probability of a man's paternity prior to the testing. The example will show that the final test results concerning the probability of a man's paternity are highly dependent upon the assumed prior (pre-test) probability of paternity. In addition it will be shown that the assumptions concerning prior probability commonly made in paternity testing are arbitrary and inconsistent with standard recognized statistical methodology. The implications concerning advocacy in contested paternity cases will be obvious. A man is accused of being the father of a child. He is found to have a genetic marker that only occurs in one percent of the male population. The child is tested and is also found to have the same genetic marker. The mother does not have the genetic marker. It is known that whenever a father has the marker it is always pasted to the child. In this case the man contests paternity. Let: A = The man is the father of the child B = The child has the same genetic marker as the man A' = The man is not the father of the child P(A/B) = The probability that the man is the father of the child given that the child has the same genetic marker as the man. P(B/A) = The probability that the child will have the same genetic marker as the man given that the man is the father. P(B/A') = The probability that the child will have the genetic marker given that the man is not the father. P(A) = The assumed prior probability before testing that the man is the father. P(A') = The assumed prior probability before testing that the man is not the father. Bayes formula is as follows: P(A/B) = [P(B/A)P(A)]/[P(B/ A)P(A)+P(B/A')P(A')] In this case P(B/A) is 1 since there is a 100 percent probability that the child will get the genetic marker if the man is the father*. P(B/A') is 0.01 since the child has the same probability of having the genetic marker as the general population (one percent) if the man is not the father. The reader will now recognize that only P(A) and P(A') need to be identified before plugging the values into Bayes formula. P(A') is simply 1 - P(A)**. Therefore, all that remains is to identify P(A). Remember, P(A) is the assumed probability prior to testing that the man is the father of the child. In paternity testing this is often assumed to be fifty percent (0.5). This assumption is made since there is a controversy concerning the paternity. The mother of the child claims that the man is the father. The man claims that he is not the father. A prior (pre-test) probability of fifty percent is assumed as a default value for P(A). If the above values are entered into Bayes formula the following result occurs: P(A/B) = [(1)(0.5)]/[(1)(0.5) + (0.01)(0.5)] = 0.9901 Therefore there is a greater than 99 percent probability of paternity when using a prior (pre-test) probability of fifty percent (P(A) = 0.5). The Joint AMA-ABA Guidelines 4,5 for likelihood of Paternity are as follows: Test Probability Interpretation less than 80 not useful 80-90 undecided 90-95 likely 95-99 very likely 99.1-99.75 extremely likely 99.80-99.90 practically proven In the State of Michigan paternity is presumed when the DNA profile determination determines a probability of paternity of 99 percent or higher.4,5 It should also be noted that in Michigan blood tests for paternity are generally admissible in evidence at trial.5 Consequently, the man in the above example would be presumed under Michigan law to be the father of the child. However, the results will change dramatically if a lower prior (pre-test) probability of paternity is used. Instead of a fifty-percent prior (pre-test) probability of paternity assume that P(A) is 0.001. This change to a low prior probability drastically changes the results of Bayes formula. P(A/B) = [(1)(0.001)]/[(1)(0.001) + (0.01)(0.999)] = 0.091 The change in the prior probability results in only a slightly greater than nine percent probability of paternity. This would not result in a presumption of paternity and would in most cases be viewed as strong evidence against paternity. The drastic change in probabilities that occur with a change in prior (pre-test) probability highlights a serious error in statistical methodology known as the "principle of indifference."3 The principle of indifference is the error of assuming equality when the actual probability of paternity is not known. The mother claims that the man is the father. The man denies paternity. Since it is not known who is telling the truth a fifty-fifty split on the prior (pre-test) probability is made. However, this assumption about the prior (pre-test) probability P(A) may cause a highly misleading result as the above example illustrates. It is well known by statisticians that the principle of indifference is a serious methodological error. If there is no knowledge concerning the prior (pre-test) probability it is better to make no assumptions rather than to assume a 50-50 chance based upon ignorance. Such an error leads to an assumption of a high probability that is transformed by the mathematics to an even higher probability.3 A man who is able to present credible evidence that he never previously met a woman should not be assigned a prior (pre-test) probability of fifty percent of being the father of her child. A fifty-percent prior (pre-test) probability is arbitrary value set at an unreasonably high level. Conversely, if a woman is able to produce credible evidence that she was alone with a man in an isolated location during the time period of conception may be entitled to a prior (pre-test) probability of greater than fifty-percent. This is needed since an inappropriately low prior (pre-test) probability can result in a misleadingly low test result. In both of the above cases the application of the principle of indifference can lead to misleading results with tragic consequences. In conclusion, genetic testing is seriously flawed when improper assumptions of prior probability of culpability are made. In the arena of paternity testing this has the great potential of assigning paternity to wrongly accused men. It also has the equally tragic potential of wrongly refuting paternity. In the arena of criminal law the same errors concerning assumptions about prior probability present the great risk of loss of life and liberty. The skillful legal advocate must know the potential of abuse of genetic testing and be prepared to expose the abuse when it occurs. Endnotes * In probability mathematics a 100 percent probability is 1. A 50 percent probability is 0.5. ** P(A') is the opposite of P(A). P(A') is equal to one minus P(A) since in probability mathematics the sum of all the possibilities is one. 1. Borowsi EJ, Borwein JM. The Harper Collins Dictionary of Mathematics. Copyright 1991. Harper Collins Publishers. New York, New York. Page 47. 2. Freund JE. Introduction to Probability. Copyright 1973. Dover Publications, Inc. Mineola, New York. Page 159. 3. Isaac R. The Pleasures of Probability. Copyright 1995. Springer-Verlag New York, Inc. New York, New York. Pages 39-40. 4. Hummel. Joint AMA-ABA Guidelines: Present Status of Serologic Testing in Problems of Disputed Parentage, 10 Fam LQ 247 (1976). 5. Kilmer JB. "Paternity and Surrogate Parenting Agreements ." Michigan Family Law 4th Edition. Edited by Curtis JA. Bassett S. Collins LM. Copyright 1993. The Institute of Continuing Legal Education. Ann Arbor, Michigan. § 17-14 and § 17.15. Ernest P. Chiodo, M.D., J.D., M.P.H. is a physician and an attorney licensed to practice medicine and law in the State of Michigan. Dr. Chiodo received his medical and law degrees from Wayne State University and his public health degree from Harvard University. He is board certified in the specialties of internal medicine, occupational and environmental medicine, and in public health and general preventive medicine. Prior to entering private practice he served as the Medical Director of the Detroit Health Department. His medical practice includes evaluation of difficult cases for determination of causation of disease. His legal practice focuses upon the cross-examinations of technician experts.