The DNA·VIEW® Mixture Solution
#348
ISFG2015
CH Brenner, DNA·VIEW & Human Rights Center, UC Berkeley
90x120
Mixture L as ABCZ+0 unknowns
Maximum likelihood
proportions:
Continuous-model mixture analysis
Mixture Solution™ is a computer program for solving
mixture problems by a “continuous” approach – that
is, the calculation takes into account the significance
of peak height including varying contribution
amounts along with random peak height variation.
• Visual aids – answer “black box” concern.
• Coherent simple model for likelihood
computations
– based mainly on stochastic variation,
incorporates dropout, drop-in, stutter and
allelic stacking naturally and without
additional “moving parts.”
– Robust: not sensitive to exact parameter
values
Stochastic variation (follows gamma distribution)
(typical, 3130) Stochastic Variation Model
expected Peak Height Ratio
PHR
1
0.9
moderate misfit penalty
0.8
0.7
0.6
90th %ile
68th %ile
Median peak height ratio
32nd %ile
10th %ile
0.5
0.4
0.3
0.2
0.1
0
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Expected RFU
Likelihood of observed mixture
case 2015:0095 M 4SL
“Casework model” (of Mixture Solution)
-61
log Likeliho
od
• Multiple potential contributors S, T, U, …
• May be 2-person, may be 3-person … mixture
• Explore automatically all Hp-Hd combinations
-62
Hp=prosecution
hypothesis
Hd=defense
hypothesis
LR=evidence for
Hp vs Hd
Continuous evaluation model
• LR for Hp vs Hd
• Stochastic behavior
• Dropout, dropin, stutter, …
A Abby 27.0% +/O Oscar 41.1% +/unk #1 the rest
-63
-64
-65
0%
8%
pro
%
por 17
tion
fr
om
LR=
• Find best Hp & best Hd, & LR
A
O
reference contributors
log Likelihoo
d
-62
-63
-64
7%
1
por
ti
pro
on f
%
rom 33
AA
2%
4
bby
68%
63% #1
56% unk
50% m
44%
fro
39% tion
r
o
p
ro
p
Prosecution
hypotheses
Computation
seconds
AO
A Abby 32.6% +/unk #1 56.3% +/unk #2 the rest
-65
0%
A&2unk
3 # of
2 unknown
1 contributors
0
0
o
p
o
Likelihood of observed mixture
-61
Best hypotheses to:
defend A
defend O
prosecute
65 seconds total time
10 hypotheses
10
AA
bby
case 2015:0095 M 4SL
• Explores many hypotheses
• Decides appropriate # of unknown
contributors
• Evaluates many different combinations
of references as contributors
• Uses mathematics, not MCMC
20
%
35
pr
Explore & Solve
30
%
27
60% r
50% sca
41% O
31% m O
22% fro
n
% 13% tio
2
r
4
AO&2unk LR=190 vs O
AO&3unk
94
AO&1unk
10
AO&0unk
0
Defense hypotheses
.
A&3unk O&2unk
O&3unk O&1unk A&1unk
225
110
13
0
LR=660 vs A
330
38
0
1000
510
60
0
2E+13
1E+13
1E+12
0
8E+13
4E+13
4E+12
0
Strength of evidence (Likelihood Ratios)
References
Evaluating forensic DNA profiles using peak heights, allowing for multiple donors, allelic dropout and stutters,
Roberto Puch-Solis, Lauren Rodgers, Anjali Mazumder, Susan Pope, Ian Evett, James Curran, David
Balding, Forensic Science International: Genetics 7 (2013) 555–563
Computational aspects of DNA mixture analysis / Exact inference using auxiliary variables in a Bayesian network,
Therese Graversen &Steffen Lauritzen, Stat Comput DOI 10.1007/s11222-014-9451-7