2 Person Mixture #4

Found UnderwearMajor/minor Mixture

Scenario

• Victim and Accused were both at a party held at a local park

• Victim says Accused raped her behind a bush• Underwear found behind bush submitted• Sperm found• Differential extraction wasn’t great

Scenario

• Subject says he had nothing to do with anything

• But… • He does say that “some girl” masturbated him• So IF his DNA shows up on in a pair of panties

or someone’s lady parts…• Maybe “that girl” didn’t wash her hands

before she used the restroom• (Actual defense theory proffered to me!)

The Egram

The Data Table

V and S

1 2 3 4

25% 25%25%25%1. Both included, but that’s all I can do

2. The minor cannot be interpreted (inconclusive)

3. Not sure how many contributors

4. I can separate major from minor (2 stats)

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Interpretation

• Consistent with 2 people• Major/minor (or close enough – D7)• Some minor alleles >300 – restricted RMP• Some minor alleles <300 – modified RMP• FGA shows only a single allele• Cannot assume anyone or anything as far as

being a contributor

Match to Victim

• All of Victim’s alleles are present• She claims they are her underwear, but they

were found behind the bush…

Match to Suspect

• Let’s skip this step for now• (Don’t consider the references…)• This profile may be missing things• It looks like a more complicated stat may be

coming

Stat method I would use…

1 2 3 4 5

20% 20% 20%20%20%1. CPI2. LR3. 2 person u/mRMP4. 2 person rRMP5. Split into 2 stats,

one for the major, one for the minor

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Stat method

• We can discuss all 5 of those stat options• Some will have more success than others• Some are (much) more complicated than

others

The CPI stat

• If it is a mixture of 2 people, why would you use it? (It’s not indeterminate)

• You cannot use loci with alleles in the Danger Zone (<300 for this data)

• That leaves only 6 loci to use for CPI

The CPI stat

• D8, D7, D2 – are OK• D16 – minor is >300 by a bit but is in stutter

position – better check it• vWA – only 2 alleles, what if minor dropped

out?• FGA – only 1 allele, CPI would only account for

a single homozygote

The RMP stat

• Three options• First the Fast Way

– modified RMP

• Then the Almost As Fast Way– restricted where we can– modified where we can’t restrict

• Then the Slow Way– Major/minor– A stat for each

The Fast Way

• Just open the window and click the “Mixture Frequency”

The Fast Way

• Then open the Frequency Report• This is a modified RMP

– Either Allele, Any– Or restricted RMP

The Fast Way

D8 = “CPI”

D21 = “CPI” +Allele, Any

CSF = “CPI” butsubtract Homozygotes(no need forAllele, Any)

NOTE: “CPI” herejust means “sum ‘emand square ‘em”

The Fast Way

• If you want to really study a locus, just hover over it

• This is CSF• Or hit the “Calculations” tab

The Fast Way

• Every calculation for every locus is this way• If you copy and paste into Excel you can check

the math– Add “=“, change 2 to ^2, and replace []

The Fast Way

• The overall final stat (modified RMP)• 1 in 3.71 Million

The Almost as Fast Way

• The loci where we’re not concerned about drop out we’ll use restricted rather than modified

• Also for any 4 allele loci• Remember, you set the rules here, not the

program

The Egram

Loci We Can Restrict

D8 D7

D16 D2

vWA

FGA**

CSF

THO1

At these loci everything is above 300 or 4 alleles, and I’m conditioning it on 2 contributors

The Almost As Fast Way

• So we’ll switch the following loci to restricted RMP:– CSF– THO1– D8– D7– D16– D2– vWA– FGA (well, maybe 22, Any)

This is very easy: I just tell it to use restricted for the loci I want in from that “Mixture Frequency” window in the Interpretation window

The Almost As Fast Way

• Lot’s more going on here– D8 (1st line) restricted (4 of 6 types) – D21 (2nd line) still mRMP/uRMP (Any)– D7 (3rd line) unrestricted (6 of 6 types – can’t restrict)– CSF (4th line) restricted (2 types) etc…..

The Almost As Fast Way

• The overall final stat– About ½ modified RMP– About ½ restricted RMP– Plus Allele, Any at FGA

• 1 in 6.8 million - about twice what it was

The Slow Way

• We’ll do what we can to come up with a major and a minor profile

• Use the “Popout Calls” feature after hitting “View call report”

• This will give us two new profiles we can name Major and Minor

• Remember the Egram

The Slow Way

• Start with 4 Allele loci• We need to keep track of loci with alleles

<300 rfu• Be ready for the “obligate” function and

Anys for the minor• I didn’t really figure out a way to do power

point slides to show these steps very well• Please bear with me

The Egram

Loci With 4 Alleles

THO1

CSF

The Slow Way

• We’ll start with 4 allele loci• Most information• We can get a “for sure” mixture proportion• CSF and THO1 give us a Major at 83%

The Egram

Loci With >300 rfu Alleles

D8 D7

D16**

D2

vWA

FGA

Loci With <300 rfu Alleles

The Slow Way

• Remind me to look at D16 after I finish splitting into major/minor– Minor allele in stutter position– Is it really >300?– Should we use Alelle, Any to be safe?– We need to find out

The Slow Way

• This is D16 corrected for 50% stutter• Use the “obligate” function• The 11 is 308 rfu, so Allele, Any not needed• Our validation data shows 50% correction is

reasonable

The Slow Way

• D7 is a problem (I kind of figured that)

• Not really Major/minor• Multiple options for Major• Multiple options for minor• We’ll deal with this on the stat page

The Slow Way

• At D7 major is anything with a 12 except the 12, 12– I’ll click in all three alleles into my major profile

• At D7 the minor is anything 8,12– I’ll click in all three alleles into my minor profile

• On the stat page I have to pick the genotypes I want – both Major and minor are rRMP here

The Slow Way

• vWA• 2 Alleles• Two options look OK• Two don’t• Probably not a 16,16 and 17,17

– 50/50 mixture

• Probably not 16,16 minor at 3%– That is 5x less DNA than we’ve been seeing

The Slow Way

• If we throw out the bad 50/50 and 97/3 • Major is 16, 17 and we are given either 16, 17

or 17, 17 for minor• But at smaller loci the minor is <300, so I’ll do

17, Any as minor at vWA (Major is 16,17)

• FGA• I know this locus doesn’t amp well• I’ll punt on this minor• If all other minor alleles were >300, maybe I’d

at least do a 22, Any

The Slow Way

The Slow Way

• Let’s see how we did• We can match the Victim and Suspect

references against what we just interpreted (partially deconvoluted)

The Slow Way

• Match to Victim• Victim matches the Major (Except D7, where

we left 2 choices for Major)

The Slow Way

• Match to Suspect• All alleles of Suspect are included in the minor

profile

The Slow Way

• Match to Suspect (continued)• Some loci were Allele, Any but because the

Suspect has that required allele, it lights up yellow

• D21 just needs 30

The Slow Way

• Match to Suspect (continued)• Some loci required an obligate allele and an

additional specific allele(s), but because the Suspect has that required allele – and the additional allele – it lights up yellow

• D8 needs 13 and a 10 OR 12

The Slow Way

• Calculating the stat for the Major is quick• Just hit the “Mixture” button under

“Frequency Calculations” ribbon• Yes, I know I said mixture and we came up

with a single source profile• Not quite though – remember D7?• The Major could be anything but a

homozygote

The Slow Way

• D7 on the stat page with all three homozygote options

• I realize you can’t read this, but there are 3 types calculated and summed up for the locus

The Slow Way

• Final overall stat for the Major Contributor• 1 in 221 Quintillion

The Slow Way

• Calculating the stat for the Minor is also quick• Just send it to the mixture stat page• This time, we really need the mixture as there

are several loci where we have to consider more than one distinct genotype

• Remember that obligate function?

The Slow Way

• D8 has 3 alleles– 10, 12, and 13– 13 is an obligate– So 10, 13 and 12, 13 and 13, 13 calculated

• D21 has 30, Any

The Slow Way

• D7 is also a problem here (no easy Major/minor)

• But everything except 8, 12 is OK for the minor

The Slow Way

• Final overall stat for minor• Remember, we dropped FGA• 1 in 119 Million

Final Stat Comparison

• Full modified RMP– 1 in 3.71 Million

• Mix and match mod RMP and rest RMP– 1 in 6.8 Million

• Major profile– 1 in 221 Quintillion

• Minor profile– 1 in 119 Million

Another Thought

• Let’s look at D5 and TPOX again• We said 13, Any for D5 (<300)• We said 9, Any for TPOX (<300)• Not stutter, “eyeball” imbalance for Major

Another Thought

• Due to all the “Any’s” and “Allele*’s” (obligates) we didn’t get many loci with P

• But we do have P = 16% for minor

Another Thought

• Although the minor alleles are <300 at these two loci, they’re close enough to 300 that the probability of drop out may be small

• Especially for D5 at 233 rfu• Plus, we admit our 300 rfu threshold is on the

“cautious” side – and we’re not happy about it• Some folks (Dr. Buckleton) would say the

probability of drop out is low so “Any” is not the best approach to use – Continuous LR?

Another Thought

• What does SWGDAM say?3.2. Application of Peak Height Thresholds to Allelic Peaks Amplification of low-level DNA samples may be subject to stochastic effects, where two alleles at a heterozygous locus exhibit considerably different peak heights (i.e., peak height ratio generally <60%) or an allele fails to amplify to a detectable level (i.e., allelic dropout). Stochastic effects within an amplification may affect one or more loci irrespective of allele size. Such low-level samples exhibit peak heights within a given range which is dependent on quantitation system, amplification kit and detection instrumentation. A threshold value can be applied to alert the DNA analyst that all of the DNA typing information may not have been detected for a given sample. This threshold, referred to as a stochastic threshold, is defined as the value above which it is reasonable to assume that allelic dropout has not occurred within a single-source sample. The application of a stochastic threshold to the interpretation of mixtures should take into account the additive effects of potential allele sharing.

Another Thought

• To me that means we don’t automatically have to assume drop out when in the “Danger Zone”

• Especially when I have a great tool to investigate “the additive effects of potential allele sharing”

• So if my math (PHR and P) shows me I see two alleles of the minor, but one is shared by the Major, I can use a restricted RMP (SS maybe?)

Another Thought

• So, D5:• If minor ≈16%, then this says:• Not a homozygote (7%)• A major about 1200 rfu should have good PHR

• And TPOX: (The same as D5)• If minor ≈16%, then this says:• Not a homozygote (8%)• A major about 1000 rfu should have good PHR

Another Thought

Another Thought

• Why would ½ the DNA of the minor just disappear? The “real” chance of drop out is probably pretty low

• If you consider masking, you just found the other ½ of the minor DNA

What about a LR?

• The LR assumes contributors• We set up 2 competing hypotheses• It is essentially one RMP divided by a different

RMP (sort of)• But how do you choose the hypotheses?

What about LR

• Hp says “Victim and this Suspect!”• Would Hd say that “because the panties were

found under the bush it’s 2 unknowns?”• They might, but they shouldn’t

– If V + S alleles are present, the LR is usually impressive enough if Hd is V + U

– If V + S alleles are present, and the Hd is U + U, the LR usually becomes crazy

What about LR

• Can we use LR here?• All alleles of both people are present• But…

– When we did the RMP, we allowed for drop out due to low level alleles

– If we must account for potential drop out in the RMP, why would we not do so for the LR?

What about LR

• Remember, the Hd says “It may be the Victim, but it’s not my client”

• Furthermore, Hd may say “Not only is it not my client, but you may be missing alleles from the REAL bad guy, so your LR calculation is not fair to my client”

What about LR

• So, we have to consider that there may be drop out.

• At vWA we didn’t detect any minor alleles at all, defense says we need to be concerned about 2 alleles dropping out

Which LR model?

• UC model (Unrestrained Combinatorial)– This is the “PopStats” model– Fine if there is no concern about dropout

• F model– F is any allele, including one that’s already

detected– Think of F as missing one “dose” of allele– But no “non-concordance” with the detected

alleles of V and POI/U

Which LR model?

• Q model – Doesn’t directly deal with drop out, but it does

work Θ back in for homozygotes– Allows for dealing with distinct genotypes in a LR

Which LR model?

• The non-concordance model– “The D model”– We can allow for multiple stochastic events– Need to combine with F or Q model for

concordant alleles– Can restrict based on phr models– Can get pretty messy to calculate by hand

D Model

• Can be used with non-concordance– Ex: Locus has 11, 12, 13 alleles– V is 11, 12– POI is 13, 14 – a non-concordance

• This example we’ve been working with doesn’t have non-concordance (except for FGA), but Hd says “The real guy may have dropped out” so we need D model if we’re to do LR

D Model

• vWA• V is 16, 17• POI is 17, 17• Hd says “Yea, but it’s our theory that both

alleles of the REAL bad guy have dropped out”

D Model

• We need to introduce 2 terms– Drop

• The probability that an allele dropped out• You have to determine this, probably related to the

height of the minor alleles that you do see elsewhere

– Not Drop• The probability that an allele did not drop out• (This one is pretty easy, if you see the allele, it didn’t

drop out.)

D

D

D Model

• Hp says both are included– Must account for 16, 17 and 17,17

– But since the 17 is accounted for by V

DDDPOIVV

171716

2)(DV

D Model

• Hd says “OK, V is there….”– So we still have the 16, 17

– But Q is missing from U (if true bad guy only had one allele drop out)

– Or maybe even Q, Q is missing if both bad guys alleles dropped out

2)(DV

D Model

• Hd says “It’s possible he’s there”• So true bad guy could be

– 16, 16 or 16, 17 or 17, 17– Which means you didn’t drop anything from the

bad guy

21716

2 )()( ffDV

D Model

• Hd says “Or one allele dropped”• So we need our “Allele, Any”

– 16, Q

– Or 17, Q

))(1)((2)( 1716172 fffDD

U

Q

V

))(1)((2)( 1716162 fffDD

U

Q

V

D Model

• Hd says “But maybe both dropped out”• In other words, a Q, Q homozygote

– Q, Q

– Or simply

21716

2 ))(1()( ffD DDU

Q

U

Q

V

21716

22 ))(1()()( ffDD UV

D Model

• Think about it without the equations– U could be something we see

– Or something missing one allele

– Or something missing 2 alleles

21716

2 )()( ffDV

))(1)((2)( 17161617

2 fffDDUV

))(1)((2)( 17161716

2 fffDDUV

21716

22 ))(1()()( ffDD UV

++

+

D Model

• Final LR

21716

2 )()( ffDV

))(1)((2)( 17161717

2 fffDDUV

))(1)((2)( 17161716

2 fffDDUV

21716

2 ))(1()( ffDU +

++

2)(DV

2)(DV

D Model

• Final LR

• f16 = .2015

• f17 = .2628

• D = ??

))(1)()((2 1716171816 fffffDU

21716

2 ))(1()( ffDU +

1

21716 )( ff +

For the time being, lets just call it 0.5, maybe it dropped, maybe it didn’t

LR = 1.866

The Egram