2 Person Mixture #4
Found Underwear
Major/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. 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)
25%
1
25%
25%
2
3
25%
4
0 of 30
30
Countdown
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.
CPI
LR
2 person u/mRMP
2 person rRMP
Split into 2 stats,
one for the major,
one for the minor
20%
1
20%
20%
2
3
20%
4
20%
5
0 of 30
30
Countdown
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” but
subtract Homozygotes
(no need for
Allele, Any)
NOTE: “CPI” here
just means “sum ‘em
and 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
THO1
vWA
FGA**
D16
CSF
D2
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:
This is very easy: I just tell it to use
–
–
–
–
–
–
–
–
CSF
restricted for the loci I want in from
that “Mixture Frequency” window in
THO1
the Interpretation window
D8
D7
D16
D2
vWA
FGA (well, maybe 22, Any)
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
CSF
THO1
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
D7
D8
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)
The Slow Way
•
•
•
•
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
• 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
Another Thought
•
•
•
•
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
• 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
D
• 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
D
• 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 Model
• Hp says both are included
– Must account for 16, 17 and 17,17
V
V
POI
16
17
17
D D D
– But since the 17 is accounted for by V
V 2
(D )
D Model
• Hd says “OK, V is there….”
– So we still have the 16, 17
V 2
(D )
– 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
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
V 2
( D ) ( f16  f17 )
2
D Model
• Hd says “Or one allele dropped”
• So we need our “Allele, Any”
– 16, Q
V 2
U
D
(D )
Q
2( f16 )(1  ( f16  f17 ))
– Or 17, Q
V 2
(D )
U
D
Q
2( f17 )(1  ( f16  f17 ))
D Model
• Hd says “But maybe both dropped out”
• In other words, a Q, Q homozygote
– Q, Q
V 2
(D )
U
U
Q
Q
DD
(1  ( f16  f17 ))
– Or simply
( D ) ( D ) (1  ( f16  f17 ))
V
2
U 2
2
2
D Model
• Think about it without the equations
– U could be something we see
V 2
( D ) ( f16  f17 )
2
+
– Or something missing one allele
V 2
U
D
(D ) D
(D )
V 2
17
U
16
2( f16 )(1  ( f16  f17 ))
2( f17 )(1  ( f16  f17 ))
– Or something missing 2 alleles
( D ) ( D ) (1  ( f16  f17 ))
V
2
U 2
2
+
+
D Model
• Final LR
V 2
(D )
V
( D ) 2 ( f16  f17 ) 2
+
V
( D ) 2 D17 2( f17 )(1  ( f16  f17 ))
U
+
V 2
V
U
U 2
2
( D ) 2 D16 2( f17 )(1  ( f16  f17 )) + ( D ) ( D ) (1  ( f16  f17 ))
D Model
• Final LR
1
( f16  f17 ) + D
2
U
2( f16  f18 )( f17 )(1  ( f16  f17 ))
U 2
2
+ ( D ) (1  ( f16  f17 ))
• f16 = .2015
LR = 1.866
• f17 = .2628
• D = ?? For the time being, lets just call it 0.5,
maybe it dropped, maybe it didn’t
The Egram