DNA Matters: How to Use the Likelihood Ratio

 DNA Matters: How to Use the Likelihood Ratio

On Oct., 25, 2008, Tamir Thomas was fatally shot in the back of the head at 3 am outside the McKeesport Elks Club. The gunman fled, leaving his Glock pistol and baseball cap under a parked car, before escaping from pursuing police. Ballistics confirmed the recovered handgun was the murder weapon.

DNA mixtures from the gun and the hat pointed to suspect Leland Davis. Two evidence items— the gun and hat—are more persuasive than one. They reinforce each other, separately telling the same story.

Forensic scientists can determine a strength of match. This match statistic summarizes in a single number just how strongly a person is connected to DNA evidence. Many courts require such a statistic before accepting DNA evidence.

The crime lab calculated combined probability of inclusion (CPI) match statistics. This old manual approach overly simplifies DNA data, often giving no answer or an inaccurate number1. Able to use only 8 of 15 data points (and discarding the rest), the lab reported a weak CPI statistic of 1 in 420 for the gun. The hat statistic was much stronger.

As the crime lab testified, their human-limited CPI approach was to “throw the uncertain data out and stick only with things which are certain.” But computers can do more. Smart machines use all the DNA data, instead of throwing data out. They consider all possible genotype explanations, not just a few—and they handle uncertain data.

A genotype is a genetic bar code that is essentially unique for each person. There are a trillion trillion (a 1 followed by 24 zeros) possible genotypes. But, there are under 10 billion (a 1 followed by 10 zeros) people living on Earth. Since there are so many more bar codes than people, genotypes can help identify suspects who left their DNA at crime scenes.

TrueAllele probabilistic genotyping calculates the probability of every genotype in two different ways, answering these questions: Before looking at the DNA evidence, what is the chance of finding a genotype in the human population? And, after examining the data, what is chance of that genotype being in the biological evidence?

A DNA match statistic is the ratio of these two probabilities—the chance of a matching genotype after seeing evidence, divided by the coincidental chance before. This likelihood ratio (LR) tells us how evidence changes the probability of a suspect’s genotype2.

This is the heart of Bayesian reasoning—evidence changes belief. In forensic science, the LR probability change gives the strength of association between evidence items. A big belief change (e.g., a million) shows statistical support in the data for a match. Conversely, a small ratio (e.g., one in a million) means the data don’t indicate a match.

Once TrueAllele has determined probability for all possible genotypes, it can then objectively compare the evidence with any suspect. In this case, the computer found that a match between the handgun and Leland Davis was 18 billion times more probable than coincidence. The big LR number statistically identified Davis, connecting him to the gun.

The defense suggested that perhaps another suspect, Dominick H., had also left his DNA on the gun. If true, that could turn suspicion away from defendant Davis. TrueAllele compared Dominick’s DNA with the handgun’s genotypes. The very small LR number meant no statistical match between his DNA and the gun—an exclusionary result. Dominick’s DNA wasn’t on the gun.

The prosecutor had another concern3. What if someone besides Davis had also left their DNA on both the gun and hat? That unknown person’s presence might then point away from the defendant. Maybe a missing someone pulled the trigger. But you’d need their DNA to make a comparison. Can science prove that no one else was on both evidence items?

Yes. In separating the DNA mixtures, TrueAllele found three probabilistic genotypes on the gun, and three others on the hat. The computer compared the gun genotypes with the hat genotypes, calculating nine match statistics. Only one comparison lit up—at Davis’ DNA. The other eight nonmatching LR statistics showed no one else was on both the gun and hat.

“Based on the genotypes that were inferred and the match statistics between them,” I testified, “there is no indication that any person other than Leland Davis contributed their DNA to both the handgun and the hat.”

Davis was convicted of third-degree murder in the slaying of Thomas. He was sentenced to 20 years in prison.

Forensic evidence helps identify or clear suspects. The modern likelihood ratio quantifies DNA match strength. For 20 years, limited CPI stats gave incomplete results. Today, computerized probabilistic genotyping routinely delivers accurate LR values. Scientists can now answer hard DNA questions, helping justice by using better math and science.

DNA Matters is Forensic's newest column, which will discuss cases that have been aided by the power of computer software in DNA analysis. It is authored by Dr. Mark Perlin, M.D., Ph.D., chief scientist, executive and founder at Cybergenetics. Twenty years ago, Perlin invented TrueAllele probabilistic genotyping for automated human identification from DNA mixtures. His company helped identify victim remains in the World Trade Center disaster, and has helped exonerate 10 innocent men. He is a Scholar in Residence at Duquesne University’s Forensic Science and Law program, and a Fellow of the American Academy of Forensic Sciences. © Mark Perlin 2021

References

1. Perlin, M.W. Inclusion probability for DNA mixtures is a subjective one-sided match statistic unrelated to identification information. Journal of Pathology Informatics, 6(1):59, 2015.

2. Perlin, M.W. Explaining the likelihood ratio in DNA mixture interpretation. Proceedings of Promega's Twenty First International Symposium on Human Identification. San Antonio, TX, 2010.

3. Perlin, M.W. and Schupansky, R.C. TrueAllele® interpretation of Allegheny County DNA mixtures – Murder in McKeesport. Continuing Legal Education, Pittsburgh, PA, 2014.

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