Exact computation of the distribution of likelihood ratios with forensic applications

A Novel SNP-STR System Based on a Capillary Electrophoresis Platform

Various compound markers encompassing two or more variants within a small region can be regarded as generalized microhaplotypes. Many of these markers have been investigated for various forensic purposes, such as individual identification, deconvolution of DNA mixtures, or forensic ancestry inference. SNP-STR is a compound biomarker composed of a single nucleotide polymorphism (SNP) and a closely linked short tandem repeat polymorphism (STR), and possess the advantages of both SNPs and STRs. In addition, in conjunction with a polymerase chain reaction (PCR) technique based on the amplification refractory mutation system (ARMS), SNP-STRs can be used for forensic unbalanced DNA mixture analysis based on capillary electrophoresis (CE), which is the most commonly used platform in worldwide forensic laboratories. Our previous research reported 11 SNP-STRs, but few of them are derived from the commonly used STR loci, for which existing STR databases can be used as a reference. For maximum compatibility with existing DNA databases, in this study, we screened 18 SNP-STR loci, of which 14 were derived from the expanded CODIS core loci set. Stable and sensitive SNP-STR multiplex PCR panels based on the CE platform were established. Assays on simulated two-person DNA mixtures showed that all allele-specific primers could detect minor DNA components in 1:500 mixtures. Population data based on 113 unrelated Chengdu Han individuals were investigated. A Bayesian framework was developed for the likelihood ratio (LR) evaluation of SNP-STR profiling results obtained from two-person mixtures. Furthermore, we report on the first use of SNP-STRs in casework to show the advantages and limitations for use in practice. Compared to 2.86 × 10³ for autosomal STR kits, the combined LR reached 7.14 × 10⁷ using the SNP-STR method in this casework example.

Using the Nondonor Distribution to Improve Communication and Inform Decision Making for Low LRs from Minor Contributors in Mixed DNA Profiles

The reporting of a likelihood ratio (LR) calculated from probabilistic genotyping software has become more popular since 2015 and has allowed for the use of more complex mixtures at court. The meaning of "inconclusive" LRs and how to communicate the significance of low LRs at court is now important. We present a method here using the distribution of LRs obtained from nondonors. The nondonor distribution is useful for examining calibration and discrimination for profiles that have produced LRs less than about 10⁴ . In this paper, a range of mixed DNA profiles of varying quantity were constructed and the LR distribution considering the minor contributor for a number of nondonors was compared to the expectation given a calibrated system. It is demonstrated that conditioning genotypes should be used where reasonable given the background information to decrease the rate of nondonor LRs above 1. In all 17 cases examined, the LR for the minor donor was higher than the nondonor LRs, and in 12 of the 17 cases, the 99.9 percentile of the nondonor distribution was lower when appropriate conditioning information was used. The output of the tool is a graph that can show the position of the LR for the person of interest set against the nondonor LR distribution. This may assist communication between scientists and the court.

Four model variants within a continuous forensic DNA mixture interpretation framework: Effects on evidential inference and reporting

Continuous mixture interpretation methods that employ probabilistic genotyping to compute the Likelihood Ratio (LR) utilize more information than threshold-based systems. The continuous interpretation schemes described in the literature, however, do not all use the same underlying probabilistic model and standards outlining which probabilistic models may or may not be implemented into casework do not exist; thus, it is the individual forensic laboratory or expert that decides which model and corresponding software program to implement. For countries, such as the United States, with an adversarial legal system, one can envision a scenario where two probabilistic models are used to present the weight of evidence, and two LRs are presented by two experts. Conversely, if no independent review of the evidence is requested, one expert using one model may present one LR as there is no standard or guideline requiring the uncertainty in the LR estimate be presented. The choice of model determines the underlying probability calculation, and changes to it can result in non-negligible differences in the reported LR or corresponding verbal categorization presented to the trier-of-fact. In this paper, we study the impact of model differences on the LR and on the corresponding verbal expression computed using four variants of a continuous mixture interpretation method. The four models were tested five times each on 101, 1-, 2- and 3-person experimental samples with known contributors. For each sample, LRs were computed using the known contributor as the person of interest. In all four models, intra-model variability increased with an increase in the number of contributors and with a decrease in the contributor’s template mass. Inter-model variability in the associated verbal expression of the LR was observed in 32 of the 195 LRs used for comparison. Moreover, in 11 of these profiles there was a change from LR > 1 to LR < 1. These results indicate that modifications to existing continuous models do have the potential to significantly impact the final statistic, justifying the continuation of broad-based, large-scale, independent studies to quantify the limits of reliability and variability of existing forensically relevant systems.

Efficient construction of match strength distributions for uncertain multi-locus genotypes

Natural variation in biological evidence leads to uncertain genotypes. Forensic comparison of a probabilistic genotype with a person's reference gives a numerical strength of DNA association. The distribution of match strength for all possible references usefully represents a genotype's potential information. But testing more genetic loci exponentially increases the number of multi-locus possibilities, making direct computation infeasible. At each locus, Bayesian probability can quickly assemble a match strength random variable. Multi-locus match strength is the sum of these independent variables. A multi-locus genotype's match strength distribution is efficiently constructed by convolving together the separate locus distributions. This convolution construction can accurately collate all trillion trillion reference outcomes in a fraction of a second. This paper shows how to rapidly construct multi-locus match strength distributions by convolution. Function convergence demonstrates that distribution accuracy increases with numerical resolution. Convolution construction has quadratic computational complexity, relative to the exponential number of reference genotypes. A suitably defined random variable reduces high-dimensional computational cost to fast real-line arithmetic. Match strength distributions are used in forensic validation studies. They provide error rates for match results. The convolution construction applies to discrete or continuous variables in the forensic, natural and social sciences. Computer-derived match strength distributions elicit the information inherent in DNA evidence, often overlooked by human analysis.

Separation/extraction, detection, and interpretation of DNA mixtures in forensic science (review)

Interpreting mixed DNA samples containing material from multiple contributors has long been considered a major challenge in forensic casework, especially when encountering low-template DNA (LT-DNA) or high-order mixtures that may involve missing alleles (dropout) and unrelated alleles (drop-in), among others. In the last decades, extraordinary progress has been made in the analysis of mixed DNA samples, which has led to increasing attention to this research field. The advent of new methods for the separation and extraction of DNA from mixtures, novel or jointly applied genetic markers for detection and reliable interpretation approaches for estimating the weight of evidence, as well as the powerful massively parallel sequencing (MPS) technology, has greatly extended the range of mixed samples that can be correctly analyzed. Here, we summarized the investigative approaches and progress in the field of forensic DNA mixture analysis, hoping to provide some assistance to forensic practitioners and to promote further development involving this issue.

Noninvasive Prenatal Paternity Testing (NIPAT) through Maternal Plasma DNA Sequencing: A Pilot Study

Short tandem repeats (STRs) and single nucleotide polymorphisms (SNPs) have been already used to perform noninvasive prenatal paternity testing from maternal plasma DNA. The frequently used technologies were PCR followed by capillary electrophoresis and SNP typing array, respectively. Here, we developed a noninvasive prenatal paternity testing (NIPAT) based on SNP typing with maternal plasma DNA sequencing. We evaluated the influence factors (minor allele frequency (MAF), the number of total SNP, fetal fraction and effective sequencing depth) and designed three different selective SNP panels in order to verify the performance in clinical cases. Combining targeted deep sequencing of selective SNP and informative bioinformatics pipeline, we calculated the combined paternity index (CPI) of 17 cases to determine paternity. Sequencing-based NIPAT results fully agreed with invasive prenatal paternity test using STR multiplex system. Our study here proved that the maternal plasma DNA sequencing-based technology is feasible and accurate in determining paternity, which may provide an alternative in forensic application in the future.

Cell type determination and association with the DNA donor

In forensic casework, evidence regarding the type of cell material contained in a stain can be crucial in determining what happened. For example, a DNA match in a sexual offense can become substantially more incriminating when there is evidence supporting that semen cells are present. Besides the question which cell types are present in a sample, also the question who donated what (association) is very relevant. This question is surprisingly difficult, even for stains with a single donor. The evidential value of a DNA profile needs to be combined with knowledge regarding the specificity and sensitivity of cell type tests. This, together with prior probabilities for the different donor-cell type combinations, determines the most likely combination. We present a Bayesian network that can assist in associating donors and cell types. A literature overview on the sensitivity and specificity of three cell type tests (PSA test for seminal fluid, RSID saliva and RSID semen) is helpful in assigning conditional probabilities. The Bayesian network is linked with a software package for interpreting mixed DNA profiles. This allows for a sensitivity analysis that shows to what extent the conclusion depends on the quantity of available research data. This can aid in making decisions regarding further research. It is shown that the common assumption that an individual (e.g. the victim) is one of the donors in a mixed DNA profile can have unwanted consequences for the association between donors and cell types.

An assessment of the information content of likelihood ratios derived from complex mixtures

With the increasing sensitivity of DNA typing methodologies, as well as increasing awareness by law enforcement of the perceived capabilities of DNA typing, complex mixtures consisting of DNA from two or more contributors are increasingly being encountered. However, insufficient research has been conducted to characterize the ability to distinguish a true contributor (TC) from a known non-contributor (KNC) in these complex samples, and under what specific conditions. In order to investigate this question, sets of six 15-locus Caucasian genotype profiles were simulated and used to create mixtures containing 2-5 contributors. Likelihood ratios were computed for various situations, including varying numbers of contributors and unknowns in the evidence profile, as well as comparisons of the evidence profile to TCs and KNCs. This work was intended to illustrate the best-case scenario, in which all alleles from the TC were detected in the simulated evidence samples. Therefore the possibility of drop-out was not modeled in this study. The computer program DNAMIX was then used to compute LRs comparing the evidence profile to TCs and KNCs. This resulted in 140,000 LRs for each of the two scenarios. These complex mixture simulations show that, even when all alleles are detected (i.e. no drop-out), TCs can generate LRs less than 1 across a 15-locus profile. However, this outcome was rare, 7 of 140,000 replicates (0.005%), and associated only with mixtures comprising 5 contributors in which the numerator hypothesis includes one or more unknown contributors. For KNCs, LRs were found to be greater than 1 in a small number of replicates (75 of 140,000 replicates, or 0.05%). These replicates were limited to 4 and 5 person mixtures with 1 or more unknowns in the numerator. Only 5 of these 75 replicates (0.004%) yielded an LR greater than 1,000. Thus, overall, these results imply that the weight of evidence that can be derived from complex mixtures containing up to 5 contributors, under a scenario in which no drop-out is required to explain any of the contributors, is remarkably high. This is a useful benchmark result on top of which to layer the effects of additional factors, such as drop-out, peak height, and other variables.

Lab Retriever: a software tool for calculating likelihood ratios incorporating a probability of drop-out for forensic DNA profiles

Background

Technological advances have enabled the analysis of very small amounts of DNA in forensic cases. However, the DNA profiles from such evidence are frequently incomplete and can contain contributions from multiple individuals. The complexity of such samples confounds the assessment of the statistical weight of such evidence. One approach to account for this uncertainty is to use a likelihood ratio framework to compare the probability of the evidence profile under different scenarios. While researchers favor the likelihood ratio framework, few open-source software solutions with a graphical user interface implementing these calculations are available for practicing forensic scientists.

Results

To address this need, we developed Lab Retriever, an open-source, freely available program that forensic scientists can use to calculate likelihood ratios for complex DNA profiles. Lab Retriever adds a graphical user interface, written primarily in JavaScript, on top of a C++ implementation of the previously published R code of Balding. We redesigned parts of the original Balding algorithm to improve computational speed. In addition to incorporating a probability of allelic drop-out and other critical parameters, Lab Retriever computes likelihood ratios for hypotheses that can include up to four unknown contributors to a mixed sample. These computations are completed nearly instantaneously on a modern PC or Mac computer.

Conclusions

Lab Retriever provides a practical software solution to forensic scientists who wish to assess the statistical weight of evidence for complex DNA profiles. Executable versions of the program are freely available for Mac OSX and Windows operating systems.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0740-8) contains supplementary material, which is available to authorized users.

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.

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 Hd 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 (LRPOI), designated as p, and the average LR for Hd true tests. Theory predicts that p should always be less than or equal to 1/LRPOI and hence the observation of this in any particular case is of limited use. A better diagnostic is the average LR for Hd 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.

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.

Regression models for DNA-mixtures

This paper deals with the statistical interpretation of DNA mixture evidence. The conventional methods used in forensic casework today use something like 16 STR-markers. Power can be increased by rather using SNP-markers. New statistical methods are then needed, and we present a regression framework. The basic idea is that the traditional forensic hypotheses, commonly denoted HD and HP, are replaced by parametric versions: a person contributes to a mixture if and only if the fraction he contributes is greater than 0. This contributed fraction is a parameter of the regression model. The regression model uses the peak heights directly and there is no need to specify or estimate the number of contributors to the mixture. Also, drop-in and drop-out pose no principal problems. Data from 25 controlled blinded experiments were used to test the model. The number of contributors varied between 2 and 5, and the fractions contributed ranged from 0.01 to 0.99. The fractions were accurately estimated by the regression analyses. There were no false positives (i.e., in no cases were non-contributors declared to contributors). Some false negatives occurred for fractions of 0.1 or lower. Simulations were performed to test the model further. The analyses show that useful estimates can be obtained from a relatively small number of SNP-markers. Reasonable results are achieved using 300 markers which is close to the 313 SNPs in the controlled experiment. Increasing the number of SNPs, the analyses demonstrate that individuals contributing as little as 1% can reliably be detected, which suggests that cases beyond the reach of conventional forensic methods today can be reported.