Identifying common donors in DNA mixtures,with applications to database searches

Several methods exist to compute the likelihood ratio LR(M, g) evaluating the possible contribution of a person of interest with genotype g to a mixed trace M. In this paper we generalize this LR to a likelihood ratio LR(M₁, M₂) involving two possibly mixed traces M₁ and M₂, where the question is whether there is a donor in common to both traces. In case one of the traces is in fact a single genotype, then this likelihood ratio reduces to the usual LR(M, g). We explain how our method conceptually is a logical consequence of the fact that LR calculations of the form LR(M, g) can be equivalently regarded as a probabilistic deconvolution of the mixture.Based on simulated data, and using a semi-continuous mixture evaluation model, we derive ROC curves of our method applied to various types of mixtures. From these data we conclude that searches for a common donor are often feasible in the sense that a very small false positive rate can be combined with a high probability to detect a common donor if there is one. We also show how database searches comparing all traces to each other can be carried out efficiently, as illustrated by the application of the method to the mixed traces in the Dutch DNA database.     

Evaluation of DNA mixtures involving two pairs of relatives

This paper considers the statistical evaluation of DNA mixtures in the following situations: (1) two unknown contributors are related respectively to two typed persons, (2) two of the unknown or untyped contributors are related and the third unknown contributor is related to a typed person, or (3) there are two pairs of related unknown contributors to the DNA mixture. The corresponding formulas for evaluating the likelihood ratios on the strength of DNA evidence are derived and the kinship coefficients for the related persons are incorporated into the calculations. Two examples are analyzed for illustration.     

Familial searching on DNA mixtures with dropout

Familial searching, the act of searching a database for a relative of an unknown individual whose DNA profile has been obtained, is usually restricted to cases where the DNA profile of that person has been unambiguously determined. Therefore, it is normally applied only with a good quality single source profile as starting point. In this article we investigate the performance of the method if applied to mixtures with and without allelic dropout, when likelihood ratios are computed with a semi-continuous (binary) model. We show that mixtures with dropout do not necessarily perform worse than mixtures without, especially if some separation between the donors is possible due to their different dropout probabilities. The familial searching true and false positive rates of mixed profiles on 15 loci are in some cases better than those of single source profiles on 10 loci. Thus, the information loss due to the fact that the person of interest's DNA has been mixed with that of other, and is affected by dropout, can be less than the loss of information corresponding to having 5 fewer loci available for a single source trace. Profiles typed on 10 autosomal loci are often involved in familial searching casework since many databases, including the Dutch one, in part consist of such profiles. Therefore, from this point of view, there seems to be no objection to extend familial searching to mixed or degraded profiles.     

The Yara Gambirasio case: Combining evidence in a complex DNA mixture case

Here, we illustrate how statistical methods can help extract information from mixed DNA profiles pertaining to an Italian case, referred to by the media as The murder of Yara Gambirasio. We base the analysis on a model for DNA mixtures that takes fully into account the peak heights and possible artefacts, like stutter and dropout that might occur in the DNA amplification process. We show how to combine the evidence from multiple samples and from different marker systems all within the model framework. The combined evidence is used for deconvolution, where the focus is to find likely profiles for the donors to the sample. We also show how a mixture can be used to establish familial relationships between a reference profile and a donor to the mixed DNA sample. We compare results based on a single mixed DNA profile, combination of replicates, combinations of different samples and combinations of different kits. Based on the Yara case, we discuss just a few of the plethora of possibilities of combining evidential information.     

Forensic identification of an individual in complex DNA mixtures

The identification of a suspect in a complex DNA mixture typed with standard short tandem repeat (STR) kits has proved difficult. In the current study we present the theoretical framework of a method aimed to resolve this problem in forensic cases. The method suggests genotyping a specially designed panel of 1000–3000 single nucleotide polymorphisms (SNPs), each with a relatively low (<0.1) minor allele frequency (MAF). The rationale of this method is that any individual will carry a specific set of dozens of rare alleles and the complex DNA mixture will carry this particular set only if the one individual is represented in the DNA mixture. The efficiency of the method is evaluated by estimating the probability that a random man will not be excluded (RMNE) from the mixture. When this probability, P(RMNE), is low, one can conclude that the suspect's DNA is present in the DNA mixture. Essentially, a P(RMNE) < 10⁻⁹ is considered as proof, whereas a P(RMNE) < 10⁻⁶ is considered strong evidence. For completeness, we also analyzed the method using the likelihood ratio (LR) approach. We have analyzed the method for a variety of conditions and found that generally the method will provide highly significant results even for complex mixtures combining up to 10 individuals. The method performs well even when close relatives (one or two brothers) are present in the complex DNA mixture and when contributors or suspects come from different populations. We have also found that the method can accurately identify the number of contributors to the mixture, something that in some instances has significant forensic value on its own.     

Accurate assessment of the weight of evidence for DNA mixtures by integrating the likelihood ratio

Several methods exist for weight of evidence calculations on DNA mixtures. Especially if dropout is a possibility, it may be difficult to estimate mixture specific parameters needed for the evaluation. For semi-continuous models, the LR for a person to have contributed to a mixture depends on the specified number of contributors and the probability of dropout for each. We show here that, for the semi-continuous model that we consider, the weight of evidence can be accurately obtained by applying the standard statistical technique of integrating the likelihood ratio against the parameter likelihoods obtained from the mixture data. This method takes into account all likelihood ratios belonging to every choice of parameters, but LR's belonging to parameters that provide a better explanation to the mixture data put in more weight into the final result. We therefore avoid having to estimate the number of contributors or their probabilities of dropout, and let the whole evaluation depend on the mixture data and the allele frequencies, which is a practical advantage as well as a gain in objectivity. Using simulated mixtures, we compare the LR obtained in this way with the best informed LR, i.e., the LR using the parameters that were used to generate the data, and show that results obtained by integration of the LR approximate closely these ideal values. We investigate both contributors and non-contributors for mixtures with various numbers of contributors. For contributors we always obtain a result close to the best informed LR whereas non-contributors are excluded more strongly if a smaller dropout probability is imposed for them. The results therefore naturally lead us to reconsider what we mean by a contributor, or by the number of contributors.     

Testing likelihood ratios produced from complex DNA profiles

The performance of any model used to analyse DNA profile evidence should be tested using simulation, large scale validation studies based on ground-truth cases, or alignment with trends predicted by theory. We investigate a number of diagnostics to assess the performance of the model using H_d true tests. Of particular focus in this work is the proportion of comparisons to non-contributors that yield a likelihood ratio (LR) higher than or equal to the likelihood ratio of a known contributor (LR_POI), designated as p, and the average LR for H_d true tests. Theory predicts that p should always be less than or equal to 1/LR_POI and hence the observation of this in any particular case is of limited use. A better diagnostic is the average LR for H_d true which should be near to 1. We test the performance of a continuous interpretation model on nine DNA profiles of varying quality and complexity and verify the theoretical expectations.     

Evaluating forensic DNA mixtures with contributors of different structured ethnic origins: a computer software

The effect of a structured population on the likelihood ratio of a DNA mixture has been studied by the current authors and others. In practice, contributors of a DNA mixture may belong to different ethnic/racial origins, a situation especially common in multi-racial countries such as the USA and Singapore. We have developed a computer software which is available on the web for evaluating DNA mixtures in multi-structured populations. The software can deal with various DNA mixture problems that cannot be handled by the methods given in a recent article of Fung and Hu.     

Evaluating forensic DNA profiles using peak heights,allowing for multiple donors,allelic dropout and stutters

Increases in the sensitivity of DNA profiling technology now allow profiles to be obtained from smaller and more degraded DNA samples than was previously possible. The resulting profiles can be highly informative, but the subjective elements in the interpretation make it problematic to achieve the valid and efficient evaluation of evidential strength required in criminal cases. The problems arise from stochastic phenomena such as “dropout” (absence of an allele in the profile that is present in the underlying DNA) and experimental artefacts such as “stutter” that can generate peaks of ambiguous allelic status. Currently in the UK, evidential strength evaluation uses an approach in which the complex signals in the DNA profiles are interpreted in a semi-manual fashion by trained experts aided by a set of guidelines, but also relying substantially on professional judgment. We introduce a statistical model to calculate likelihood ratios for evaluating DNA evidence arising from multiple known and unknown contributors that allows for such stochastic phenomena by incorporating peak heights. Efficient use of peak heights allows for more crime scene profiles to be reported to courts than is currently possible. The model parameters are estimated from experimental data incorporating multiple sources of variability in the profiling system. We report and analyse experimental results from the SGMPlus system, run at 28 amplification cycles with no enhancements, currently used in the UK. Our methods are readily adapted to other DNA profiling systems provided that the experimental data for the parameter estimation is available.     

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.     

Evaluation of large-scale highly polymorphic microhaplotypes in complex DNA mixtures analysis using RMNE method

DNA mixture interpretation is one of the most challenging problems in forensics. Complex DNA mixtures are more difficult to analyze when there are more than two contributors or related contributors. Microhaplotypes (MHs) are polymorphic genetic markers recently discovered and employed in DNA mixture analysis. However, the evidentiary interpretation of the MH genotyping data needs more debate. The Random Man Not Excluded (RMNE) method analyzes DNA mixtures without using allelic peak height data or the number of contributors (NoC) assumptions. This study aimed to assess how well RMNE interpreted mixed MH genotyping data. We classified the MH loci from the 1000 Genomes Project database into groups based on their Ae values. Then we performed simulations of DNA mixtures with 2–10 unrelated contributors and DNA mixtures with a pair of sibling contributors. For each simulated DNA mixture, incorrectly included ratios were estimated for three types of non-contributors: random men, parents of contributors, and siblings of contributors. Meanwhile, RMNE probability was calculated for contributors and three types of non-contributors, allowing loci mismatch. The results showed that the MH number, the MH Ae values, and the NoC affected the RMNE probability of the mixture and the incorrectly included ratio of non-contributors. When there were more MHs, MHs with higher Ae values, and a mixture with less NoC, the RMNE probability, and the incorrectly included ratio decreased. The existence of kinship in mixtures complicated the mixture interpretation. Contributors’ relatives as non-contributors and related contributors in the mixture increased the demands on the genetic markers to identify the contributors correctly. When 500 highly polymorphic MHs with Ae values higher than 5 were used, the four individual types could be distinguished according to the RMNE probabilities. This study reveals the promising potential of MH as a genetic marker for mixed DNA interpretation and the broadening of RMNE as a parameter indicating the relationship of a specific individual with a DNA mixture in the DNA database search.     

Paternity testing and other inference about relationships from DNA mixtures

We present methods for inference about relationships between contributors to a DNA mixture and other individuals of known genotype: a basic example would be testing whether a contributor to a mixture is the father of a child of known genotype. The evidence for such a relationship is evaluated as the likelihood ratio for the specified relationship versus the alternative that there is no relationship. We analyse real casework examples from a criminal case and a disputed paternity case; in both examples part of the evidence was from a DNA mixture. DNA samples are of varying quality and therefore present challenging problems in interpretation. Our methods are based on a recent statistical model for DNA mixtures, in which a Bayesian network (BN) is used as a computational device; the present work builds on that approach, but makes more explicit use of the BN in the modelling. The R code for the analyses presented is freely available as supplementary material.We show how additional information of specific genotypes relevant to the relationship under analysis greatly strengthens the resulting inference. We find that taking full account of the uncertainty inherent in a DNA mixture can yield likelihood ratios very close to what one would obtain if we had a single source DNA profile. Furthermore, the methods can be readily extended to analyse different scenarios as our methods are not limited to the particular genotyping kits used in the examples, to the allele frequency databases used, to the numbers of contributors assumed, to the number of traces analysed simultaneously, nor to the specific hypotheses tested.     

Complex DNA mixture analysis in a forensic context: Evaluating the probative value using a likelihood ratio model

The interpretation of mixed DNA profiles obtained from low template DNA samples has proven to be a particularly difficult task in forensic casework. Newly developed likelihood ratio (LR) models that account for PCR-related stochastic effects, such as allelic drop-out, drop-in and stutters, have enabled the analysis of complex cases that would otherwise have been reported as inconclusive. In such samples, there are uncertainties about the number of contributors, and the correct sets of propositions to consider. Using experimental samples, where the genotypes of the donors are known, we evaluated the feasibility and the relevance of the interpretation of high order mixtures, of three, four and five donors.The relative risks of analyzing high order mixtures of three, four, and five donors, were established by comparison of a ‘gold standard’ LR, to the LR that would be obtained in casework. The ‘gold standard’ LR is the ideal LR: since the genotypes and number of contributors are known, it follows that the parameters needed to compute the LR can be determined per contributor. The ‘casework LR’ was calculated as used in standard practice, where unknown donors are assumed; the parameters were estimated from the available data. Both LRs were calculated using the basic standard model, also termed the drop-out/drop-in model, implemented in the LRmix module of the R package Forensim.We show how our results furthered the understanding of the relevance of analyzing high order mixtures in a forensic context. Limitations are highlighted, and it is illustrated how our study serves as a guide to implement likelihood ratio interpretation of complex DNA profiles in forensic casework.     

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.     

Genotyping and interpretation of STR-DNA: Low-template,mixtures and database matches—Twenty years of research and development

The introduction of Short Tandem Repeat (STR) DNA was a revolution within a revolution that transformed forensic DNA profiling into a tool that could be used, for the first time, to create National DNA databases. This transformation would not have been possible without the concurrent development of fluorescent automated sequencers, combined with the ability to multiplex several loci together. Use of the polymerase chain reaction (PCR) increased the sensitivity of the method to enable the analysis of a handful of cells. The first multiplexes were simple: ‘the quad’, introduced by the defunct UK Forensic Science Service (FSS) in 1994, rapidly followed by a more discriminating ‘six-plex’ (Second Generation Multiplex) in 1995 that was used to create the world's first national DNA database. The success of the database rapidly outgrew the functionality of the original system – by the year 2000 a new multiplex of ten-loci was introduced to reduce the chance of adventitious matches. The technology was adopted world-wide, albeit with different loci. The political requirement to introduce pan-European databases encouraged standardisation – the development of European Standard Set (ESS) of markers comprising twelve-loci is the latest iteration. Although development has been impressive, the methods used to interpret evidence have lagged behind. For example, the theory to interpret complex DNA profiles (low-level mixtures), had been developed fifteen years ago, but only in the past year or so, are the concepts starting to be widely adopted. A plethora of different models (some commercial and others non-commercial) have appeared. This has led to a confusing ‘debate’ about the ‘best’ to use. The different models available are described along with their advantages and disadvantages. A section discusses the development of national DNA databases, along with details of an associated controversy to estimate the strength of evidence of matches. Current methodology is limited to searches of complete profiles – another example where the interpretation of matches has not kept pace with development of theory. STRs have also transformed the area of Disaster Victim Identification (DVI) which frequently requires kinship analysis. However, genotyping efficiency is complicated by complex, degraded DNA profiles. Finally, there is now a detailed understanding of the causes of stochastic effects that cause DNA profiles to exhibit the phenomena of drop-out and drop-in, along with artefacts such as stutters. The phenomena discussed include: heterozygote balance; stutter; degradation; the effect of decreasing quantities of DNA; the dilution effect.     

Optimizing the information increase through the addition of relatives and genetic markers in identification and kinship cases

In kinship testing powerful statistical results are usually obtained when genetic information is required to be shared between a set of individuals, under the assumption of one of the hypotheses. This is the case when the hypotheses parenthood or identity are compared with the hypothesis of no relatedness, even when only a pair of individuals is analyzed. In this work we will consider kinship problems where the sharing of genetic information is not required when a pair of individuals is analyzed, such as is the case of the hypotheses full-siblings or avuncular. Statistical evaluation was computed through the quantification of likelihood ratios, assuming the genotypic configuration of 100,000 simulated families, for each of the kinship problems analyzed: full-siblings vs. unrelated, full-siblings vs. half-siblings, half-siblings vs. unrelated, avuncular vs. unrelated, first cousins vs. unrelated, and half-first cousins vs. unrelated. For each of the six studied cases we have obtained results allowing us to weight the informative power impact of increasing the number of markers and of the addition of an extra individual, considering (a.) the use of different sets of STRs (from 8 to 35), and (b.) the introduction of a third undoubted relative. Based on these results we were able to provide recommendations for each case both on the minimal number of STRs to be used and on the third relative whose genetic analysis should be privileged.     

Validation of SmartRank: A likelihood ratio software for searching national DNA databases with complex DNA profiles

Searching a national DNA database with complex and incomplete profiles usually yields very large numbers of possible matches that can present many candidate suspects to be further investigated by the forensic scientist and/or police. Current practice in most forensic laboratories consists of ordering these ‘hits’ based on the number of matching alleles with the searched profile. Thus, candidate profiles that share the same number of matching alleles are not differentiated and due to the lack of other ranking criteria for the candidate list it may be difficult to discern a true match from the false positives or notice that all candidates are in fact false positives. SmartRank was developed to put forward only relevant candidates and rank them accordingly. The SmartRank software computes a likelihood ratio (LR) for the searched profile and each profile in the DNA database and ranks database entries above a defined LR threshold according to the calculated LR. In this study, we examined for mixed DNA profiles of variable complexity whether the true donors are retrieved, what the number of false positives above an LR threshold is and the ranking position of the true donors. Using 343 mixed DNA profiles over 750 SmartRank searches were performed. In addition, the performance of SmartRank and CODIS were compared regarding DNA database searches and SmartRank was found complementary to CODIS. We also describe the applicable domain of SmartRank and provide guidelines. The SmartRank software is open-source and freely available. Using the best practice guidelines, SmartRank enables obtaining investigative leads in criminal cases lacking a suspect.     

Analysis of nondegraded and degraded DNA mixtures of close relatives using massively parallel sequencing

Identification of the minor contributor in DNA mixture of close relatives remains a dilemma in forensic genetics. Massively parallel sequencing (MPS) can analyze multiple short tandem repeats (STRs) and single nucleotide polymorphism (SNPs) concurrently and detect non-overlapping alleles of the minor contributors in DNA mixtures. A commercial kit for MPS of 59 identity informative STRs (iiSTRs) and 94 autosomal identity-informative SNPs (iiSNPs) was used to analyzed 34 nondegraded and 33 highly degraded two-person artificial DNA mixtures of close relatives with various minor to major ratios (1:9, 1:19, 1:29, 1:39, 1:79, 1:99). EuroForMix software was used to determine the minor contributors in the mixtures based on the likelihood ratios calculated from the MPS data, and relMix software was used to perform kinship analysis of the contributors. The STRs and SNPs of the 34 nondegraded and 33 degraded DNA mixtures were genotyped using MPS. Using EuroForMix based on the genotypes of autosomal iiSTRs and autosomal iiSNPs, 82.4% (28/34) and 54.5% (18/33) of minor donors could be accurately assigned for the nondegraded and degraded DNA mixtures, respectively. The relMix software correctly inferred the relationship between contributors in 97.1% (33/34) of nondegraded mixtures and in 97.0% (32/33) of degraded mixtures. In conclusion, combined EuroForMix and MPS data of STRs and SNPs can assist in the assignment of minor donors in nondegraded DNA mixtures of close relatives, and relMix can be used to infer relationship among contributors.     

SNP-microarrays can accurately identify the presence of an individual in complex forensic DNA mixtures

Common forensic and mass disaster scenarios present DNA evidence that comprises a mixture of several contributors. Identifying the presence of an individual in such mixtures has proven difficult. In the current study, we evaluate the practical usefulness of currently available “off-the-shelf” SNP microarrays for such purposes. We found that a set of 3000 SNPs specifically selected for this purpose can accurately identify the presence of an individual in complex DNA mixtures of various compositions. For example, individuals contributing as little as 5% to a complex DNA mixture can be robustly identified even if the starting DNA amount was as little as 5.0 ng and had undergone whole-genome amplification (WGA) prior to SNP analysis. The work presented in this study represents proof-of-principle that our previously proposed approach, can work with real “forensic-type” samples. Furthermore, in the absence of a low-density focused forensic SNP microarray, the use of standard, currently available high-density SNP microarrays can be similarly used and even increase statistical power due to the larger amount of available information.     

Separation of SNP profiles from DNA mixtures with two contributors via massively parallel sequencing technology

ABSTRACT

Massively parallel sequencing technology offers the opportunity to analyse forensically challenging samples, such as degraded samples and mixtures. In the current study, we developed a perl-based pipeline to separate the DNA mixture into its components and to predict the most probable single nucleotide polymorphism (SNP) genotypes of each contributor to the mixed profile. We examined the usefulness of this method by detecting both artificially constructed DNA mixtures and mixtures from crime cases using the Precision ID Identity Panel on the Ion PGM platform. The separated genotypes of mixtures were validated by genotypes of each of the donors detected independently. The results indicate that the method performed well in identifications of both the artificially constructed mixtures and case-type mixtures, even when the two contributors are immediate relatives (mother and son), which demonstrated the practical usefulness of this method in forensic casework. Our research presents an efficient and different strategy for identification and paternity testing of DNA mixtures in forensic genetics.