Estimation of population specific values of theta for sequence-based STR profiles.

We describe the estimation of θ (theta) values from autosomal STR sequencing data for five metapopulations. The data were compiled from 20 publications and included 39 datasets comprising a total of 7005 samples. The estimates are suitable for use within the calculation of match probabilities in forensic casework. We also have constructed a phylogenetic tree using this data that aligns with our understanding of human evolution.

A comparison of likelihood ratios with and without assuming relatedness for DNA mixtures interpreted using a continuous model.

When evaluating support for the contribution of a person of interest (POI) to a mixed DNA sample, it is generally assumed that the mixture contributors are unrelated to the POI and to each other. In practice, there may be situations where this assumption is violated, for instance if two mixture contributors are siblings. The effect on the likelihood ratio of (in)correctly assuming relatedness between mixture contributors has previously been investigated using simulation studies based on simplified models ignoring peak heights. We revisit this problem using a simulation study that applies peak height models both in the simulation and mixture interpretation part of the study. Specifically, we sample sets of mixtures comprising both related and unrelated contributors and evaluate support for the contribution of the mixture donors as well as unrelated persons with and without incorporating an assumption of relatedness. The results show, consistent with earlier studies, that including a correct assumption of relatedness increases the capacity of the probabilistic genotyping system to distinguish between mixture donors and unrelated persons. Any effect of the relatedness is found to depend strongly on the mixture ratio. We further show that the results do not change materially when a sub-population correction is applied. Finally, we suggest and discuss a likelihood ratio approach that considers relatedness between mixture contributors using a prior probability.

Extending the discrete Laplace method: incorporating multi-copy loci, partial repeats and null alleles.

The discrete Laplace method can be used to estimate the frequency of a Y-chromosomal STR haplotype using a random sample from the population. Two limitations of the method are the assumptions that each profile has exactly one allele at every locus and that this allele has an integer repeat number. We relax these assumptions to allow for multi-copy loci, partial repeats and null alleles. We show how the parameters to the extension of the model can be estimated by numerical optimisation using an off-the-shelf solver. Concordance with the discrete Laplace method is obtained when the data satisfy the more stringent assumptions of the original method. We also investigate the performance of the (extended) discrete Laplace method when used to assign match probabilities for haplotypes. A simulation study shows that as more loci are used, match probabilities are underestimated more severely. This is consistent with the hypothesis that the discrete Laplace method cannot model the matches that arise by being identical by descent (IBD). As the number of loci increases the fraction of matches that are IBD increases. Simulation provides support that the discrete Laplace can model those matches that arise from identity by state (IBS) only.

Addressing uncertain assumptions in DNA evidence evaluation.

Evidential value of DNA mixtures is typically expressed by a likelihood ratio. However, selecting appropriate propositions can be contentious, because assumptions may need to be made around, for example, the contribution of a complainant's profile, or relatedness between contributors. A choice made one way or another disregards any uncertainty that may be present about such an assumption. To address this, a complex proposition that considers multiple sub-propositions with different assumptions may be more appropriate. While the use of complex propositions has been advocated in the literature, the uptake in casework has been limited. We provide a mathematical framework for evaluating DNA evidence given complex propositions and discuss its implementation in the DBLR™ software. The software simultaneously handles multiple mixed samples, reference profiles and relationships as described by a pedigree, which unlocks a variety of applications. We provide several examples to illustrate how complex propositions can efficiently evaluate DNA evidence. The addition of this feature to DBLR™ provides a tool to approach the long-accepted, but often impractical suggestion that propositions should be exhaustive within a case context.

Carrying out common DNA donor analysis using DBLR™ on two or five-cell mini-mixture subsamples for improved discrimination power in complex DNA mixtures.

Probabilistic genotyping systems are able to analyse complex mixed DNA profiles and show good power to discriminate contributors from non-contributors. However, the abilities of the statistical analyses are still unavoidably bound by the quality of information being analysed. If a profile has a high number of contributors, or a contributor that is present in trace amounts, then the amount of information about those individuals in the DNA profile is limited. Recent work has shown the ability to gain better resolution of the genotypes of contributors to complex profiles using cell subsampling. This is the process of taking many sets of a limited number of cells and individually profiling each set. These 'mini-mixtures' can provide greater information about the genotypes of underlying contributors. In our work we take the resulting profiles from multiple subsamplings of complex DNA profiles in equal amounts and show how testing for, and then assuming, a common DNA donor can further improve the ability to resolve the genotypes of contributors. Using direct cell sub-sampling and statistical analysis software DBLR™, we were able to recover single source profiles of uploadable quality from five out of the six contributors of an equally proportioned mixture. Through the analysis of mixtures in this work we provide a template for carrying out common donor analysis for maximum effect.

Developmental validation of STRmix™ NGS, a probabilistic genotyping tool for the interpretation of autosomal STRs from forensic profiles generated using NGS.

We describe the developmental validation of the probabilistic genotyping software - STRmix™ NGS - developed for the interpretation of forensic DNA profiles containing autosomal STRs generated using next generation sequencing (NGS) also known as massively parallel sequencing (MPS) technologies. Developmental validation was carried out in accordance with the Scientific Working Group on DNA Analysis Methods (SWGDAM) Guidelines for the Validation of Probabilistic Genotyping Systems and the International Society for Forensic Genetics (ISFG) recommendations and included sensitivity and specificity testing, accuracy, precision, and the interpretation of case-types samples. The results of developmental validation demonstrate the appropriateness of the software for the interpretation of profiles developed using NGS technology.

The number of alleles in DNA mixtures with related contributors.

The maximum allele count (MAC) across loci and the total allele count (TAC) are often used to gauge the number of contributors to a DNA mixture. Computational strategies that predict the total number of alleles in a mixture arising from a certain number of contributors of a given population have been developed. Previous work considered the restricted case where all of the contributors to a mixture are unrelated. We relax this assumption and allow mixture contributors to be related according to a pedigree. We introduce an efficient computational strategy. This strategy based on first determining a probability distribution on the number of independent alleles per locus, and then conditioning on this distribution to compute a distribution of the number of distinct alleles per locus. The distribution of the number of independent alleles per locus is obtained by leveraging the Identical by Descent (IBD) pattern distribution which can be computed from the pedigree. We explain how allelic dropout and a subpopulation correction can be accounted for in the calculations.

A tool for simulating single source and mixed DNA profiles.

Simulation studies play an important role in the study of probabilistic genotyping systems, as a low cost and fast alternative to in vitro studies. With ongoing calls for further study of the behaviour of probabilistic genotyping systems, there is a continuous need for such studies. In most cases, researchers use simplified models, for example ignoring complexities such as peak height variability due to lack of availability of advanced tools. We fill this void and describe a tool that can simulate DNA profiles in silico for the validation and investigation of probabilistic genotyping software. Contributor genotypes are simulated by randomly sampling alleles from selected allele frequencies. Some or all contributors may be related to a pedigree and the genotypes of non-founders are obtained by random gene dropping. The number of contributors per profile, and ranges for parameters such as DNA template amount and degradation parameters can be configured. Peak height variability is modelled using a lognormal distribution or a gamma distribution. Profile behaviour of simulated profiles is shown to be broadly similar to laboratory generated profiles though the latter shows more variation. Simulation studies do not remove the need for experimental data. The tool has been made available as an R-package named simDNAmixtures.

Evaluating DNA Mixtures with Contributors from Different Populations Using Probabilistic Genotyping.

It is common practice to evaluate DNA profiling evidence with likelihood ratios using allele frequency estimates from a relevant population. When multiple populations may be relevant, a choice has to be made. For two-person mixtures without dropout, it has been reported that conservative estimates can be obtained by using the Person of Interest's population with a θ value of 3%. More accurate estimates can be obtained by explicitly modelling different populations. One option is to present a minimum likelihood ratio across populations; another is to present a stratified likelihood ratio that incorporates a weighted average of likelihoods across multiple populations. For high template single source profiles, any difference between the methods is immaterial as far as conclusions are concerned. We revisit this issue in the context of potentially low-level and mixed samples where the contributors may originate from different populations and study likelihood ratio behaviour. We first present a method for evaluating DNA profiling evidence using probabilistic genotyping when the contributors may originate from different ethnic groups. In this method, likelihoods are weighted across a prior distribution that assigns sample donors to ethnic groups. The prior distribution can be constrained such that all sample donors are from the same ethnic group, or all permutations can be considered. A simulation study is used to determine the effect of either assumption on the likelihood ratio. The likelihood ratios are also compared to the minimum likelihood ratio across populations. We demonstrate that the common practise of taking a minimum likelihood ratio across populations is not always conservative when FST=0. Population stratification methods may also be non-conservative in some cases. When FST>0 is used in the likelihood ratio calculations, as is recommended, all compared approaches become conservative on average to varying degrees.

Exploring likelihood ratios assigned for siblings of the true mixture contributor as an alternate contributor.

Relatives tend to have more DNA in common than unrelated people. The closer the biological relationship, the higher the chance of alleles being identical by descent between the individuals. Therefore, when considering a mixed DNA profile, close relatives of the true contributor may not always be excluded as a possible contributor to a mixture due to allele sharing. In these situations, it might be more appropriate under the alternate proposition to consider that the DNA could have originated from a relative of the person of interest rather than an unrelated individual. The probabilistic genotyping software STRmix™ automatically provides LRs considering close biological relatives as alternate sources of the DNA. In this paper, we investigate the support for siblings of the true contributor to a mixture (who are not present in the mixture themselves). We interpret the mixtures and assign LRs using STRmix™ and investigate whether the resulting LRs could be used to indicate whether the true contributor could be a sibling of the POI. Most siblings will have one or more alleles that are not observed in the mixture profile. Support for siblings to have contributed can only occur when allelic dropout is a possibility at the loci where the siblings have alleles that are not observed in the profile. In these data, that was only observed in components with assigned template of 588 rfu or less.

Evaluating DNA evidence possibly involving multiple (mixed) samples, common donors and related contributors.

Forensic DNA profiling is used in various circumstances to evaluate support for two competing propositions with the assignment of a likelihood ratio. Many software implementations exist that tackle a range of inference problems spanning identification and relationship testing. We propose a flexible likelihood ratio framework that caters to inference problems in forensic genetics. The framework allows for investigation of the degree of support for the contribution of multiple persons to multiple samples allowing for persons to be related according to a pedigree, including inbred relationships. We explain how a number of routine as well as more complex problems can be treated within this framework.

Estimating the number of contributors to a DNA profile using decision trees.

The interpretation of DNA profiles typically starts with an assessment of the number of contributors. In the last two decades, several methods have been proposed to assist with this assessment. We describe a relatively simple method using decision trees, that is fast to run and fully transparent to a forensic analyst. We use mixtures from the publicly available PROVEDIt dataset to demonstrate the performance of the method. We show that the performance of the method crucially depends on the performance of filters for stutter and other artefacts. We compare the performance of the decision tree method with other published methods for the same dataset.

Combining evidence across multiple mixed DNA profiles for improved resolution of a donor when a common contributor can be assumed.

In casework there are often multiple mixed DNA profiles with a single unknown offender who is believed to be a contributor. Sometimes none of these profiles are individually informative enough to evaluate whether a person of interest (PoI) is a contributor. We propose a method that combines evidence across multiple mixtures to better resolve the genotype of a queried common donor. This method can also resolve genotypes of a queried non-common donor (i.e. unique to one profile), when other donors of that mixture have contributed to multiple samples. The approach has similarities with the analysis of replicate PCRs, with the difference being that we do not necessarily assume that all the contributors are the same across the evidential profiles, nor do we assume that parameters such as the mixture ratio are constant. Our method can be used to compute an LR for a PoI being the common contributor to multiple stains. It is also possible to interrogate a database of reference profiles to search for the queried donor (common or non-common). We show that the method can identify a queried contributor in cases where individual comparisons have limited capacity to discriminate between donors and non-donors, when some assumption(s) can be made about multiple contributors being from the same sources (queried or not).

Are low LRs reliable?

To answer the question "Are low likelihood ratios reliable?" requires both a definition of reliable and then a test of whether low likelihood ratios (LRs) meet that definition. We offer, from a purely statistical standpoint, that reliability can be determined by assessing whether the rate of inclusionary support for non-donors over many cases is not larger than expected from the LR value. Thus, it is not the magnitude of the LR alone that determines reliability. Turing's rule is used to inform the expected rate of non-donor inclusionary support, where the rate of non-donor inclusionary support is at most the reciprocal of the LR, i.e. Pr(LR > x|Ha) ≤1/x. There are parallel concerns about whether the value of the evidence can be communicated. We do not discuss that in depth here although it is an important consideration to be addressed with training. In this paper, we use a mixture of real and simulated data to show that the rate of non-donor inclusionary support for these data is significantly lower than the upper bound given by Turing's rule. We take this as strong evidence that low LRs are reliable.

Exploring the probative value of mixed DNA profiles.

Probabilistic genotyping typically proceeds by first deconvoluting a mixture into separate components and then computing a likelihood ratio for a potential contributor. The typical range of likelihood ratios for contributors and unrelated profiles depends, to a large extent, on how well the mixture is resolved. This in turn depends on the quality and complexity of the sample. Some samples are highly discriminatory while others are likely to yield only inconclusive results. Knowing the power of discrimination is helpful when deciding on whether or not to proceed with investigating a case or to do potential rework and for deciding on database inclusion. We present a method for exploring the range of likelihood ratios expected under a proposition of choice. We describe the results of several case scenarios exploring questions such as: 'Is the profile's minor contributor likely to yield a large likelihood ratio?', 'Is it feasible to find a donor among a large database of unrelated profiles?', or 'What is the probability that a brother of a true donor yields a large likelihood ratio?'. We demonstrate the efficiency and speed of the method for a number of examples.

The efficacy of DNA mixture to mixture matching.

Standard practice in forensic science is to compare a person of interest's (POI) reference DNA profile with an evidence DNA profile and calculate a likelihood ratio that considers propositions including and excluding the POI as a DNA donor. A method has recently been published that provides the ability to compare two evidence profiles (of any number of contributors and of any level of resolution) comparing propositions that consider the profiles either have a common contributor, or do not have any common contributors. Using this method, forensic analysts can provide intelligence to law enforcement by linking crime scenes when no suspects may be available. The method could also be used as a quality assurance measure to identify potential sample to sample contamination. In this work we analyse a number of constructed mixtures, ranging from two to five contributors, and with known numbers of common contributors, in order to investigate the performance of using likelihood ratios for mixture to mixture comparisons. Our findings demonstrate the ability to identify common donors in DNA mixtures with the power of discrimination depending largely on the least informative mixture of the pair being considered. The ability to match mixtures to mixtures may provide intelligence information to investigators by identifying possible links between cases which otherwise may not have been considered connected.

Inter-sample contamination detection using mixture deconvolution comparison.

A recent publication has provided the ability to compare two mixed DNA profiles and consider their probability of occurrence if they do, compared to if they do not, have a common contributor. This ability has applications to both quality assurance (to test for sample to sample contamination) and for intelligence gathering purposes (did the same unknown offender donate DNA to multiple samples). We use a mixture to mixture comparison tool to investigate the prevalence of sample to sample contamination that could occur from two laboratory mechanisms, one during DNA extraction and one during electrophoresis. By carrying out pairwise comparisons of all samples (deconvoluted using probabilistic genotyping software STRmix™) within extraction or run batches we identify any potential common DNA donors and investigate these with respect to their risk of contamination from the two proposed mechanisms. While not identifying any contamination, we inadvertently find a potential intelligence link between samples, showing the use of a mixture to mixture comparison tool for investigative purposes.

A sensitivity analysis to determine the robustness of STRmix™ with respect to laboratory calibration.

STRmix™ uses several laboratory specific parameters to calibrate the stochastic model for peak heights. These are modelled on empirical observations specific to the instruments and protocol used in the analysis. The extent to which these parameters can be borrowed from laboratories with similar technology and protocols without affecting the accuracy of the system is investigated using a sensitivity analysis. Parameters are first calibrated to a publicly available dataset, after which a large number of likelihood ratios are computed for true contributors and non-contributors using both the calibrated parameters and several borrowed parameters. Differences in the LR caused by using different sets of parameter values are found to be negligible.

Internal validation of STRmix™ - A multi laboratory response to PCAST.

We report a large compilation of the internal validations of the probabilistic genotyping software STRmix™. Thirty one laboratories contributed data resulting in 2825 mixtures comprising three to six donors and a wide range of multiplex, equipment, mixture proportions and templates. Previously reported trends in the LR were confirmed including less discriminatory LRs occurring both for donors and non-donors at low template (for the donor in question) and at high contributor number. We were unable to isolate an effect of allelic sharing. Any apparent effect appears to be largely confounded with increased contributor number.