Solving the problem of mixed DNA profiles

Forensic Bioinformatics (www.bioforensics.com)

Dan E. Krane, Wright State University

Courtroom Knowledge of Forensic Technology and the Impact on Frye and Daubert Standards

Wednesday, August 10, 2016

DNA profile

Comparing electropherograms

Evidence sample Suspect #1’s reference

EXCLUDE

Comparing electropherograms

Evidence sample Suspect #2’s reference

CANNOT EXCLUDE

What weight should be given to DNA evidence?

Statistics do not lie.But, you have to pay close attention to the questions they are addressing.What is the chance that a randomly chosen, unrelated individual from a given population would have the same DNA profile observed in a sample?

Single source statistics:

Random Match Probability (RMP)

Single source samples

Formulae for RMNE:

At a locus:Heterozygotes:Homozygotes:

Multiply across all loci

p2

Statistical estimates: the product rule

2pq 2pq 2pq 2pq

2pq 2pq 2pq 2pq

2pq 2pq

2pq 2pq

2pqp2 p2

p2

x x x x

x x x x

x x x x

x

x

0.1454 x 0.1097 x 2

Statistical estimate: Single source sample

3.2% 6.0% 4.6% 1.2%

9.8% 9.5% 6.3% 2.2% 1.0%

2.9% 5.1% 29.9% 4.0%

1.1% 6.6%

X X X X

XXXXX

X X X X

X

Statistical estimate: Single source sample

1 in 608,961,665,956,361,000,000

1 in 608 quintillion(“less than one in one billion”)

= 0.0320.1454 0.1097 2x x

What weight should be given to DNA evidence?

Statistics do not lie.But, you have to pay close attention to the questions they are addressing.What is the chance that a randomly chosen, unrelated individual from a given population would have the same DNA profile observed in a sample?

Mixture statistics:

Combined Probability of Inclusion (CPI)

Mixed DNA samples

Put two people’s names into a mixture.

How many names can you take out of this two-person mixture?

How many names can you take out of this two-person mixture?

CPI statistics

• Probability that a random, unrelated person could be included as a possible contributor to a mixed profile

• For a mixed profile with the alleles 14, 16, 17, 18; contributors could have any of 10 genotypes:

14, 14 14, 16 14, 17 14, 18 16, 16 16, 17 16, 18

17, 17 17, 18 18, 18

Probability works out as:

CPI = (p[14] + p[16] + p[17] + p[18])2

(0.102 + 0.202 + 0.263 + 0.222)2 = 0.621

Combined Probability of InclusionCPI statistics

Mixed DNA samples

Mixtures with drop out

• Probability that a random, unrelated person could be included as a possible contributor to a mixed profile

• For a mixed profile with the alleles 14, 16, 17, 18; contributors could have any of 10 genotypes:

14, 14 14, 16 14, 17 14, 18 16, 16 16, 17 16, 18

17, 17 17, 18 18, 18

Probability works out as:

CPI = (p[14] + p[16] + p[17] + p[18])2

(0.102 + 0.202 + 0.263 + 0.222)2 = 0.621

Combined Probability of Inclusion

CPI statistics without dropout

The testing lab’s conclusions

Ignoring loci with “missing” alleles

• Some laboratories assert that this is a “conservative” approach

• Ignores potentially exculpatory information

• “It fails to acknowledge that choosing the omitted loci is suspect-centric and therefore prejudicial against the suspect.”– Gill, et al. “DNA commission of the International Society

of Forensic Genetics: Recommendations on the interpretation of mixtures.” FSI. 2006.

LCN statistics

•No generally accepted method for attaching weight to mixed samples with an unknown number of contributors where dropout may have occurred.

•No stats = not admissible.

– More challenging evidence samples• Touch DNA• Guns, steering wheels, doorknobs, etc.

– Resulting DNA profiles often:• Small amounts of DNA• Complex mixtures (3 or more persons)• Degradation (differential degradation)• Minor components in major/minor

mixtures– Stochastic effects!

– Existing test kits were not designed to test these kinds of samples

– Existing statistical methods used in the US are poorly suited to reporting these kinds of samples

Why has this become an issue?

30

Applied Biosystems AmpFlSTR® Identifiler® Plus User Guide pg 17

The stochastic threshold

• The amount of template DNA where random factors influence test results as much as the actual template.– Exaggerated peak height imbalance– Exaggerated stutter– Allelic drop-in– Allelic drop-out

• Sampling error is at the heart of it all

Allele Drop In

1ng

8pg

STR Kit Amplification with conventional SOP and with LCN protocol

Data from Debbie Hobson (FBI) – LCN Workshop AAFS 2003Input DNA

SOP

LCN

Allele Drop Out

50 µL PCR

5 µL PCR

Peak Height Imbalance

PHR = 87%

PHR = 50%

Equal Mixture of DNA from two persons: Person A: 9, 13 Person B: 21, 24

Amplification 1

Amplification 2

Amplification 3

Amplification 4

Amplify same sample 4 times with insufficient DNA

But ambiguities can arise…Evidence

Do these profiles match?

Likelihood ratios (LRs)– Compares two alternative hypothesis

• “Prosecution” explanation Hp (or H1)• “Defense” explanation Hd (or H2)

– The likelihood ratio is better able to deal with to continuous data• Enables scientist model stochastic effects and

complex mixtures• Complicated – need computer program

– Track record:• Widely used in UK, Europe, Australia & New

Zealand• Not much in US (other than Paternity Index)

Likelihood ratio =Pr(E|Hd)Pr(E|Hp)

DNA evidence is:A mixture of two

persons consisting of victim and defendant

DNA evidence is:A mixture of two

persons consisting of victim and an

unknown person

1,000,000+ <0.000001

1

100,000

10,000

1,000

100 10 0.1 0.01

0.001

0.0001

0.00001

Defense explanation of the DNA

“VERY STRONG”

Support for PROSECUTION

explanation

Likelihood Ratio: Drawbacks

• Choice of hypotheses can be challenging:– Prosecution Hypothesis (Hp) is usually easy

(based on specific allegation)– Defense Hypothesis (Hd) may be more difficult

to anticipate• Can do multiple pairs of hypotheses• In mixtures need to specify number of

contributors– Can have different numbers of contributors in

Hp and Hd• Always look at the hypotheses carefully to check

they accurately represent the facts of the case

Why do we need probabilistic genotyping?

Existing statistical methods used in the US are poorly suited to reporting these kinds of

samples

– More challenging evidence samples• Touch DNA• Guns, steering wheels, doorknobs, etc.

– Resulting DNA profiles often:• Small amounts of DNA• Complex mixtures (3 or more persons)• Degradation (differential degradation)• Minor components in major/minor

mixtures– Stochastic effects!

Software Models

Lab Retriever (Rudin et.al.)LRmix Studio (Haned et.al.)Forensic Statistical Tool (OCME NY)LikeLTD (Balding)

SEMI-CONTINUOUS

MODELS

Do NOT take peak height into

account

CONTINUOUS MODELS

Take peak height into account

ArmedXpert (Niche Vision)

DNA View (Brenner)

STRMix (Buckleton et.al.)

TrueAllele (Perlin)

So, what do most of these programs do (… in plain language)? Part I

• Run DNA test (as usual) – resulting in e-data• Analyze electronic data with GeneMapper ID (as usual)• Review electropherograms (as usual)• Interpret (as usual)

– Decide on MATCHES, EXCLUSIONS and INCONCLUSIVES

USUALLY AT THIS STAGE ANALYST WOULD USE POPSTATS TO CALCULATE STATS AND THEN WRITE REPORT

• Consider the LR hypotheses you may want to use– Victim present?– Number of contributors?

• Return to GeneMapper and prepare a special tabular export of the allele calls (including peak heights) for the evidence sample and refs. that you want to compare– Remove artifacts and rare alleles– May or may not include stutter peaks– May drop analytical threshold to a lower level to capture more peaks

• Import tabular data into Probabilistic Software• Frame LR Hypotheses, for example:

– HP = VICTIM plus DEFENDANT plus ONE UNKNOWN PERSON– Hd = VICTIM plus TWO UNKNOWN PERSONS

• Set drop-out estimate– Methods differ in how this is done– May be based on the data– May be flat estimate

• Set drop-in estimate– Usually use flat estimate

• Set up additional variables– Depends of software program

• Run program!• Review output• Program will give a numerical value indicating the Likelihood Ratio

– If above 1, supports prosecution hypothesis– If below 1, supports defense hypothesis– Inconclusive range around 1

So, what do most of these programs do (… in plain language)? Part II

• Run DNA test (as usual) – resulting in e-data• Analyze electronic data with GeneMapper ID (as usual)• Review electropherograms (as usual)• Interpret (as usual)

– Decide on MATCHES, EXCLUSIONS and INCONCLUSIVES

USUALLY AT THIS STAGE ANALYST WOULD USE POPSTATS TO CALCULATE STATS AND THEN WRITE REPORT

• Consider the LR hypotheses you may want to use– Victim present?– Number of contributors?

• Return to GeneMapper and prepare a special tabular export of the allele calls (including peak heights) for the evidence sample and refs. that you want to compare– Remove artifacts and rare alleles– May or may not include stutter peaks– May drop analytical threshold to a lower level to capture more peaks

TrueAllele DOES THE REST

(and most of the other page as well)

This is true for most of the programs, but TrueAllele is different

TrueAllele

– Continuous approach• Models peak heights• Uses MCMC

– Imports raw electronic data– Uses its own smoothing (not GeneMapper)

• Perlin says it is “equivalent” to ABI’s data in terms of peak heights

• But peak heights are not the same– TrueAllele performs all the analysis of the data

• Including the GeneMapper analysis usually done by the lab analyst

– TrueAllele is intended to replace the analyst• Interpret the data• Make the “matches”• Calculate the statistics

TrueAllele

– Models 100s of variables:• Some are known, such as degradation and relative amounts of

DNA:• The vast majority have not been described

– Uses a very low analytical threshold (10 RFU)

– Unlike STRMix and other approaches, TrueAllele does not need a lab or test kit-specific variance factor

– The program is able to take into account such things as:• Stutter (plus and minus)• Biochemical and electrical artifacts• Type of test (Identifiler, Profiler etc.)• Type of instrument (3130, 3500)• What else?

TrueAllele

– Proponents say that validation studies show that it ”gets the right answers”:

• Known mixtures rarely have LRs for known non-contributors that are greater than those for known contributors

• Several peer-reviewed papers outline general approach

– Detractors worry about the black box and failure to define limitations:

• At least a dozen hotly debated questions must have been resolved to generate a reliable result

• Software engineering concerns/right to confrontation• Validation studies do find known non-contributors with positive

LRs• No clear features of samples for which TrueAllele is known to

not generate reliable results

Solving the problem of mixed DNA profiles

Forensic Bioinformatics (www.bioforensics.com)

Dan E. Krane, Wright State University

Courtroom Knowledge of Forensic Technology and the Impact on Frye and Daubert Standards

Wednesday, August 10, 2016