Cole v. Cole
328 S.E.2d 446, 74 N.C. App. 247 (1985)

The main issue in this case is whether defendant is the father of Jonathan Derrick Cole. Plaintiff and defendant were married on 19 April 1970. They bore a child on 19 August 1971 and another on 29 September 1975. Defendant had a bilateral vasectomy on 20 February 1976. On 20 May 1976, the physician who performed the vasectomy made a sperm count on a specimen brought in by defendant, and it was negative. Also, a pathology test was performed on the sections of the vasa deferentia removed from defendant, and the tests confirmed that the vasectomy had been successful.

On 10 September 1982 the plaintiff gave birth to a son, Jonathan Derrick Cole. The defendant acknowledged that he was the child's father on the child's birth certificate. In the Spring of 1983 the parties' marriage deteriorated. They separated on 9 July 1983. On 18 August 1983 the plaintiff filed a complaint requesting alimony, temporary alimony, custody of the children, child support and attorney's fees. The defendant filed an answer denying he was the father of Jonathan Derrick Cole.

On 15 September 1983, Dr. John Grimes performed a semen analysis on defendant and determined that he was sterile. Dr. Grimes testified that he believed defendant was sterile during the years 1981-82 and that the likelihood of defendant becoming fertile after his vasectomy was "one in a million and probably less than that now.''

A blood test was performed on defendant, on the child Jonathan Cole, and on plaintiff. The test indicated that the probability of defendant being Jonathan's father was 95.98%, assuming that defendant "was a fertile male at the time of presumed conception. Undisputed evidence to the contrary would drop the probability of paternity to 0%.''

The district judge ruled that the defendant is the biological father of Jonathan Derrick Cole. Defendant appeals this judgement....

[We] are presented with what appears to be a sharp contrast in the medical evidence, between the results of fertility tests done on defendant, and blood tests done on defendant, plaintiff and Jonathan Cole. Because the results of the blood test appear to suggest such a high probability of paternity, we believe it is necessary to discuss how that probability is calculated, and why it should be discounted in cases where there is strong evidence of the father's infertility.

While much progress has been made in the blood tests used in cases of disputed paternity, by expanding the number of antigens examined, the test's greatest value still lies primarily in excluding falsely accused fathers. A "probability of paternity'' can now be calculated for alleged fathers not excluded, and this is admissible on the issue of paternity, but it is not conclusive.

Serious questions have been raised about the validity of the method used to calculate the probability. I. Ellman and D. Kaye, Probabilities and Proof: Can HLA and Blood Group Testing Prove Paternity? 54 N.Y.U.L. Rev. 1131 (1979); Jaffee, Comment on the Judicial Use of HLA Paternity Test Results and Other Statistical Evidence: A Response to Terasaki, 17 J. Fam. L. 457 (1978-79). Critics of the probability of paternity calculation have focused on the assumptions made in the calculations, which greatly limit the usefulness of the probability in certain cases. For example, the calculation generally assumes that all possible fathers are unrelated. If the alleged father and the true father are related, then their HLA and red blood cell antigen profiles are likely to be very similar. Even the strongest proponent of the probability of paternity calculation admits it cannot be used in the case where potential fathers are related. P. Terasaki, Resolution by HLA Testing of 1,000 Paternity Cases Not Excluded by ABO Testing, 16 J. Fam. L. 543, 549 (1977-78).

Further, the calculation assumes that all possible fathers are fertile. In a case like the present, where there is strong evidence that the defendant is not fertile, the calculation, if it does not take into account this information, is likely to overestimate substantially the probability of paternity.

The source of much controversy is the statistical formula generally used to calculate the probability of paternity: the Bayes Theorem. Terasaki, supra at 544. Briefly, the Bayes Theorem shows how new statistical information alters a previously established probability. Ellman and Kaye, supra at 1147-48. When a laboratory uses the Bayes Theorem to calculate a probability of paternity it must first calculate a "prior probability of paternity,'' i.e., a probability that the alleged father is the true father, based on information other than that gotten from the blood test. This prior probability usually has no connection to the case at hand. Sometimes it reflects the previous success of the laboratory at excluding falsely accused fathers. Traditionally, laboratories use the figure 50%, which may or may not be appropriate in a given case. E.G. Reisner and T.A. Bolk, A Layman's Guide to the Use of Blood Group Analysis in Paternity Testing, 20 J. Fam. L. 657, 673-74 (1981-82).

Critics suggest that this prior probability should take into account the circumstances of the particular case. Ellman and Kaye, supra at 1151. For example, if the woman has accused three men of fathering her child, or if there are reasons to doubt her credibility, or if there is evidence that the husband is infertile, as in the present case, then the prior probability should be reduced to less than 50%. Most laboratories, however, do not do this.

The importance of the prior probability to the final probability cannot be overemphasized. The Bayes Theorem calculates a final probability only by applying new statistical information to the prior probability. In paternity cases, where the defendant has not been previously excluded as the father, and where 50% is used as the prior probability, the Bayes Theorem ensures that every alleged father is "probably'' the father, i.e., the blood test results only improve upon the 50% prior probability of paternity.

Thus, the probability of paternity is generally probative, at best, where it is 90%, or as some have suggested, 95%. See Joint AMA-ABA Guidelines: Present Status of Serologic Testing in Problems of Disputed Parentage, 10 Fam. L.Q. 247, 262 (table IV) (1976-77). And this assumes, of course, that potential fathers are not related, and that there is no evidence that the alleged father is infertile. In the present case, then, what appears to be a very high probability of paternity based on blood tests actually indicates that it is "likely'' to "very likely'' that defendant fathered Jonathan Cole. Moreover, if the overwhelming evidence of defendant's infertility is factored in, this apparently high probability drops dramatically. This is why the laboratory test result sheet in the present case contained the proviso that "undisputed evidence'' [of infertility] would drop the possibility to 0%. If the district judge relied on the probability of paternity, despite the evidence of defendant's successful vasectomy, then he erred.

Finally, we deal with the district court judge's finding that after a vasectomy, "each sexual act would give a very small possibility of impregnation.'' Even if this were true, it is apparently based on a statistical generalization about all couples in which the husband has had a vasectomy, and not about the much smaller group of couples in which the husband has had a vasectomy and has had subsequent sperm counts and a pathology test showing complete sterility. Given that the judge has made much more specific findings about the success of defendant's vasectomy, his general finding that "each sexual act would give a very small possibility of impregnation'' is not pertinent to the circumstances of this case and does not support the conclusion that defendant fathered Jonathan Cole.

Thus in light of the district judge's findings that scientific evidence demonstrated that defendant was sterile at the time Jonathan Cole was conceived, and that if defendant was sterile, the blood grouping probability of paternity was reduced to 0%, his conclusion that defendant fathered Jonathan Cole is erroneous. Rather, the judge's findings compel the conclusion that defendant did not father Jonathan Cole.



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