Continuous models for mixtures

Continuous models for mixtures
Thore Egeland
Copenhagen April 20-23 2015
Continuous models
Norwegian University of Life Sciences
1
http://www.cstl.nist.gov/strbase/training/ISFG2013workshops.htm
Continuous models
Norwegian University of Life Sciences
2
Continuous models
Norwegian University of Life Sciences
3
Binary model
1. Qualitative binary model (aka unrestricted…)
–Treats alleles as present or absent and does not take
into account peak height information
2. Semi-quantitative binary model (aka restricted …)
–Declares some of the combinations as possible or
impossible
Continuous models
Norwegian University of Life Sciences
4
Example
6 genotype combinations
{7/9,11/13},{7/11,9/13},{7/13,9/11}
{11/13,7/9},{9/13,7/11},{9/11,7/13}
Continuous models
Norwegian University of Life Sciences
5
Suspect 7/11
H P : S+NN1, H D : NN1 + NN2
Assume only combinations are 7/11, 9/13
2 p9 p13
1
LR2 =
2 p7 p9 2 p11 p13 + 2 p11 p13 2 p7 p9 4 p7 p11
Ignoring peak information
2 p9 p13
1
=
LR1 =
24 p7 p9 p11 p13 12 p7 p11
LR2 = 3LR1
Continuous models
Norwegian University of Life Sciences
6
Semi continuous models
• Artefacts:
–Drop-out
–Drop-in
–Stutters
Continuous models
Norwegian University of Life Sciences
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Semi-continuous model include a drop-out probability d
Software: LRmixStudio (NFI, Haned,...), ....
Continuous models
Norwegian University of Life Sciences
8
Continuous model
6 genotype combinations
{7/9,11/13},{7/11,9/13},{7/13,9/11}
{11/13,7/9},{9/13,7/11},{9/11,7/13}
weighed according to a
probability distribution
Continuous models
Norwegian University of Life Sciences
9
Suspect 7/11
H P : S+NN1, H D : NN1 + NN2
w2 2 p9 p13
LR =
w1 2 p7 p9 2 p11 p13 + w2 2 p7 p11 2 p9 p13 + ... + w6 2 p9 p11 2 p7 p13
Qualitative binary model: w1= ...= w6= 1
w3 =
w4 =
w6 =
Semi − quantitative binary model: w2 =
1, w6 =
1, w1 =
0
Continuous models
Norwegian University of Life Sciences
10
Computation
LR =
w2 2 p9 p13
w1 2 p7 p9 2 p11 p13 + ... + w6 2 p9 p11 2 p7 p13 + drop − terms
• Hard part: Modelling and estimating weights
w j = Pr(peak heights|known contributors)
 Bayesian networks (Graversen, Cowell, Lauritzen, ...
o DNAmixtures
 MCMC (Taylor, Bright,...)
o STRMIX http://strmix.esr.cri.nz/
 gammadnamix efm.
http://rpackages.ianhowson.com/rforge/gammadnamix/
(Bleka)
Continuous models
Norwegian University of Life Sciences
11
© ESR 2013