The relevance of "matching" DNA: is the window half open or half shut?

• Author: Kaye, D.H.

The basic concepts are always the hardest. This is particularly true in the study of evidence. Relevant evidence is evidence that alte the probability of a fact that matters, and relevant evidence generall is admissible unless it is too prejudicial.(1) Despite this seemingly formulation, questions of relevance relating to DNA evidence - even to the most elementary concept of a "match" between two DNA samples - can be confusing.

Well established methods of molecular biology permit laboratories to compare DNA from a crime scene to DNA from a defendant.(2) If the DNA in these samples is similar, the match usually is powerful evidence that the incriminating DNA came from the defendant. To describe the incriminating effect of the resemblance, scientists may use numbers. The numbers seen most frequently in criminal cases are numbers referred to as the match frequency. These are estimates of the relative frequency of other people whose DNA also would match the crime scene DNA according to the criteria the laboratory uses for declaring a match.(3)

In court, the most successful objection to these numbers has been that the standard computational method does not account adequately for "population structure."(4) Arguments targeting the criteria for de a match have not fared as well.(5) In a recent article on the "DNA War," Professor William C. Thompson sought to correct this situation.(6) Already a veteran of a few skirmishes in the war,(7) Pro Thompson believes that when a defendant argues that "the match criteri should have been drawn in a narrower manner that excludes him," the finding of a match "could properly be excluded under Federal Rule 403."(8) At the very least, he believes that the court should allow expert testimony to the jury that the match criteria are too inc In contrast, I have argued that:

Disputes over the strictness of particular windows or the optimal matc window - when there is no such thing - may confuse and perplex the jury when it considers the probative value of a match. As a result, a has discretion to exclude this testimony.(10)

This Article shows that Professor Thompson's call for exclusion of DNA evidence or for expert testimony on the definition of a match is not responsive to the concern that animates and underlies his propo If anything, a more radical response - rejecting the very notion of a simple "match" - may be in order. To reach these conclusions, Parts I and II describe the basic ideas of "matching" and "binning" that are central to the usual analysis of DNA evidence. Part III outli a theory of probative value that illuminates the limitations of match-binning. With these fundamentals in place, Parts IV and V addres Professor Thompson's concern and demonstrate that, depending on circumstances yet to be established, it could warrant a modification in the way that DNA evidence is presented, though not necessarily the one that Professor Thompson endorses.

The analysis demands a careful definition of probative value and a clear understanding of the matching process and its statistical properties. These can be obtained only in the currency of some mathema notation and concepts. This price, however, is well worth paying. At the most practical level the exercise promises to improve the presentation of DNA evidence. In addition, it illuminates the workings of a theory of probative value and inductive proof that evide scholars have been propounding for some time.(11)

1. Matching

   The most common form of DNA analysis in criminal cases utilizes four or five "single locus VNTR probes" to produce a "multilocus genot or, more simply, a "DNA profile." Technicians use techniques of molecular biology to excise fragments of chromosomes(12) that begin and end with certain sequences of DNA base pairs from samples found in blood, semen, or other material containing sufficient DNA.(13 The beginning and ending sequences are chosen so that the material they bracket tends to vary in size from person to person.

   The lengths of the DNA fragments are measured by seeing how far they move, relative to DNA fragments of known lengths, through a slab of gelatinous material, under the pull of an electric charge. The procedure is known as electrophoresis. In a given time, shorter fragme (with low molecular weight) migrate farther down the electrophoretic gel than longer fragments (with high molecular weight).(14) Fragments of approximately the same size will stop at more or less the same point, coalescing to form a spot or band. By measuring the locati of the bands it is possible to determine the approximate lengths of the fragments.(15) The prevailing method of agarose gel electrophoresi of VNTR fragments is not sensitive enough to distinguish between fragments that are extremely close in size. Measurement error creeps in.

   The likely extent of this measurement error is found through reprodu studies. For example, a laboratory may compare the fragment lengths in DNA obtained from vaginal swabs with that of DNA in blood taken from the same woman.(16) Such studies enable the laboratory to choose a "window" wide enough to be likely to result in match when two samples come from the same source. For instance, studies conducted by the South Carolina Law Enforcement Division DNA laboratory found that corresponding bands never differed by more than [+ or -] 2.82% of their average length.(17) The FBI reports biggest difference observed in its laboratory is less than [+ or -] 2.

   Once a laboratory establishes a numerical matching rule, technicians can compare the crime scene fragment lengths to fragment lengths from a suspect. Suppose that a window of width [+ or -] 2.5% i chosen.(19) If a visual match is declared, and if all pairs of corresponding bands in the two profiles differ by no more than [+ or -] 2.5%, then t profiles are said to match.

   The match window does not have to be any particular size. Big windows are likely to result in the declaration of a match when the DNA samples come from the same person. In this case, the procedure is highly sensitive - it has a large probability of declaring a match When the samples have a common source. Along with a high sensitivity, a suitable window should yield a high specificity. Specificity refers to the probability that the procedure will not declare a match when the samples do not come from the same person. A wide window enhances sensitivity; a narrow window favors specificity. When the sensitivity is high, DNA from the same sources almost always match and there are relatively few false negatives.(20) When the specificity is DNA from different people almost always fail to match and there are few false positives.(21) Thus, statistical reasoning gives the operati characteristics of the matching procedure,(22) but scientific values d not dictate the choice of a unique match window.(23)

   Once a reproducibility study shows that a window has reasonable specificity, the evidentiary analysis should focus on ensuring that th testimony about the match fairly describes the probative value of the laboratory results. Will testimony about the properties of different windows aid in this task? Are there situations where the difficulty of expressing the probative value makes it better to exclude the evidence of a match? To answer these questions, it is necessary to analyze plau ways to express the probative value of the "match." At least three possibilities exist: proportions, similarity likelihood ratios, and match-binning likelihood ratios. Parts II and III describe these measures. Part IV applies them to expose the flaws in Professor Thompson's argum for admitting testimony about the desirability of smaller match windows. Part V describes an alternative approach that may be better tailored to the possible problem.

2. Binning

   The conventional procedure for presenting incriminating DNA evidence in this country entails not just the declaration of a match, but also an estimate of the relative frequency with which other people in some population would match the crime scene DNA. This matching proportion of the population, designated as some number P, plainly has some connection to the probative value of the match.(24) I P approaches 1, then so many innocent people would match that the match proves little; if P approaches zero, then it may prove a great deal.(25)

   It is possible to estimate P from a random sample of people from a suitable reference population. For example, consider a case in which a woman is kidnapped, assaulted, and robbed at a rest stop on an interstate highway by a truck driver who is white,(26) and in which the DNA comparison is limited to a single band.(27) With DNA from a suitable random sample of Caucasians, P could be estimated on the basis of the proportions of bands that fall into predefined intervals molecular weights. Figure 1 shows a hypothetical distribution of band weights over ten intervals, or fixed "bins,"(28) numbered zero through

   The height of each column is proportional to the fraction of bands tha lie within each "bin," which are 12%, 8%, 16%, 8%, 4%, 8%, 20%, 8%, 12%, and 4%, respectively. No bands lie outside the numbered intervals.

   Suppose that the crime scene DNA band is in the center of bin 0 and that the bins are much wider than the match window.(30) Then an estima twelve percent of the bands from the Caucasian population would "match." Under the simplified scenario of examining a randomly chosen single band, P = .12. In this hypothetical case, the prosecutio might offer testimony that the samples match and that such matches would be seen in no more than twelve percent of the Caucasian population.

3. Probative Value

   The best developed and most plausible theory of probative value articulated by legal scholars builds on a statistical concept known as the likelihood ratio, or, more generally, the likelihood function.(31) The idea is elegantly simple and exceedingly powerful. Evidence has probative value with respect to competing hypotheses about the...