Computational aspects of DNA mixture analysis

Graversen, Therese; Lauritzen, Steffen

doi:10.1007/s11222-014-9451-7

Cited by 24 publications

(37 citation statements)

References 17 publications

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“…We ignore the possibility that

H_{a}

might have tiny stutter contributions

H_{a + 2}^{normals}, H_{a + 3}^{normals}, \dots

from peaks at a +2, a +3,…. Including this is straightforward in principle, but it has strong effects on the complexity of computations (Graversen and Lauritzen, ). The new peak height

H_{a}

is also gamma distributed as

H_{a} \sim Γ false{italicρ D_{a} (ϕ, ξ, n), italicη false}

where now

D_{a} false(italicϕ, italicξ, boldn false) = false(1 - italicξ false) . 8 p t B_{a} false(italicϕ, boldn false) + ξ . 8 p t B_{a + 1} false(italicϕ, boldn false)

are the effective allele counts after stutter .…”

Section: A Gamma Model With Artefactsmentioning

confidence: 99%

“…For a given hypothesis

scriptH

, the full likelihood is obtained by summing over all possible combinations of genotypes n with probabilities

P (n | H)

associated with the hypothesis to give

L false(scriptH false) = Pr false(E false| scriptH false) = \sum_{boldn} . 35 p t L false(italicρ, italicξ, italicϕ, italicη false| boldz, boldn false) . 2 p t P false(boldn false| scriptH false) .

The number of terms in this sum is huge for a hypothesis which involves several unknown contributors to the mixture, but they can be calculated by Bayesian network techniques (Graversen and Lauritzen, ); some details are given in Section .…”

Section: A Gamma Model With Artefactsmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of Forensic DNA Mixtures with Artefacts

Cowell

Graversen

Lauritzen

et al. 2014

Journal of the Royal Statistical Society Series C: Applied Statistics

108

144

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DNA is now routinely used in criminal investigations and court cases, although DNA samples taken at crime scenes are of varying quality and therefore present challenging problems for their interpretation. We present a statistical model for the quantitative peak information obtained from an electropherogram of a forensic DNA sample and illustrate its potential use for the analysis of criminal cases. In contrast with most previously used methods, we directly model the peak height information and incorporate important artefacts that are associated with the production of the electropherogram. Our model has a number of unknown parameters, and we show that these can be estimated by the method of maximum likelihood in the presence of multiple unknown individuals contributing to the sample, and their approximate standard errors calculated; the computations exploit a Bayesian network representation of the model. A case example from a UK trial, as reported in the literature, is used to illustrate the efficacy and use of the model, both in finding likelihood ratios to quantify the strength of evidence, and in the deconvolution of mixtures for finding likely profiles of the individuals contributing to the sample. Our model is readily extended to simultaneous analysis of more than one mixture as illustrated in a case example. We show that the combination of evidence from several samples may give an evidential strength which is close to that of a single-source trace and thus modelling of peak height information provides a potentially very efficient mixture analysis.

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“…We ignore the possibility that

H_{a}

might have tiny stutter contributions

H_{a + 2}^{normals}, H_{a + 3}^{normals}, \dots

from peaks at a +2, a +3,…. Including this is straightforward in principle, but it has strong effects on the complexity of computations (Graversen and Lauritzen, ). The new peak height

H_{a}

is also gamma distributed as

H_{a} \sim Γ false{italicρ D_{a} (ϕ, ξ, n), italicη false}

where now

D_{a} false(italicϕ, italicξ, boldn false) = false(1 - italicξ false) . 8 p t B_{a} false(italicϕ, boldn false) + ξ . 8 p t B_{a + 1} false(italicϕ, boldn false)

are the effective allele counts after stutter .…”

Section: A Gamma Model With Artefactsmentioning

confidence: 99%

“…For a given hypothesis

scriptH

, the full likelihood is obtained by summing over all possible combinations of genotypes n with probabilities

P (n | H)

associated with the hypothesis to give

L false(scriptH false) = Pr false(E false| scriptH false) = \sum_{boldn} . 35 p t L false(italicρ, italicξ, italicϕ, italicη false| boldz, boldn false) . 2 p t P false(boldn false| scriptH false) .

Section: A Gamma Model With Artefactsmentioning

confidence: 99%

Analysis of Forensic DNA Mixtures with Artefacts

Cowell

Graversen

Lauritzen

et al. 2014

Journal of the Royal Statistical Society Series C: Applied Statistics

108

144

View full text Add to dashboard Cite

show abstract

“…The computation of likelihood ratios (LRs) for complex forensic DNA evidence has progressed in recent years from using only presence/absence of alleles inferred from an electropherogram (epg), (Gill et al, 2000(Gill et al, , 2008(Gill et al, , 2012Balding and Buckleton, 2009;Balding, 2013) to the use of quantitative peak heights (Perlin et al, 2011;Bright et al, 2013b;Puch-Solis et al, 2013;Graversen and Lauritzen, 2014;Cowell et al, 2015;Bleka et al, 2016). The LR approach to evaluating weight of evidence has long been preferred for standard DNA profiles (Gill et al, 2006(Gill et al, , 2012, and for complex profiles there appears to be no realistic alternative.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of low-template DNA profiles using peak heights

Steele

Greenhalgh

Balding

2016

Statistical Applications in Genetics and Molecular Biology

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In recent years statistical models for the analysis of complex (low-template and/or mixed) DNA profiles have moved from using only presence/absence information about allelic peaks in an electropherogram, to quantitative use of peak heights. This is challenging because peak heights are very variable and affected by a number of factors. We present a new peak-height model with important novel features, including over- and double-stutter, and a new approach to dropin. Our model is incorporated in open-source R code likeLTD. We apply it to 108 laboratory-generated crime-scene profiles and demonstrate techniques of model validation that are novel in the field. We use the results to explore the benefits of modeling peak heights, finding that it is not always advantageous, and to assess the merits of pre-extraction replication. We also introduce an approximation that can reduce computational complexity when there are multiple low-level contributors who are not of interest to the investigation, and we present a simple approximate adjustment for linkage between loci, making it possible to accommodate linkage when evaluating complex DNA profiles.

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“…Other continuous models are considered in Cowell et al [4], Cowell et al [5] and Puch-Solis et al [13]. DNAmixtures adapts the "HUGIN Expert System" [10] to efficiently compute the likelihood function using a probabilistic expert system [9]. In order to eliminate unknown parameters, DNAmixtures maximizes the likelihood function using numerical restricted optimization routines.…”

Section: Introductionmentioning

confidence: 99%

EuroForMix: An open source software based on a continuous model to evaluate STR DNA profiles from a mixture of contributors with artefacts

Bleka

Storvik

Gill

2016

Forensic Science International: Genetics

199

146

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We have released a software named EuroForMix to analyze STR DNA profiles in a user-friendly graphical user interface. The software implements a model to explain the allelic peak height on a continuous scale in order to carry out weight-of-evidence calculations for profiles which could be from a mixture of contributors. Through a properly parameterized model we are able to do inference on mixture proportions, the peak height properties, stutter proportion and degradation. In addition, EuroForMix includes models for allele drop-out, allele drop-in and sub-population structure. EuroForMix supports two inference approaches for likelihood ratio calculations. The first approach uses maximum likelihood estimation of the unknown parameters. The second approach is Bayesian based which requires prior distributions to be specified for the parameters involved. The user may specify any number of known and unknown contributors in the model, however we find that there is a practical computing time limit which restricts the model to a maximum of four unknown contributors. EuroForMix is the first freely open source, continuous model (accommodating peak height, stutter, drop-in, drop-out, population substructure and degradation), to be reported in the literature. It therefore serves an important purpose to act as an unrestricted platform to compare different solutions that are available. The implementation of the continuous model used in the software showed close to identical results to the R-package DNAmixtures, which requires a HUGIN Expert license to be used. An additional feature in EuroForMix is the ability for the user to adapt the Bayesian inference framework by incorporating their own prior information.

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Computational aspects of DNA mixture analysis

Cited by 24 publications

References 17 publications

Analysis of Forensic DNA Mixtures with Artefacts

Analysis of Forensic DNA Mixtures with Artefacts

Evaluation of low-template DNA profiles using peak heights

EuroForMix: An open source software based on a continuous model to evaluate STR DNA profiles from a mixture of contributors with artefacts

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