Showing posts with label LT-DNA. Show all posts
Showing posts with label LT-DNA. Show all posts

Wednesday, 3 July 2013

Activity vs. Source Level Propositions: It Looks like Raffaele Sollecito's DNA Was on the Bra Clasp, But How Did It Get There?

Was Italian Judge Claudio Pratillo Hellman's refusal to order more DNA testing of a knife in the Knox-Sollecito case "bad judicial math"or a considered judgment that little would be gained by waiting for more tests of low template DNA (as the court-appointed experts advised him)? That was the question addressed in discussions here back in March and May.

Now, an article in the Proceedings of the National Academy of Sciences of the USA reports that a different mixed profile does not seem to reflect Amanda Knox's DNA. Seeking to clarify a New Scientist news report entitled "Software says Amanda Knox's DNA Wasn't at Crime Scene," Professor David Balding, a statistical geneticist at University College London who has made important contributions to the statistical evaluation of forensic DNA profiles, describes this finding on his website as follows:
I do reanalyse a crime scene profile from the murder of Meredith Kercher in Perugia, Italy, in 2009 and find no support for the presence of DNA from Amanda Knox as they say, but the main question for that item was whether there is DNA from Raffaele Sollecito, and my analysis finds strong support for this even allowing for many of the problems with the DNA evidence highlighted at the appeal in 2011.
As the PNAS article makes clear, Dr. Balding used software that he is developing for LT-DNA profiles to evaluate the "five loci from exhibit 165B of the trial in Perugia, Italy, in 2009. The exhibit includes the clasp of a bra, attached to some apparently blood-stained fabric, that was found near the murdered woman, Meredith Kercher."

The prosecution's expert testified at the trial that the profile of the clasp DNA matched all the alleles of the victim and one of Sollecito's. The court's experts (Vecchiotti and Conti) agreed "but also reported many additional epg [electropherogram] peaks. ... Of the 24 additional peaks ... , of which 6 had heights below the threshold of 50 relative fluorescence units, 9 are included in [Knox's] profile ... providing apparent support for the presence of DNA from her. However, four of her alleles were not observed, including two homozygotes, which are less prone to dropout [in such small samples]." In other words, it is hard to know what to make of the data by eyeballing it.

The statistical software (to the extent I understand it) models allelic "drop in" and "drop out" and uses allele frequencies in the population to generate likelihood ratios for the peaks that the analyst regards as the result of true alleles as well as those designated as "uncertain" alleles. In this case, the well established alleles indicated a mixture of DNA from three or more people, and Balding considered two competing hypotheses: (1) the DNA is a mixture from Kercher, Sollecito, and one unknown individual vs. (2) the DNA is from Kercher and two unknown individuals.

He found that the perceived pattern of alleles was 42 million times more probable if Sollecito's DNA was there. As for Knox, however, "separate analysis with her as the queried contributor returned an LR < 1." That is, the designated pattern would arise more often if Knox's DNA were in the mixture than if it were not -- a finding "favoring a conclusion of no DNA from her."

What this means for the case depends on what some forensic scientists call "activity level" hypotheses and what lawyers call "relevance." What activity would cause Sollecito's (but not Knox's) DNA to be detected on the bra clasp (but not on the fabric)? The defense theory, of course, is that neither of them touched the bra, but Sollecito's DNA molecules were transferred there at a later time. The prosecution theory could be that Sollecito (but not Knox) touched the bra during the murder.

Related postings

Thursday, 30 May 2013

People v. Garcia and Low Template DNA (LT-DNA)

Recent postings (March 27, May 25) about the appeal of Amanda Knox and Raffaele Sollecito suggested that the court’s decision not to order more DNA tests on the kitchen knife was less a manifestation of bad judicial mathematics than a judgment about the possible costs and benefits of additional low template (LT-DNA) testing as perceived by court-appointed experts. As a publication of the Royal Statistical Society noted last year, “Many questions at the extremities of LTDNA technology remain unanswered, and scientific disputes between experts are sometimes ventilated in litigation.” (Puch-Solis et al. 2012, at 85 ¶ 60.20, discussing English Court of Appeal cases in ¶¶ 60.21 & 60. 22).

In the United States, appellate courts have yet to address the admission of LT-DNA results. The latest opinion I have seen comes from a trial court in Bronx County, New York. In People v. Garcia, 39 Misc.3d 482, 963 N.Y.S.2d 517 (N.Y. Sup. Ct. 2013), a woman was found suffocated, with a sock in her mouth, and bound, with duct tape binding her face and limbs. Pablo Garcia was charged with her murder and related crimes. A piece of the duct tape contained DNA from at least two individuals. The New York City Office of the Chief Medical Examiner (OCME) reported that the mixture “is 586 times more probable if the sample originated from this defendant and one unknown, unrelated person than if it originated from two unknown, unrelated persons.”

Now, it is easy to see how a murderer applying the tape would leave some DNA on it, but why would there be additional DNA from an “unknown” rather than from the victim? One would think that duct tape used to bind an individual would include that person’s DNA rather than “one unknown, unrelated person.” However, it could be—I am speculating here—that the sample came from duct tape wrapped on top of other duct tape rather than a piece attached directly to the skin. Would the additional DNA profile have come from someone in the factory where the tape was made? From someone besides the murderer who touched its edges after the package had been opened? These are the kinds of possibilities that need to be considered when dealing with extremely small quantities of “contact DNA.”

Hoping to exclude the LT-DNA evidence, Garcia requested a pretrial hearing on whether the OCME’s protocols for typing LT-DNA and computing likelihood ratios were generally accpeted in the relevant scientific community. Judge Nicholas Iacovetta denied the request. He found that Garcia failed to raise much doubt about general acceptance. He wrote that “There is nothing new or novel about LCN DNA profiling. It simply represents the application of accepted and reliable procedures [like PCR and electrophoesis] that are applied in a modified manner.”

This reasoning, which has been used in previous cases, seems far too facile, After all,
PCR-based STR profiling with capillary electrophoreses is generally accepted for the purpose of producing identifying profiles because experiments have demonstrated its validity and it fits into well-established theories of chemistry and biology. It satisfies the validity standard of Daubert for the same reasons. But this foundation might not extend to the domain of the smaller samples. A light microscope works wells for studying bacteria but its magnification is not adequate for viewing much smaller viruses. For that purpose, an electron microscope is required. Radar can track airplanes or flocks of birds, but the signal-to-noise ratio is too low for it to be useful in tracking the flight path of a solitary, high-flying butterfly. The radar equipment is identical, and the operator is no less skilled at interpreting what he sees on the screen, but the procedure has not been validated (and would not be valid) for butterfly tracking.

Likewise, in the case of touch DNA, the relevant question is not whether the instrumentation and chemicals are identical or whether the analysts are using the same standards for interpretation. It is whether the system has been validated in the range in which it is being used. This is not a question about how well a validated or generally accepted procedure worked on a particular occasion ... . It is a ... question about the ability, under the best of conditions, of the equipment and its operators to pick out a weak but true signal from the noise. Until this trans-case question is resolved, admissibility is unjustified under Frye and Daubert.
Kaye, Bernstein and Mnookin (2011, § 9.2.3 at 428).

These observations do not necessarily mean that all forms of LT-DNA profiling--including the OCME's methodology--should be held inadmissible under the general acceptance standard for scientific evidence followed in New York. They simply mean that one must look to suitable experiments published in scientific journals or other places where they would be subject to critical review by other interested scientists, to the testimony or published views of appropriate scientists who have studied the matter, and to other indications of general acceptance.

Judge Iacovetta did some of this scrutiny and concluded “[s]eparately ... that LCN DNA testing conducted by OCME and its [statistical analysis] are both generally accepted as reliable in the forensic scientific community.”

The bases for this separate conclusion, however, are not uniformly compelling. First, the court pointed to “a lengthy Frye hearing” conducted by another trial court that determined “that LCN DNA testing ... when properly performed, ... is generally accepted as reliable in the scientific community.” Before accepting the conclusion of another judge who did conduct an evidentiary hearing, however, a court should ensure that the hearing actually aired the views of a cross-section of the scientific community. Especially in the early days of a scientific technique, imbalanced hearings are not uncommon. For examples in the DNA area, see Kaye (2010).

Second, the Garcia opinion stated that “[o]ther New York trial courts have also admitted LCN DNA results in evidence after denying defense requests for a Frye hearing ... LCN DNA testing has been admitted in New York State trial courts over 125 times, and in a federal district court in the Southern District of New York without a Frye hearing and in courts of multiple other countries including Germany, The United Kingdom, Sweden and Switzerland.” Again, a history of usage—especially without any hearings on the necessary foundational research and with no meaningful appellate review of the trial rulings—is a weak indicator of scientific acceptance.

Third, the court noted that “[a]lthough OCME is the only government facility currently using LCN DNA testing, several private and academic laboratories, such as the University of North Texas, use LCN DNA testing. OCME ... has been certified to conduct LCN DNA testing since 2005, using it to help identify the remains of victims of the World Trade Center terror attack in 2001 ... .” This is better. Usage of a method outside the courtroom, especially in matters that supply feedback on how well the method works, helps establish acceptance. (However, more details demonstrating the equivalence of the other uses to the one in Garcia itself would have been helpful.)

Fourth, the court observes that “OCME's own validation studies of LCN DNA testing ... were examined and certified by the New York State Commission On Forensic Science (NYSCFS) in 2005” and that “OCME is also audited yearly.” Favorable review by outside scientific staff of the commission and an auditing organization of a suitable set of the validity studies (as opposed to audits to show that the laboratory follows its protocols, investigates and corrects problems, and the like) argues in favor of general acceptance.

Finally, in discussing the software the OCME developed to help interpret mixed, partial DNA profiles from small samples, the opinion alludes to "peer reviewed articles in professional journals such as the International Journal of Forensic Genetics." I am not familiar with a journal by this name, and it does not seem to have a web site. Perhaps the court was referring to papers in Forensic Science International: Genetics (Mitchell et al. 2011; Mitchell et al. 2012). See also Caragine et al. (2009). The best evidence of general acceptance of validated technologies is publication in established scientific journals followed (ultimately) by a cessation of debate over the findings.The OCME publications support the laboratory procedures as well as the software for interpreting the data from those procedures.

Focusing on the software (named FST), Garcia states that
Other software programs such as True Allele, Life TD, Forenism, and Locomation, a software tool designed in the 1990's, also use Bayes Theorem to perform functions similar to the FST. The difference is that the FST uses empirically established drop-in and drop-out rates generated by thousands of tests, rather than just estimating them, which makes the FST more accurate as a predictor of likelihood ratios.
At the risk of quibbling (an occupational and personal hazard), these programs do not "predict likelihood ratios." If they predict anything, they predict genotypes, and which program's LRs best express the probative value of the inferred genotypes depends on more than how each program handles drop-in and drop-out probabilities.

To sum up, even if is wrong to regard the application of established technologies to LT-DNA as a trivial variation that requires no further legal scrutiny to establish admissibility, it also appears that one can make a reasonable case for general scientific acceptance of LT-DNA typing as required under New York law. The Garcia opinion shows how one trial judge was convinced.

References

Saturday, 25 May 2013

Bad Math or Passable Law? DNA Testing in the Continuing Prosecution of Amanda Knox and Raffaele Sollecito

In an previous posting, I raised some questions about an op-ed ("Justice Flunks Math") on the judge's refusal to depart from the court-appointed expert's written report in the prosecution of Amanda Knox and Raffaele Sollecito. This week, a flurry of opinionated comments appeared, and I let those that seemed to have at least some analysis or substance through the gate.

In my previous posting, I took issue with the op-ed's assertion that the trial judge "demonstrated a clear mathematical fallacy: assuming that repeating the test could tell us nothing about the reliability of the original results" and its apparent suggestion that retesting the same DNA sample would be comparable to testing a coin for bias by repeatedly tossing it. I argued that "[w]ithout some specification of precisely what made the initial testing problematic and whether those problems could be reduced sufficiently with retesting, it seems precipitous to convict the judge who overturned the guilty verdict of 'bad math.'"

Whatever the merits of the indictment of the judge, my thanks to those who offered information on whether retesting might be significantly more revealing than the initial testing. That is an interesting question in its own right.

In this regard, an author of the op-ed, Professor Leila Schneps kindly explained that the "confirming retest" (the phrase in her op-ed) did not mean a retest of the same sample (like flipping a coin again) but rather an analysis of a "new knife blade sample," a "rich sample ... from the place where the blade joins the handle of the knife." This new sample, she suggests, might be "positive for Meredith Kercher," in which case, "it would have correctly settled two of the questions left outstanding in the courtroom: was the first electropherogram showing the DNA on the knife correctly interpreted as Meredith's, and was Meredith's DNA actually on the knife?"

If we posit that the new sample is large enough to produce unambiguous results, then it could reveal whether "Meredith's DNA [was] actually on the knife." But Professor Schneps also states that the "rich sample" was "significantly lower than the quantity 'advised' by the kit, although the kit's website shows many examples of tests on smaller samples, some even smaller than the knife blade DNA, that gave positive and accurate results."

If the sample is this impoverished, are we not back in the realm of low-template DNA testing, where the worry is that stochastic effects can be dominant? The mathematical argument here seems to be that even though it might not be surprising to spot, by chance alone, some peaks in a new test that also are present in Meredith's genotype, the probability of those peaks plus the ones seen in the original testing of a different sample from the knife would be negligible unless Meredith's DNA was on the knife. In this way, the additional testing overcomes the low signal-to-noise ratio in each sample. That is a fair argument (as far as it goes), and the same logic underlies some protocols for testing contact DNA.

Still, given the difficulties and the level of discord over the best approaches to conducting and interpreting LT-DNA testing (see, e.g., A. Carracedo, P.M. Schneider, J. Butler & M. Prinz, Focus issue—Analysis and Biostatistical Interpretation of Complex and Low Template DNA Samples, Forensic Science International: Genetics 6 (2012) 677–678), and the court's experts' concerns about contamination, I wonder whether even the most mathematically erudite judge would have been so quick to order additional DNA testing in this case. Consequently, I am not yet prepared to give the judge a flunking grade for "a clear mathematical fallacy."

Wednesday, 27 March 2013

Are Two Heads Better than One? Mathematics and the Amanda Knox Case

In yesterday’s New York Times, “Leila Schneps, a mathematician and mystery writer, and her daughter Coralie Colmez” wrote an op-ed entitled “Justice Flunks Math.” They gave this failing grade to an Italian judge who declined to order a second DNA test in the notorious murder case against the American student, Amanda Knox and her Italian boyfriend, Raffaele Sollecito.

If only the judge understood probability theory, they suggest, he might have ruled in favor of the prosecution's request for another DNA test. In their words:
Whatever concerns the judge might have had regarding the reliability of DNA tests, he demonstrated a clear mathematical fallacy: assuming that repeating the test could tell us nothing about the reliability of the original results. In fact, doing a test twice and obtaining the same result would tell us something about the likely accuracy of the first result. Getting the same result after a third test would give yet more credence to the original finding.
This claim of a mathematical fallacy in the judge’s reasoning, however, rests on an important assumption — that the test results are statistically independent (at least in substantial part). To illustrate their point, Schneps and Colmez explain:
Imagine, for example, that you toss a coin and it lands on heads 8 or 9 times out of 10. You might suspect that the coin is biased. Now, suppose you then toss it another 10 times and again get 8 or 9 heads. Wouldn’t that add a lot to your conviction that something’s wrong with the coin? It should.
But consider this example instead:
You test the surface of a gold coin and test it to make sure it is gold. The test is 90% certain to indicate gold when the metal is gold, so following the advice of Schneps and Colmez, you repeat the test three times and strike gold each time. When you try to sell the coin, however, a more astute buyer weighs it and finds that it does not have the density of gold. It is, in fact a thickly gold plated, lead coin.
Which example is more apt in the Knox case? A Nature blog explained that "[v]ery small amounts of Knox’s DNA were found on a knife located at the crime scene 46 days after Kercher’s murder," but this is not correct. The knife came from Sollecito's kitchen, and a more informed account in the New York Times states that "the court-appointed experts concluded that ... Ms. Knox's DNA was in fact on the handle" -- hardly a surprise given that she may have used it to cook dinner in her boyfriend's apartment. The only thing that made the knife incriminating was a police laboratory finding of DNA from the victim, Meredith Kercher, on the blade. But there was evidence that the knife could not have produced all the wounds, and the court-appointed experts were skeptical of the finding about the blade as well the police laboratory's analysis of "a bra clasp that belonged to the victim found on the floor at the scene 46 days after her murder" said to show Sollecito’s DNA.

Returning to Nature's account:
Speaking at the request of the defence, two forensic scientists, Stefano Conti and Carla Vecchiotti from Sapienza University in Rome, said police investigators failed to follow international protocols for collecting and handling evidence and conducting tests on small genetic samples known as low-copy-number (LCN) DNA analysis. For example, officers were not wearing protective masks or hair caps at the crime scene. ... In addition, Conti said police often used plastic bags, rather than paper, to wrap evidence, heightening the risk of contamination. ... “There are various circumstances do not adhere to protocols and procedures,” Conti told the court.

Consequently, the independent experts concluded that they could not rule out the possibility that the knife and bra had been contaminated by other sources of Knox’s and Sollecito’s DNA, such as other evidence at the crime lab where forensic testing was taking place.
If these experts’ concern — that the original DNA test was simply detecting traces of Kercher's and Sollecito’s DNA that investigators inadvertently transferred to the knife and bra clasp, respectively — then repeating the tests could well continue to detect that DNA — and prove nothing more than the original tests did. If the bra clasp sample showed a mixture of DNA from the victim and Sollecito (and nothing else), for example, then repeating it over and over would not reinforce the prosecution case in the slightest. It would be no different than retesting the surface of the lead coin with its gold plated contamination. The inability of the DNA evidence to demonstrate a convincing link to the defendants would remain after even an infinity of new tests.

Consequently, it is hard to judge Schneps' and Colmez's suggestion that "[t]he judge’s rejection of the retest — at least based on the notion that a confirming retest could tell us nothing about the likelihood that the DNA was a match — was a serious error, one that scuppered an opportunity to get at the truth of Ms. Kercher’s murder."

The judge’s decision may have been mathematically sound, or it may have been as naive and fallacious as Schneps and Colmez propose. They have a nice theory but it is fair to assume that there were uncontaminated samples for new testing? Without some specification of precisely what made the initial testing problematic and whether those problems could be reduced sufficiently with retesting, it seems precipitous to convict the judge who overturned the guilty verdict of "bad math."

Indeed, Schneps and Colmez seem to believe that the judge ignorantly opposed retesting of the small sample of DNA on the blade despite an improvement in the technology of testing low template DNA. They wrote that
Even though the identification of the DNA sample with Ms. Kercher seemed clear, there was too little genetic material to obtain a fully reliable result — at least back in 2007. By the time Ms. Knox’s appeal was decided in 2011, however, techniques had advanced sufficiently to make a retest of the knife possible, and the prosecution asked the judge to have one done. But he refused.
Yet, the judge clearly was open to new methods. He asked the two university experts to ascertain "whether it is possible, by means of a new technical analysis, to identify the DNA present on items 165b (bra clasp) and 36 (knife)." The Conti-Vecchiotti Report, Assignment. Finding "no evidence of cellular material in the samples analyzed," however, his experts concluded that "no DNA suitable for further laboratory investigations (amplification, electrophoresis) was present either on the swabs [tamponature] (A-B-C-D-E-F-G-H-I) taken from Exhibit 36 (knife) or on those (L-M) taken from Exhibit 165B (hooks of the bra)." Id. Conclusions (1). They based this conclusion on the absence of cellular material and the failure of "quantification of the extracts ... conducted via Real Time PCR [to] reveal the presence of DNA." Id. Conclusions (2).

The prosecution disagreed. It asked for still more testing. But Judge Claudio Pratillo Hellmann had had enough. Rather than prolong the appeal -- and the imprisonment of the defendants -- still longer to await tests that his experts told him would be useless, he and the jurors returned their not-guilty verdict. It remains to be seen why this verdict now has been overturned, but it is hardly obvious that "bad judicial math" is the reason.

References
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