ProbRank: An efficient DNA database search method for complex mixtures per a quantitative likelihood ratio model

Searching a DNA Database with a DNA profile from an evidentiary trace can provide investigative leads in a forensic case. Various searching approaches exist such as conventional methods based on matching alleles or more advanced methods computing likelihood ratios (LR) while considering drop-in and drop-out. Here we examine the potential of using a quantitative LR model (EuroForMix model incorporated in ProbRank method) that takes peak heights into account in comparison to a qualitative LR model (LRmix model implemented in SmartRank method). Both methods present DNA database candidates in order of decreasing LR. Especially regarding minor contributors in complex mixtures, the method using the quantitative model outperforms the method using the qualitative model in terms of sensitivity and specificity as more true donors and less adventitious matches are retrieved. ProbRank is to be implemented in DNAStatistX and is sufficiently fast for daily use.     

Searching mixed DNA profiles directly against profile databases

DNA databases have revolutionised forensic science. They are a powerful investigative tool as they have the potential to identify persons of interest in criminal investigations. Routinely, a DNA profile generated from a crime sample could only be searched for in a database of individuals if the stain was from single contributor (single source) or if a contributor could unambiguously be determined from a mixed DNA profile. This meant that a significant number of samples were unsuitable for database searching. The advent of continuous methods for the interpretation of DNA profiles offers an advanced way to draw inferential power from the considerable investment made in DNA databases. Using these methods, each profile on the database may be considered a possible contributor to a mixture and a likelihood ratio (LR) can be formed. Those profiles which produce a sufficiently large LR can serve as an investigative lead.In this paper empirical studies are described to determine what constitutes a large LR. We investigate the effect on a database search of complex mixed DNA profiles with contributors in equal proportions with dropout as a consideration, and also the effect of an incorrect assignment of the number of contributors to a profile. In addition, we give, as a demonstration of the method, the results using two crime samples that were previously unsuitable for database comparison. We show that effective management of the selection of samples for searching and the interpretation of the output can be highly informative.     

Searching for first-degree familial relationships in California's offender DNA database: validation of a likelihood ratio-based approach

A validation study was performed to measure the effectiveness of using a likelihood ratio-based approach to search for possible first-degree familial relationships (full-sibling and parent–child) by comparing an evidence autosomal short tandem repeat (STR) profile to California's ∼1,000,000-profile State DNA Index System (SDIS) database. Test searches used autosomal STR and Y-STR profiles generated for 100 artificial test families. When the test sample and the first-degree relative in the database were characterized at the 15 Identifiler^® (Applied Biosystems^®, Foster City, CA) STR loci, the search procedure included 96% of the fathers and 72% of the full-siblings. When the relative profile was limited to the 13 Combined DNA Index System (CODIS) core loci, the search procedure included 93% of the fathers and 61% of the full-siblings. These results, combined with those of functional tests using three real families, support the effectiveness of this tool. Based upon these results, the validated approach was implemented as a key, pragmatic and demonstrably practical component of the California Department of Justice's Familial Search Program. An investigative lead created through this process recently led to an arrest in the Los Angeles Grim Sleeper serial murders.     

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.     

Euroforgen-NoE collaborative exercise on LRmix to demonstrate standardization of the interpretation of complex DNA profiles

There has been very little work published on the variation of reporting practices of mixtures between laboratories, but it has been previously demonstrated that there is little consistency. This is because there is no current uniformity of practice, so different laboratories will operate using different rules. The interpretation of mixtures is not solely a matter of using some software to provide ‘an answer’. An assessment of a case will usually begin with a consideration of the circumstances of a crime. Assumptions made about the numbers of contributors follow from an examination of the electropherogram(s) – and these may differ between the prosecution and the defence hypotheses. There may be a necessity to evaluate several sets of hypotheses for any given case if the circumstances are uncertain. Once the hypotheses are formulated, the mathematical analysis is complex and can only be accomplished by the use of specialist software. In order to obtain meaningful results, it is essential that scientists are trained, not only in the use of the software, but also in the methodology to understand the likelihood ratio concept that is used. The Euroforgen-NoE initiative has developed a training course that utilizes the LRmix program to carry out the calculations. This software encompasses the recommendations of the ISFG DNA commissions on mixture interpretation and is able to interpret samples that may come from two or more contributors and may also be partial profiles. Recently, eighteen different laboratories were trained in the methodology. Afterwards they were asked to independently analyze two different cases with partial mixture DNA evidence and to write a statement court-report. We show that by introducing a structured training programme, it is possible to demonstrate, for the first time, that a high degree of standardization, leading to uniformity of results can be achieved by participating laboratories.     

Verifying likelihoods for low template DNA profiles using multiple replicates

To date there is no generally accepted method to test the validity of algorithms used to compute likelihood ratios (LR) evaluating forensic DNA profiles from low-template and/or degraded samples. An upper bound on the LR is provided by the inverse of the match probability, which is the usual measure of weight of evidence for standard DNA profiles not subject to the stochastic effects that are the hallmark of low-template profiles. However, even for low-template profiles the LR in favour of a true prosecution hypothesis should approach this bound as the number of profiling replicates increases, provided that the queried contributor is the major contributor. Moreover, for sufficiently many replicates the standard LR for mixtures is often surpassed by the low-template LR. It follows that multiple LTDNA replicates can provide stronger evidence for a contributor to a mixture than a standard analysis of a good-quality profile. Here, we examine the performance of the likeLTD software for up to eight replicate profiling runs. We consider simulated and laboratory-generated replicates as well as resampling replicates from a real crime case. We show that LRs generated by likeLTD usually do exceed the mixture LR given sufficient replicates, are bounded above by the inverse match probability and do approach this bound closely when this is expected. We also show good performance of likeLTD even when a large majority of alleles are designated as uncertain, and suggest that there can be advantages to using different profiling sensitivities for different replicates. Overall, our results support both the validity of the underlying mathematical model and its correct implementation in the likeLTD software.     

A series of recommended tests when validating probabilistic DNA profile interpretation software

There has been a recent push from many jurisdictions for the standardisation of forensic DNA interpretation methods. Current research is moving from threshold-based interpretation strategies towards continuous interpretation strategies. However laboratory uptake of software employing probabilistic models is slow. Some of this reluctance could be due to the perceived intimidating calculations to replicate the software answers and the lack of formal internal validation requirements for interpretation software. In this paper we describe a set of experiments which may be used to internally validate in part probabilistic interpretation software. These experiments included both single source and mixed profiles calculated with and without dropout and drop-in and studies to determine the reproducibility of the software with replicate analyses. We do this by way of example using three software packages: STRmix™, LRmix, and Lab Retriever. We outline and demonstrate the profile examples where the expected answer may be calculated and provide all calculations.     

DNA reviews: the national DNA database of the United Kingdom

The national DNA database in United Kingdom has now been operational for over 10 years. This review looks at the history and development of this investigative resource. From the development of commercial DNA profiling kits to the current statistics for matches obtained in relation to criminal investigation in the United Kingdom, before moving onto discussing potential future direction that national DNA databases might take, including international collaboration on a European and global scale.     

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.     

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 variability in likelihood ratios due to different mechanisms

Recently there has been a drive towards standardisation of forensic DNA interpretation methods resulting in the uptake of probabilistic interpretation software. Some of these software solutions utilise Markov chain Monte Carlo techniques (MCMC). They will not produce an identical answer after repeat interpretations of the same evidence profile because of the Monte Carlo aspect. This is a new source of variability within the forensic DNA analysis process. In this paper we explore the size of the MCMC variability within the interpretation software STRmix™ compared to other sources of variability in forensic DNA profiling including PCR, capillary electrophoresis load and injection, and the makeup of allele frequency databases. The MCMC variability within STRmix™ was shown to be the smallest source of variability in this process.     

An investigation into the performance of methods for adjusting for sampling uncertainty in DNA likelihood ratio calculations

There is a variety of methods for assessing sampling uncertainty in likelihood ratio calculations in DNA casework. Sampling uncertainty arises because all DNA statistical methods rely on a database of collected profiles. Such databases can be regarded as a sample from the population of interest. The act of taking a sample incurs sampling uncertainty. In some circumstances it may be desirable to provide some estimate of this uncertainty. We have addressed this topic in two previous publications [1] and [2]. In this paper we reconsider the performance of the methods using 15 locus Identifiler™ profiles, rather than the 6 locus data used in [1]. We also examine the differences in performance observed when using a uniform prior versus a 1/k prior in the Bayesian highest posterior density (HPD) method of Curran et al. [1].     

Likelihood ratio and posterior odds in forensic genetics: Two sides of the same coin

It has become widely accepted in forensics that, owing to a lack of sensible priors, the evidential value of matching DNA profiles in trace donor identification or kinship analysis is most sensibly communicated in the form of a likelihood ratio (LR). This restraint does not abate the fact that the posterior odds (PO) would be the preferred basis for returning a verdict. A completely different situation holds for Forensic DNA Phenotyping (FDP), which is aimed at predicting externally visible characteristics (EVCs) of a trace donor from DNA left behind at the crime scene. FDP is intended to provide leads to the police investigation helping them to find unknown trace donors that are unidentifiable by DNA profiling. The statistical models underlying FDP typically yield posterior odds (PO) for an individual possessing a certain EVC. This apparent discrepancy has led to confusion as to when LR or PO is the appropriate outcome of forensic DNA analysis to be communicated to the investigating authorities. We thus set out to clarify the distinction between LR and PO in the context of forensic DNA profiling and FDP from a statistical point of view. In so doing, we also addressed the influence of population affiliation on LR and PO. In contrast to the well-known population dependency of the LR in DNA profiling, the PO as obtained in FDP may be widely population-independent. The actual degree of independence, however, is a matter of (i) how much of the causality of the respective EVC is captured by the genetic markers used for FDP and (ii) by the extent to which non-genetic such as environmental causal factors of the same EVC are distributed equally throughout populations. The fact that an LR should be communicated in cases of DNA profiling whereas the PO are suitable for FDP does not conflict with theory, but rather reflects the immanent differences between these two forensic applications of DNA information.     

DNAxs/DNAStatistX: Development and validation of a software suite for the data management and probabilistic interpretation of DNA profiles

The data management, interpretation and comparison of sets of DNA profiles can be complex, time-consuming and error-prone when performed manually. This, combined with the growing numbers of genetic markers in forensic identification systems calls for expert systems that can automatically compare genotyping results within (large) sets of DNA profiles and assist in profile interpretation. To that aim, we developed a user-friendly software program or DNA eXpert System that is denoted DNAxs. This software includes features to view, infer and match autosomal short tandem repeat profiles with connectivity to up and downstream software programs. Furthermore, DNAxs has imbedded the ‘DNAStatistX’ module, a statistical library that contains a probabilistic algorithm to calculate likelihood ratios (LRs). This algorithm is largely based on the source code of the quantitative probabilistic genotyping system EuroForMix [1]. The statistical library, DNAStatistX, supports parallel computing which can be delegated to a computer cluster and enables automated queuing of requested LR calculations. DNAStatistX is written in Java and is accessible separately or via DNAxs. Using true and non-contributors to DNA profiles with up to four contributors, the DNAStatistX accuracy and precision were assessed by comparing the DNAStatistX results to those of EuroForMix. Results were the same up to rare differences that could be attributed to the different optimizers used in both software programs. Implementation of dye specific detection thresholds resulted in larger likelihood values and thus a better explanation of the data used in this study. Furthermore, processing time, robustness of DNAStatistX results and the circumstances under which model validations failed were examined. Finally, guidelines for application of the software are shared as an example. The DNAxs software is future-proof as it applies a modular approach by which novel functionalities can be incorporated.     

An assessment of the performance of the probabilistic genotyping software EuroForMix: Trends in likelihood ratios and analysis of Type I & II errors

Continuous probabilistic genotyping software enables the interpretation of highly complex DNA profiles that are prone to stochastic effects and/or consist of multiple contributions. The process of introducing probabilistic genotyping into an accredited forensic laboratory requires testing, validation, documentation and training. Documents that include guidelines and/or requirements have been published in order to guide forensic laboratories through this extensive process and there has been encouragements to share the results obtained from internal laboratory studies. To this end, we present the results obtained from the quantitative probabilistic genotyping system EuroForMix applied to mixed DNA profiles with known contributions mixed in known proportions, levels of allele sharing and levels of allelic drop-out. The mixtures were profiled using the PowerPlex® Fusion 6C (PPF6C) kit. Using these mixtures, 427 Hp-true tests and 408 Hd-true tests were performed. In the Hd-true tests, non-contributors were selected deliberately to a have large overlap with the alleles within the mixture and worst-case scenarios were examined in which a simulated relative of one of the true donors was considered as the person of interest under the prosecution hypothesis. The effects of selecting different EuroForMix modelling options, the use of PCR replicates, allelic drop-out, and varying the assigned number of contributors were examined. Instances of Type I and Type II errors are discussed. In addition 330 likelihood ratio results from EuroForMix are compared to the semi-continuous model LRmix Studio. Results demonstrate the performance and trends of EuroForMix when applied to PPF6C profiles.     

The effect of FBI CODIS Core STR Loci expansion on familial DNA database searching

1000 profiles chosen randomly from an in-house database of 6000 profiles were searched against the database for matches with at least one shared allele per locus. The database contains profiles that have been analyzed with Identifiler Plus (15 markers) for biological relationship and DNA identification purposes and both true and false matches are expected to be obtained. 100 pairs of at least one true paternity match and one false match were selected and were initially supplemented with 5 additional STRs representing the new Core CODIS set. Study of the LR value showed that when false matches were treated as paternity matches, the expansion of the marker set severely diminished the LR values obtained compared to true matches and the false positive ratio of familial database searching. When false matches were treated as full-sibling matches, the expansion to 20 STRs also diminished the number of false matches and the corresponding LR values compared to true full-sibling cases, but the effect was less dramatic. Addition of the SE33 marker, further promoted distinction between true and false matches both in paternity and full-sibling cases. Counting the number of shared alleles presented improved distinction efficiency between true and false matches after STR expansion to20 and 21 STRs but remains a less valuable method of familial DNA database searching compared to LR.     

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.     

A more straightforward derivation of the LR for a database search

Matching DNA profiles of an accused person and a crime scene trace are one of the most common forms of forensic evidence. A number of years ago the so-called ‘DNA controversy’ was concerned with how to quantify the value of such evidence. Given its importance, the lack of understanding of such a basic issue was quite surprising and concerning. Deriving the equation for the likelihood ratio of a DNA database match in a much more direct and simple way is the topic of this paper. As it is much easier to follow it is hoped that this derivation will contribute to the understanding.     

The evaluation of mixed stains from different ethnic origins: general result and common cases

In some situations, it can be inferred from the crime circumstances that the mixed stain donors are of different ethnic groups. The evaluation of DNA mixtures with contributors coming from more than one ethnic group is considered under the assumption of independence of alleles within and between ethnic groups. A general formula is derived for the assessment of the weight of evidence in mixed stain problems. This formula is equivalent to that of Fukshansky and Bär, but we give a different derivation. For the convenience of practitioners, the explicit expressions of the likelihood ratios for 14 common cases are presented. The effect of different ethnic groups to the assessment of the evidence is shown in the well-known Simpson case.     

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.