Likelihood ratio formulae for disputed parentage when the product of conception is trisomic.

We present here the derivation of paternity index formulae that covers situations of a disputed paternity trio with a trisomic product of conception. We consider six possible mechanisms for trisomy to occur: dispermy, dieggy, paternal meiosis I or II, and maternal meiosis I or II in the calculation. We also provide a biological explanation for how each of the mechanisms could give rise to a trisomy. The paper is set out in a general manner so that the tables presented can be used on any instance of trisomic offspring. This work is motivated by a case of disputed paternity where the product of conception was trisomic, i.e. the electropherogram of the product of conception possessed three alleles at each locus. The outcome was extremely strong support for the alleged father's paternity of the product of conception.

Evaluation of forensic DNA mixture evidence: protocol for evaluation, interpretation, and statistical calculations using the combined probability of inclusion.

BACKGROUND: The evaluation and interpretation of forensic DNA mixture evidence faces greater interpretational challenges due to increasingly complex mixture evidence. Such challenges include: casework involving low quantity or degraded evidence leading to allele and locus dropout; allele sharing of contributors leading to allele stacking; and differentiation of PCR stutter artifacts from true alleles. There is variation in statistical approaches used to evaluate the strength of the evidence when inclusion of a specific known individual(s) is determined, and the approaches used must be supportable. There are concerns that methods utilized for interpretation of complex forensic DNA mixtures may not be implemented properly in some casework. Similar questions are being raised in a number of U.S. jurisdictions, leading to some confusion about mixture interpretation for current and previous casework. RESULTS: Key elements necessary for the interpretation and statistical evaluation of forensic DNA mixtures are described. Given the most common method for statistical evaluation of DNA mixtures in many parts of the world, including the USA, is the Combined Probability of Inclusion/Exclusion (CPI/CPE). Exposition and elucidation of this method and a protocol for use is the focus of this article. Formulae and other supporting materials are provided. CONCLUSIONS: Guidance and details of a DNA mixture interpretation protocol is provided for application of the CPI/CPE method in the analysis of more complex forensic DNA mixtures. This description, in turn, should help reduce the variability of interpretation with application of this methodology and thereby improve the quality of DNA mixture interpretation throughout the forensic community.

Modeling forward stutter: toward increased objectivity in forensic DNA interpretation.

Forward stutter, or over stutter, one repeat unit length larger than the parent allele (N + 1 stutter), is a relatively rare product of the PCR amplification of STRs used in forensic DNA analysis. We have investigated possible explanatory variables for the occurrence and size of forward stutter for four different autosomal multiplexes. In addition, we have investigated models used to predict the expected heights of forward stutter. For all tetra and penta-nucleotide repeats we can find no correlation between allelic peak height, marker, or longest uninterrupted sequence in the allele. The data fit a gamma distribution with no explanatory variables. For the single trinucleotide repeat present in two of the four multiplexes (D22S1045) forward stutter is much more common and the best explanatory variable appears to be back stutter height. This suggests some fundamental cocausation of high backward and forward stutter for this locus.

Comparison of the performance of different models for the interpretation of low level mixed DNA profiles.

DNA analyses from forensic casework samples commonly result in complex DNA profiles. Often, these profiles consist of multiple contributors and display multiple stochastic events such as peak height imbalance, allelic or locus drop-out, allelic drop-in, and excessive or indistinguishable stutter. This increased complexity has established a need for more sophisticated methods of DNA mixture interpretation. This study compares the effectiveness of statistical models in the interpretation of artificially created low template two person mixed DNA profiles at varying proportions and template quantities. Two binary models (combined probability of inclusion and random match probability), a semicontinuous (Lab retriever), and continuous model (STRmix™) were compared. Generally, as the sophistication of the models increases, the power of discrimination increases. Differences in discrimination often correlate to each model's ability to use observed data effectively. Binary models require static thresholds resulting in unused data and outliers that may lead to difficult or incorrect interpretation. Semicontinuous and continuous models eliminate the stochastic threshold, however Lab Retriever does not account for stochastic events beyond drop-out and drop-in leading to possible less effective use of the data. STRmix™ incorporates all stochastic events listed above into the calculation making the most effective use of the observed data.

The 'factor of two' issue in mixed DNA profiles.

A commonly used idea in forensic fields is known as the 'hierarchy of propositions'. DNA analysts commonly report at the sub-source level in the hierarchy. This means that they simply comment on the probability of the evidence for the given propositions that consider contributors that lead to a DNA profile and not on the source of specific biological components, not the activity that led to the transfer or the offence that is reported to have occurred. However DNA analysts also commonly report at a level even lower than the sub-source level. In this 'sub-sub-source' level only reference comparisons to components of a mixture are reported. The difference between the sub-source level and sub-sub-source level is the difference between comparing an individual to a mixture as a whole, or comparing them to only one component of a mixture. This idea has been expressed in the past as the 'two trace' problem or the 'factor of two' problem. With the advent of expert systems that can provide a measure of weight of evidence in the form of a likelihood ratio (LR) for any mixture, resolvable or not, the distinction between these two levels becomes more important. In this paper we explore how the LR can be constructed to report correctly at the sub-source level, by taking contributor orders and genotype set orders into account. We include worked examples of the LR calculation to help explain this confusing issue.

A comparison of statistical models for the analysis of complex forensic DNA profiles.

Complex mixtures and LtDNA profiles are difficult to interpret. As yet there is no consensus within the forensic biology community as to how these profiles should be interpreted. This paper is a review of some of the current interpretation models, highlighting their weaknesses and strengths. It also discusses what a forensic biologist requires in an interpretation model and if this can be realistically executed under current justice systems.

Geographical variation of shoeprint comparison class correspondences.

The underlying principles involved in the interpretation of shoeprint comparisons have become a topical subject due to criticisms in the 2009 National Academy of Science (NAS) report on forensic sciences[1]. Difficulties in the application and understanding of these principles were also highlighted in a recent court ruling [2-5] and subsequent discussion of the ruling. We report here a survey that may inform some aspects of this interpretation and discuss the implications of findings from this survey in the light of that court ruling and more importantly the NAS report. 1,511 shoeprints were taken from student volunteers in Auckland, Wellington and Dunedin, New Zealand. 500 shoeprints were sampled from student volunteers at Australian universities. 100 from each of the University of Technology in Sydney, University of Queensland in Brisbane, University of Newcastle, Charles Sturt University in Bathurst and University of Canberra, Australia. These cities are distributed along the east coast of Australia. The shoeprints, taken from each country, were compared against each other for the presence of any pattern correspondences However shoeprints have not been compared between countries. In all locations the pattern of some common and many rare outsole patterns was repeated, with Converse Chuck Taylor All Stars and Vans Canvas Era common in all locations.

Helping formulate propositions in forensic DNA analysis.

The Bayesian paradigm is the preferred approach to evidence interpretation. It requires the evaluation of the probability of the evidence under at least two propositions. The value of the findings (i.e., our LR) will depend on these propositions and the case information, so it is crucial to identify which propositions are useful for the case at hand. Previously, a number of principles have been advanced and largely accepted for the evaluation of evidence. In the evaluation of traces involving DNA mixtures there may be more than two propositions possible. We apply these principles to some exemplar situations. We also show that in some cases, when there are no clear propositions or no defendant, a forensic scientist may be able to generate explanations to account for observations. In that case, the scientist plays a role of investigator, rather than evaluator. We believe that it is helpful for the scientist to distinguish those two roles.

Extending the discussion on inconsistency in forensic decisions and results.

The subject of inter- and intra-laboratory inconsistency was recently raised in a commentary by Itiel Dror. We re-visit an inter-laboratory trial, with which some of the authors of this current discussion were associated, to diagnose the causes of any differences in the likelihood ratios (LRs) assigned using probabilistic genotyping software. Some of the variation was due to different decisions that would be made on a case-by-case basis, some due to laboratory policy and would hence differ between laboratories, and the final and smallest part was the run-to-run difference caused by the Monte Carlo aspect of the software used. However, the net variation in LRs was considerable. We believe that most laboratories will self-diagnose the cause of their difference from the majority answer and in some, but not all instances will take corrective action. An inter-laboratory exercise consisting of raw data files for relatively straightforward mixtures, such as two mixtures of three or four persons, would allow laboratories to calibrate their procedures and findings.

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 diagnosis of the primary difference between EuroForMix and STRmix™.

There is interest in comparing the output, principally the likelihood ratio, from the two probabilistic genotyping software EuroForMix (EFM) and STRmix™. Many of these comparison studies are descriptive and make little or no effort to diagnose the cause of difference. There are fundamental differences between EFM and STRmix™ that are causative of the largest set of likelihood ratio differences. This set of differences is for false donors where there are many instances of LRs just above or below 1 for EFM that give much lower LRs in STRmix™. This is caused by the separate estimation of parameters such as allele height variance and mixture proportion using MLE under Hp and Ha for EFM. This can result in very different estimations of these parameters under Hp and Ha . It results in a departure from calibration for EFM in the region of LRs just above and below 1.

Combining artificial neural network classification with fully continuous probabilistic genotyping to remove the need for an analytical threshold and electropherogram reading.

Standard processing of electrophoretic data within a forensic DNA laboratory is for one (or two) analysts to designate peaks as either artefactual or non-artefactual in a process commonly referred to as profile 'reading'. Recently, FaSTR™ DNA has been developed to use artificial neural networks to automatically classify fluorescence within an electropherogram as baseline, allele, stutter or pull-up. These classifications are based on probabilities assigned to each timepoint (scan) within the electropherogram. Instead of using the probabilities to assign fluorescence into a category they can be used directly in the profile analysis. This has a number of advantages; increased objectivity in DNA profile processing, the removal for the need for analysts to read profiles, the removal for the need of an analytical threshold. Models within STRmix™ were extended to incorporate the peak label probabilities assigned by FaSTR™ DNA. The performance of the model extensions was tested on a DNA mixture dataset, comprising 2-4 person samples. This dataset was processed in a 'standard' manner using an analytical threshold of 50rfu, analyst peak designations and STRmix™ V2.9 models. The same dataset was then processed in an automated manner using no analytical threshold, no analysts reading the profile and using the STRmix™ models extended to incorporate peak label probabilities. Both datasets were compared to the known DNA donors and a set of non-donors. The result between the two processes was a very close performance, but with a large efficiency gain in the 0rfu process. Utilising peak label probabilities opens up the possibility for a range of workflow process efficiency gains, but beyond this allows full use of all data within an electropherogram.

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.

An Investigation into Compound Likelihood Ratios for Forensic DNA Mixtures.

Simple propositions are defined as those with one POI and the remaining contributors unknown under Hp and all unknown contributors under Ha. Conditional propositions are defined as those with one POI, one or more assumed contributors, and the remaining contributors (if any) unknown under Hp, and the assumed contributor(s) and N unknown contributors under Ha. In this study, compound propositions are those with multiple POI and the remaining contributors unknown under Hp and all unknown contributors under Ha. We study the performance of these three proposition sets on thirty-two samples (two laboratories × four NOCs × four mixtures) consisting of four mixtures, each with N = 2, N = 3, N = 4, and N = 5 contributors using the probabilistic genotyping software, STRmix™. In this study, it was found that conditional propositions have a much higher ability to differentiate true from false donors than simple propositions. Compound propositions can misstate the weight of evidence given the propositions strongly in either direction.

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 interpretation of shoeprint comparison class correspondences.

The underlying principles involved in the interpretation of shoeprint comparisons have become a topical subject due to criticisms in the 2009 National Academy of Science (NAS) report on forensic sciences [1]. Difficulties in the application and understanding of these principles were also highlighted in a recent court ruling [2-5]. We report here a survey that may inform some aspects of this interpretation and discuss the implications of findings from this survey in the light of that court ruling and more importantly the NAS report. Five hundred shoeprints taken from student volunteers in Auckland, New Zealand were compared against each other for the presence of any pattern correspondences. Comparisons were undertaken of the full outsole and of smaller portions of the more common patterns. Of the 500 shoe impressions collected 488 (97.6%) were ultimately represented only once in the survey. The greatest number of corresponding patterns was for the most common brand of shoe (Converse Chuck Taylor All Star) and occurred in 3 of 500 observations. No instances of an imitation brand matching the authentic brand were found. Smaller sections of the common patterns showed a greater number of corresponding prints. However, the greatest number of matching partial patterns was again for the most common brand of shoe (Converse Chuck Taylor All Star) and occurred in 29 of 500 observations. We conclude that pattern match alone is of considerable evidential value even when the print is partial.

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.

Study of CTS DNA Proficiency Tests with Regard to DNA Mixture Interpretation: A NIST Scientific Foundation Review.

The National Institute of Standards and Technology has released a document entitled DNA Mixture Interpretation: A NIST Scientific Foundation Review for public comment. This has become known as the Draft NIST Foundation Review. It contains the statement: "Across these 69 data sets, there were 80 false negatives and 18 false positives reported from 110,408 possible responses (27,602 participants × two evidence items × two reference items). In the past five years, the number of participants using PGS has grown." We examine a set of proficiency test results to determine if these NIST statements could be justified. The summary reports for each relevant forensic biology test (Forensic Biology, Semen, and Mixture) in the years 2018-2021 were reviewed. Data were also provided to us by CTS upon our request. None of the false positives or negatives could be attributed to the mixture interpretation strategy and certainly not to the use of PGS.

Investigation into the effect of mixtures comprising related people on non-donor likelihood ratios, and potential practises to mitigate providing misleading opinions.

The interpretation of mixtures containing related individuals can be difficult due to allele sharing between the contributors. Challenges include the assignment of the number of contributors (NoC) to the mixture with the under assignment of NoC resulting in false exclusions of true donors. Non-donating relatives of the true contributors to mixtures of close relatives can result in likelihood ratios supporting their adventitious inclusion within the mixture. We examine the effect of non-donor likelihood ratios on mixtures of first order relatives. Mixtures of full siblings and parent-child were created by mixing the DNA from known family members in vitro, or by in silico simulation. Mixtures were interpreted using the probabilistic genotyping software STRmix™ and likelihood ratios were assigned for the true donors and non-donors who were either further relatives of the true donors or unrelated to the true donors. The two donor balanced mixtures deconvoluted straightforwardly when analysed as NoC = 2 giving approximately the experimental design 1:1 ratio. When analysed as NoC = 3 a very large number of non-donor genotypes produced LRs close to 1 including many instances of adventitious support. The in vitro three donor balanced mixtures proved difficult to assign as NoC = 3 by a blind examination of the profile. It is likely that many of these would be misassigned as NoC = 2. The analysis of the in vitro and in silico mixtures assuming NoC = 3 with no use of a conditioning profile or with the use of a conditioning profile but without informed priors on the mixture proportions (Mx priors) was ineffective. If the profile can be assigned as NoC = 3 then assignment of the Mx priors is straightforward. This analysis gave no false exclusions. Adventitious support did happen for relatives with high allele sharing. Adventitious support was not observed for any unrelated non-donors. The analysis of the three-person mixtures as NoC = 2 produced many false exclusions and fewer instances of adventitious support. The three donor unbalanced mixtures could all be assigned as NoC= 3. Analysis without Mx priors produced an alternate genotype explanation.