Familial searches and cold hit statistics

Forensic Bioinformatics (www.bioforensics.com)

Dan KraneWright State University, Dayton, OH 45435

Familial search

• Database search yields a close but imperfect DNA match

• Can suggest a relative is the true perpetrator

• Great Britain performs them routinely

• Reluctance to perform them in US since 1992 NRC report

• Neither the current or next generation of CODIS software performs effective searches

Relatedness does make a difference

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

2 4 6 8 10 12 14 16 18 20 22 24

Number of pairwise shared alleles

Percent of total (%)

Randomized Individuals

Simulated Cousins

Simulated Siblings

Dr. Fred Bieber (leading proponent of searches)

“We’ve been doing familial searches for years. The difference between investigating identical twins and other siblings is just a matter of degree.”

Three strategies for familial searches

• Search for rare alleles (inefficient)

• Count matching alleles (arbitrary)

• Likelihood ratios with kinship analyses

Example

• 2003 North Carolina performed post-conviction DNA testing on evidence from a 1984 rape and murder

• Darryl Hunt (who had served 18 years of a life sentence) was exonerated

• Database search yielded best match to Anthony Brown with 16/26 alleles

• Brother Willard Brown tested and found to be a perfect match

Thresholds for similarity

• United Kingdom: being among those who match at the most alleles

• Virginia: “be very, very close”*

• California: “appear useful”*

• Florida: match at least 21 out of 26 alleles

• North Carolina: 16 out of 26 is enough

* As quoted in a front page story in USA Today (by Richard Willing, Suspects get snared by a relative’s DNA, 6/7/2005). Virginia has since stated that they do not and never have done familial searches. California has said that they did not do them but have just adopted a policy to allow them now.

Bieber et al.’s Monte Carlo simulations

• 50% of the time, a sibling has the best match in a database of 50,000

• 80% of the time, a sibling is in the top 10 matches

• Investigating the relatives of people in the top 10 could increase cold hit rate from 10% to 14%

• 30,000 cold-hits in the U.S. as of 2006 could have been 33,000

Bieber, Brenner and Lazer. 2006. Finding criminals through DNA of their relatives. Science. 312:1315-1316.

Is 16/26 close enough?

• How many pairs of randomly generated individuals match at 16+ alleles with unrelated databases of size…

• 1,000: 562 pairs of individuals

• 5,000: 13,872 pairs of individuals

• 10,000: 52,982 pairs of individuals

• Arizona DPS found 144 pairs of individuals matching at 9 or more loci in a database of 65,493 individuals

Approximate likelihood of finding a matching pair of DNA profiles in a database of unrelated individuals

Database Size

1 in10 billion

1 in 100 billion

1 in 1 trillion

1000 1 in 20,000 1 in 200,000 1 in 2 million

10,000 1 in 200 1 in 2000 1 in 20,000

100,000 1 in 2.5 1 in 20 1 in 200

1,000,000 1 in 1 1 in 1 1 in 2.5

Profile frequency

The birthday paradox

• The chance of a single, randomly chosen person having the same birthday as mine is approximately 1 in 365

• But, in a group of 23 or more people there is at least a 50% chance that two will share the same birthday

• The number of pairwise comparisons is equal to N x (N-1)/2

• Not an issue for an individual search, but how many searches are being performed?

Three strategies for familial searches

• Search for rare alleles (inefficient)

• Count matching alleles (arbitrary)

• Likelihood ratios with kinship analyses

Is the true DNA match a sibling or a random individual?

• Given a closely matching profile, who is more likely to match, a sibling or a randomly chosen, unrelated individual?

• Use a likelihood ratio

€

LR =P E | relative( )

P(E | random)

⎪⎪⎪⎩⎪⎪⎪⎨⎧ =⋅⋅+++ =⋅⋅+ =⋅⋅= 2,41 1,4 0,4)|( sharedifHFPPPP sharedifHFPPP sharedifHFPPsibEP baba babba

1

Probabilities of siblings matching at 0, 1 or 2 alleles

• Weir and NRC I only present probabilities that siblings match perfectly.

HF = 1 for homozygous loci and 2 for heterozygous loci

Probabilities of parent/child matching at 0, 1 or 2 alleles

• Weir and NRC I only present probabilities that parent/child match perfectly.

⎪⎪⎪⎩⎪⎪⎪⎨⎧ =+ === 2,2 1,2 0,0)/|( sharedifPP sharedifPsharedifchildparentEP bab

1

Other familial relationships

Cousins:

€

P(E | cousins) =

6⋅Pa ⋅Pb ⋅HF8

, if shared = 0

Pb + 6⋅Pa ⋅Pb ⋅HF8

, if shared = 1

Pa + Pb + 6⋅Pa ⋅Pb ⋅HF8

, if shared = 2

⎧

⎨

⎪ ⎪ ⎪

⎩

⎪ ⎪ ⎪

€

P(E | GG /AUNN /HS) =

2⋅Pa ⋅Pb ⋅HF4

, if shared = 0

Pb + 2⋅Pa ⋅Pb ⋅HF4

, if shared = 1

Pa + Pb + 2⋅Pa ⋅Pb ⋅HF4

, if shared = 2

⎧

⎨

⎪ ⎪ ⎪

⎩

⎪ ⎪ ⎪

Grandparent-grandchild; aunt/uncle-nephew-neice;half-sibings:

HF = 1 for homozygous loci and 2 for heterozygous loci

Two types of errors

• False positives (Type I): an initial suspect’s family is investigated even though an unrelated individual is the actual source of the evidence sample.

• False negatives (Type II): an initial suspect’s family is not be investigated even though a relative really is the source of the evidence sample.

• A wide net (low LR threshold) catches more criminals but comes at the cost of more fruitless investigations.

Paoletti, D., Doom, T., Raymer, M. and Krane, D. 2006. Assessing the implications for close relatives in the event of similar but non-matching DNA profiles. Jurimetrics, 46:161-175.

Hypothesis testing using an LR threshold (and prior odds) of 1

True state Evidence from

unrelated individual Evidence from sibling

Evidence from unrelated individual

~ 98% [Correct decision]

~4% [Type II error; false negative]

Decision

Evidence from sibling

~ 2% [Type I error; false positive]

~ 96% [Correct decision]

Type I and II errors with prior odds of 1

0%

10%

20%

30%

40%

50%

60%

70%

0.0001 0.001 0.01 0.1 1 10 100 1000 10000

Sibling false positive

Sibling false negative

Type I and II errors with prior odds of 1 and non-cognate allele frequencies

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

0.0001 0.001 0.01 0.1 1 10 100 1000 10000

AA sibling false positive

AA sibling false negative

Sibling false positive

Sibling false negative

Problem(s) with familial searches

Likelihood ratio

Chan

ce o

f err

or

use of non-cognate database

alternative suspect pool size

false positivefalse negative

What statistical weight should be given to a “familial hit”?

• Probable Cause Case– Suspect is first

identified by non-DNA evidence

– DNA evidence is used to corroborate traditional police investigation

• Cold Hit Case– Suspect is first

identified by search of DNA database

– Traditional police work is no longer focus

Surveying the three (or four) proposed statistics for cold hits

• NRC I : 1992 National Research Council Report

• NRC II: 1996 National Research Council Report

• Bayesian (aka Balding and Donnelly): Widespread in UK and Western Europe

• DAB: 2000 DNA Advisory Board to FBI

The Problem: Ascertainment bias

• First three approaches differ in how they take into account ascertainment bias. – Ascertainment bias is a statistical

effect of fact suspect first identified by search of a database

– How must RMP be modified

Dr. Fred Bieber (leading proponent of searches)

• Familial searches create “a new category of people . . . under lifetime genetic surveillance.”

• “It’s composition would reflect existing demographic disparities in the criminal justice system.”

• “Familial searches potentially amplify these existing disparities.”

Bieber, Brenner and Lazer. 2006. Finding criminals through DNA of their relatives. Science. 312:1315-1316.

Possible solutions to familial search problems

• Limit the size of the alternative suspect pool (e.g. by pre-screening with Y-STRs; investigator-initiated searches)

• Diminish the effect of incorrect allele frequency databases (e.g. with a ceiling principle approach)

• Use alleles not in common between the suspect and his relative to generate random match probability

• Limit demographic disparities (e.g. investigator-initiated searches)

Resources

• Internet– Forensic Bioinformatics Website: http://www.bioforensics.com/

• Scientists– Jason Gilder (Forensic Bioinformatics)– Fred Bieber (Harvard University)– Sandy Zabel (Northwestern University)– Larry Mueller (UC, Irvine)– Keith Inman (Forensic Analytical, Hayward, CA)

• Publications– Paoletti, D., Doom, T., Raymer, M. and Krane, D. 2006. Assessing

the implications for close relatives in the event of similar but non-matching DNA profiles. Jurimetrics, 46:161-175.

– Bieber, F., Brenner, C. and Lazer, D. 2006. Finding criminals through DNA of their relatives. Science 312:1315-1316.

– Rudin, N. and Inman, K. 2002. An introduction to forensic DNA analysis. New York, 2nd edition.

“Recommendation 4.4: If the possible contributors of the evidence

sample include relatives of the suspect, DNA profiles of those

relatives should be obtained. If these profiles cannot be obtained,

the probability of finding the evidence profile in those relatives

should be calculated.”

NRC II, 1996