Forensic Statistical Tool 

Probabilistic Genotyping: 

The Use of the Forensic 

Statistical Tool (FST) 

Craig O’Connor, PhD. 

Criminalist III/ Assistant Technical Leader, Nuclear DNA Operations 

Department of Forensic Biology 

NYC Office of Chief Medical Examiner 

coconnor@ocme.nyc.gov 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

Why Likelihood Ratio (LR)?

• National Academy of Science Report (*2009) / SWGDAM 

guidelines for interpretation of DNA mixtures 4.1 (2011) 

– Statistic should accompany all positive associations instead of 

qualitative conclusions 

– Can use RMNE (CPI) or LR 

• The DNA commission of the ISFG recommends using the LR 

– More available data is utilized 

– Can incorporate DO/DI rates 

• Statistics for complex and Low Template DNA mixtures 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 

* Strengthening Forensic Science in the United States: A Path 

Forward (2009) The National Academies Press, Washington, DC 
March 19, 2008 

0% 

10% 

20% 

30% 

40% 

50% 

60% 

70% 

80% 

90% 

100% 

Types of Profiles Generated 

Inconclusive 

mixture 

Comparison 

mixture 

Deducible 

mixture 

Non-mixture 
Forensic Statistical Tool 

LRs are Ubiquitous 

Pub Med Searches 

– Over 5,500 published articles on 

LRs in medicine and/or genetics 

– 243 articles with Likelihood ratio 

directly in their title 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

Forensic Applications of LR 

already in use 

• Random match probability (RMP) is a LR 

– RMP: 1 in a trillion 

– LR: sample is one trillion times more likely if suspect is 

the source than if a random person is the source 

• LR is used for kinship calculations 

– DNA View 

– Software used for WTC identifications 

• CODIS Popstats software (FBI) performs mixture 

analysis using LR 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

TWO COMPETING 

SCENARIOS IN FORENSICS 

The suspect is a contributor to a mixture 

OR 

The suspect is not a contributor, and an 

unknown person is the contributor 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

• TrueAllele

– Perlin et al., J Forensic Sci, 2001, 46:1372-1378; Perlin et al., PLoS One, 

2009, 4:e8327; Perlin et al., J Forensic Sci, 2011, 56:1430-1447 

• LoComatioN 

– Curran et al. Forensic Science International, 2005, 148:47-53; Gill et al. 

Forensic Science International, 2007, 166:128-138 

• Forensim 

– Haned, Forensic Science International Genetics, 2011, 5:265-268; Haned et 

al., Forensic Science International: Genetics, 2012, 6:762-774 

• LikeLTD 

– Balding et al., Forensic Science International: Genetics, 2009, 4:1-10 

• Lab Retriever 

– Lohmueller & Rudin, J Forensic Sci, 2013, 58: S243-249 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 

How did you learn about the software? 

Comparisons to other LR software
Forensic Statistical Tool 

Forensic Statistical Tool (FST) 

• Similar LR framework as other programs 

•“Semi-continuous” approach to LR calculations which 

incorporates drop-out and drop-in 

• Differences in methods used to estimate probability of 

drop-out and drop-in 

– Other programs: 

• User-specified rates 

• Probabilistic models 

• Empirical estimates using peak heights 

– FST uses empirical estimates based on the quantity of 

DNA in the sample – in house quant assay 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

FST uses in casework 

• LR statistic applied primarily to 2- and 3- person 

mixtures 

– Comparison sample is positively associated 

– Deconvoluted mixtures where the major/minor 

donor is not consistent with your suspect 

– Non-deconvoluted mixtures 

• Can be used on older cases if needed 

• All interpreting analysts trained 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

Challenges in implementing FST

• Program FST with empirically derived drop-out/ 

drop-in rates 

• Training/testimony 

– Staff 

– Police detectives and Attorneys 

– Judges and juries 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

• Challenge in incorporating drop-out and drop-in rates 

– Dynamic vs static? Simulated vs empirical 

• OCME developed and validated FST using empirical 

drop-out and drop-in rate estimates 

– Drop-out 

• Locus-specific 

• Homozygote or heterozygote genotype 

• Depends on input DNA and approximate mixture ratio 

– Drop-in 

• Most drop-in occurred in -4 stutter position of a true allele 

• Not dependent on locus 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 

Challenges in implementing FST
Forensic Statistical Tool 

Development of FST 

• Modeled after LoComatioN

• Can be used with: 

– Single source samples and mixtures 

– High and low template samples 

• Simultaneously consider data from one, two or three 

amplifications of evidence sample 

• Not an expert system 

• Approved for use with criminal casework samples by the 

New York State Forensic Science Commission, 

December 2010 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

FST Reliably Assigns a Quantitative Value 

to a Comparison of Forensic Samples 

• 400+ samples tested over a range of template 

amounts and mixture ratios 

– Purposeful mixtures from blood and buccal swabs 

– Touched items 

– 2 and 3 person mixtures 

• Many samples were purposefully or naturally 

degraded 

• 500,000+ comparisons with non-contributors 

performed

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

Validation Conclusions 

• LR for true contributors support qualitative 

assessments 

• In some cases, LR is more conservative than 

qualitative assessment 

• LRs showed a good separation between true and 

non-contributors*.

* Due to allele sharing, for some mixtures, chance positive associations 

 were noted, but FST assigned an appropriate weight. 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

Example 1: 

Single Source LR with drop-out / drop-in 

• Single source sample 

– Sp: Suspect; Sd: Unknown, unrelated person 

• The LR is constructed with two additional factors 

considered 

– “If this person is a contributor to the mixture, did any of 

their alleles drop out?”

– “Are there any alleles that are not explained by this set 

of contributors (i.e., drop-in)?”

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

Locus 1 Locus 2 Locus 3 Locus 4 

Evidence 14, 15 29 8 11, 12 

Suspect 14, 15 29 8, 12 11, 12 

• Drop-out and drop-in terms included in 

numerator and denominator 

• Drop-out of suspect’s or unknown person’s 

allele(s) may have occurred

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 

Example 1: 

Single Source LR with drop-out / drop-in 
Forensic Statistical Tool 

• When drop-out is not modeled and profiles match 

– Numerator is 1.0 

– Denominator is RMP 

• When drop-out is modeled 

– Numerator < 1.0 

– Unknown contributor’s allele(s) may have dropped out 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 

Example 1: 

Single Source LR with drop-out / drop-in 
Forensic Statistical Tool 

Example 1 – Locus 3 only 

• Numerator: 

– Suspect is 8, 12; evidence is 8 

– Pr ( Data | Sp ) = Pr (one drop-out from heterozygote) 

 x Pr (no drop-in) 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

Example 1 – Locus 3 only 

• Denominator: 

– Unknown contributor may have genotype: 

• 8, 8

• 8, w (w is any allele other than 8) 

• w, w 

– Find expected population frequency of each genotype 

– Multiply by probability of drop-out and drop-in required to 

obtain evidence profile 

p8

2 x Pr (no homozygote drop-out) x Pr (no drop-in) 

+ 2p8pw x Pr (one heterozygote drop-out) x Pr (no drop-in) 

+ pw

2 x Pr (homozygote drop-out) x Pr (one drop-in) 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

LR with Drop-out / Drop-in

DO and DI rates counted and programmed in FST 

• D0 = no drop-out (heterozygote): 1 – D1 – D2 

• D1 = one drop-out: counted 

• D2 = two drop-outs: counted 

• DH0 = no drop-out (homozygote): 1 – DH1 

• DH1 = drop-out: counted 

• C0 = no drop-in (per locus): 1 – C1 – C2+ 

• C1 = one drop-in allele: counted 

• C2+ = two or more drop-in alleles: counted 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

Example 1 

1 1

2

0 0 8 1 0

2

8

1 0

p D C 2 p p D C p D C

D C LR

H + w + w H

=

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

Example 2 

• Two-person mixture 

• Sp: Suspect and one unknown, unrelated person 

• Sd: Two unknown, unrelated people 

• Consider a single locus with three labeled alleles 

• All possible genotypes for the three unknown 

contributors (one in numerator, two in denominator) 

must be generated 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

• Evidence Sample: 11, 12, 14 

• Suspect Profile: 11, 12 

• Numerator includes one unknown person with 

possible genotypes: 

11, 11 12, 12 14, 14 w, w 

11, 12 12, 14 14, w 

11, 14 12, w 

11, w 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 

Example 2 
Example 2: Numerator 

Evidence: 11, 12, 14; Suspect 11, 12 

Drop-out? Drop-in? 

Unknown Contributor 

Genotype 

Drop-out Required? 

(Type?) 

Drop-in Required? 

(Which allele(s)?) 

11, 11 

11, 12 

11, 14 

11, w* 

12, 12 

12, 14 

12, w* 

14, 14 

14, w* 

w*, w* 

*w is any allele other than 11, 12, 14

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Example 2: Numerator 

Evidence: 11, 12, 14; Suspect 11, 12 

Drop-out? Drop-in? 

Unknown Contributor 

Genotype 

Drop-out Required? 

(Type?) 

Drop-in Required? 

(Which allele(s)?) 

11, 11 No Yes (14) 

11, 12 No Yes (14) 

11, 14 No No 

11, w* Yes (partial heterozygous) Yes (14) 

12, 12 No Yes (14) 

12, 14 No No 

12, w* Yes (partial heterozygous) Yes (14) 

14, 14 No No 

14, w* Yes (partial heterozygous) No 

w*, w* Yes (total homozygous) Yes (14) 

*w is any allele other than 11, 12, 14

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Example 2: Numerator 

Evidence: 11, 12, 14; Suspect 11, 12 

Unknown’s genotype frequency 

Unknown 

Contributor 

Frequency Drop-out? Code Drop-in? Code 

11, 11 No Yes (14) 

11, 12 No Yes (14) 

11, 14 No No 

11, w* Yes Yes (14) 

12, 12 No Yes (14) 

12, 14 No No 

12, w* Yes Yes (14) 

14, 14 No No 

14, w* Yes No 

w*, w* Yes Yes (14) 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Example 2: Numerator 

Evidence: 11, 12, 14; Suspect 11, 12 

Unknown’s genotype frequency 

Unknown 

Contributor 

Frequency Drop-out? Code Drop-in? Code 

11, 11 P11

2 No DH0 Yes (14) C1

11, 12 2P11P12 No D0 Yes (14) C1

11, 14 2P11P14 No D0 No C0

11, w* 2P11Pw Yes D1 Yes (14) C1

12, 12 P12

2 No DH0 Yes (14) C1

12, 14 2P12P14 No D0 No C0

12, w* 2P12Pw Yes D1 Yes (14) C1

14, 14 P14

2 No DH0 No C0

14, w* 2P14Pw Yes D1 No C0

w*, w* Pw

2 Yes DH1 Yes (14) C1

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Example 2: Numerator 

Evidence: 11, 12, 14; Suspect 11, 12 

Unknown 

Contributor 

Frequency Drop-out? Code Drop-in? Code 

11, 11 P11

2 No DH0 Yes (14) C1

11, 12 2P11P12 No D0 Yes (14) C1

11, 14 2P11P14 No D0 No C0

11, w 2P11Pw Yes D1 Yes (14) C1

etc...

...

2 2

2

11 14 0 0 11 1 1

0 1 11 12 0 1

2

11

etc

p p D C p p D C

p D C p p D C

w

H

+ × × + × ×

× × + × ×

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Example 2: Denominator 

Evidence: 11, 12, 14 

U1 Frequency Drop-out U2 Frequency Drop-out Drop-in 

11,11 P11

2 No (DH0) 

11, 11 P11

2 No (DH0) Yes (C2+) 

11, 12 2P11P12 No (D0) Yes (C1) 

etc...

w, w Pw

2 Yes (DH1) Yes (C2+) 

11, 12 2P11P12 No (D0) 

11, 11 P11

2 No (DH0) Yes (C1) 

11, 12 2P11P12 No (D0) Yes (C1) 

etc...

w, w Pw

2 Yes (DH1) Yes (C1) 

etc...

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Example 2: Denominator 

Evidence: 11, 12, 14 

U1 Frequency Drop-out U2 Frequency Drop-out Drop-in 

11,11 P11

2 No (DH0) 

11, 11 P11

2 No (DH0) Yes (C2+) 

11, 12 2P11P12 No (D0) Yes (C1) 

etc...

w, w Pw

2 Yes (DH1) Yes (C2+) 

(

)

2 ( ... ...

...

2

2

11 12 0 11

1 2

2

0 2 11 12 0 1

2

0 11

2

11

p p D p etc

p D C

p D p D C p p D C

w H

H H

+ × ×

+ + × ×

× × × + × ×

+

+

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

Report the lowest value 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved. 
Forensic Statistical Tool 

Thanks and Appreciations 

• NYC Office of Chief Medical 

Examiner Forensic Biology 

Department 

• National Institute of 

Standards and Technology 

©2014 City of New York Office of Chief Medical Examiner. All rights reserved.