Opinion ID: 1154894
Heading Depth: 4
Heading Rank: 2

Heading: Calculating the random match probability

Text: Absent laboratory error, a declared match means that only one of the following is true: (1) the samples came from the same individual; (2) the samples came from identical twins; [19] or (3) the samples came from different individuals but, by pure chance, the DNA segments examined match (although comparison of the entire DNA sequence from each individual would not match). It is the probability favoring a random match (the third of these three alternatives) that provides the telling and crucial bottom line of DNA evidence. [20] Cellmark uses the product rule  sometimes called the multiplication rule  to make its random match determination. This rule is described as follows: Suppose, for example, that a pair of DNA [samples] match on two bands, and that one band reflects an allele found in ten percent of the population and the other an allele found in fifty percent of the population. Applying the product rule, an analyst would conclude that the probability of a coincidental match on both alleles is 0.10 X 0.50 = 0.05, or a five percent probability. Thompson & Ford, DNA Typing, 75 Va. L.Rev. at 81-82. [21] The 0.05 result in this example means that there was a one in twenty probability of a random match (leaving a nineteen in twenty chance that the samples came from the same person). The validity, and corresponding accuracy, of the product rule depends on the presence, or absence, of several factors. As applied to this case, the individual frequencies  the necessary components of the product rule (the 0.10 and 0.50 in the example quoted above)  come from, and are based on frequencies in, Cellmark's database. That database apparently bases these frequencies on samples obtained from blood banks as well as paternity and forensic cases. See Pennell, 584 A.2d at 520. These frequency figures  vital components of the product rule  are valid and accurate only if they come from a truly random sample, and the database for the frequency figures must be large enough to be statistically significant. Cauthron, 846 P.2d at 513. [22] The nature of the product rule indicates that any errors, or shortcomings, in the database may have a profound and significant impact on the random match calculations. See Thompson & Ford, DNA Typing, 75 Va.L.Rev. at 81-82. [23] The product rule also is based on the assumption that each band on the autorad represents a DNA segment that is independent of the other bands on the autorad. For this assumption to be valid, the DNA segments tested must be in linkage equilibrium  i.e. the probability of a match on each band is unaffected by the occurrence of a match on any other band. Id. at 81. [24] If this assumption of independence is not correct, the results of the product rule may be incorrect by a substantial margin. [25] A third relevant assumption upon which the product rule is based is a truly random mating population (where mating is random and the gene pool is evenly intermixed). Cauthron, 846 P.2d at 514. Stated very simply, a large, randomly mating population, at least within a generation, is in Hardy-Weinberg equilibrium. See Thompson & Ford, DNA Typing, 75 Va.L.Rev. at 85. As with the other assumptions, if there is no Hardy-Weinberg equilibrium, the product rule results may be incorrect by a substantial margin. See id.