A mixed DNA profile controversy revisited.

Semaan et al. (J Forensic Res, 2020, 11, 453) discuss a mock case "where eight different individuals [P1 through P8 ] could not be excluded in a mixed DNA analysis. Even though … expert DNA mixture analysis software was used." Two of these are the true donors. The LRs reported are incorrect due to the incorrect entry of propositions into LRmix Studio. This forced the software to account for most of the alleles as drop-in, resulting in LRs 60-70 orders of magnitude larger than expected. P1 , P2 , P4 , P5 , and P8 can be manually excluded using peak heights. This has relevance when using LRmix which does not use peak heights. We extend the work using the same two reference genotypes who were the true contributors as Semaan et al. (J Forensic Res, 2020, 11, 453). We simulate three two-donor mixtures with peak heights using these two genotypes and analyze using STRmix™. For the simulated 1:1 mixture, one of the non-donors' LRs supported him being a contributor when no conditioning was used. When considered in combination with any other potential donors (i.e., with conditioning), this non-donor was correctly eliminated. For the 3:1 mixture, all results correctly supported that the non-donors were not contributors. The low-template 4:1 mixture LRs with no conditioning showed support for all eight profiles as donors. However, the results from pair-wise conditioning showed that only the two ground truth donors had LRs supporting that they were contributors to the mixture. We recommend the use of peak heights and conditioning profiles, as this allows better sensitivity and specificity even when the persons share many alleles.

Comparing multiple POI to DNA mixtures.

In casework, laboratories may be asked to compare DNA mixtures to multiple persons of interest (POI). Guidelines on forensic DNA mixture interpretation recommend that analysts consider several pairs of propositions; however, it is unclear if several likelihood ratios (LRs) per person should be reported or not. The propositions communicated to the court should not depend on the value of the LR. As such, we suggest that the propositions should be functionally exhaustive. This implies that all propositions with a non-zero prior probability need to be considered, at least initially. Those that have a significant posterior probability need to be used in the final evaluation. Using standard probability theory we combine various propositions so that collectively they are exhaustive. This involves a prior probability that the sub-proposition is true, given that the primary proposition is true. Imagine a case in which there are two possible donors: i and j. We focus our analysis first on donor i so that the primary proposition is that i is one of the sources of the DNA. In this example, given that i is a donor, we would further consider that j is either a donor or not. In practice, the prior weights for these sub-propositions may be difficult to assign. However, the LR is often linearly related to these priors and its behaviour is predictable. We also believe that these priors are unavoidable and are hidden in alternative methods. We term the likelihood ratio formed from these context-exhaustive propositions LRi/i¯. LRi/i¯ is trialed in a set of two- and three-person mixtures. For two-person mixtures, LRi/i¯ is often well approximated by LRij/ja, where the subscript ij describes the proposition that i and j are the donors and ja describes the proposition that j and an alternate, unknown individual (a), who is unrelated to both i and j, are the donors. For three-person mixtures, LRi/i¯ is often well approximated by LRijk/jka where the subscript ijk describes the proposition that i, j, and k are the donors and jka describes the proposition that j, k, and an unknown, unrelated (to i, j, and k) individual (a) are the donors. In our simulations, LRij/ja had fewer inclusionary LRs for non-contributors than the unconditioned LR (LRia/aa).

Relaxing the assumption of unrelatedness in the numerator and denominator of likelihood ratios for DNA mixtures.

DNA mixtures will have multiple donors under both the prosecution and alternate propositions when assigning a likelihood ratio for forensic DNA evidence. These donors are usually assumed to be unrelated to each other. In this paper, we make a small, preliminary examination of the potential effect of relaxing this assumption. We consider the simple situation of a two-person mixture with no dropout and a two-person major/minor mixture with dropout of the minor contributor. We make no adjustment for subpopulation effects. Mixtures were simulated under two assumptions: 1. that the donors were siblings 2. or that they were unrelated. Both unresolvable and major/minor mixtures were considered. We compared the likelihood ratio assuming sibship with the likelihood ratio assuming no relatedness. The LR for hypotheses assuming no relatedness is less than the LR assuming relatedness approximately 95% of the time when relatives are present in the mixture.

Are low LRs reliable?

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

A review of likelihood ratios in forensic science based on a critique of Stiffelman "No longer the Gold standard: Probabilistic genotyping is changing the nature of DNA evidence in criminal trials".

Stiffelman [1] gives a broad critique of the application of likelihood ratios (LRs) in forensic science, in particular their use in probabilistic genotyping (PG) software. These are discussed in this review. LRs do not infringe on the ultimate issue. The Bayesian paradigm clearly separates the role of the scientist from that of the decision makers and distances the scientist from comment on the ultimate and subsidiary issues. LRs do not affect the reasonable doubt standard. Fact finders must still make decisions based on all the evidence and they must do this considering all evidence, not just that given probabilistically. LRs do not infringe on the presumption of innocence. The presumption of innocence does not equate with a prior probability of zero but simply that the person of interest (POI) is no more likely than anyone else to be the donor. Propositions need to be exhaustive within the context of the case. That is, propositions deemed relevant by either defense or prosecution which are not fanciful must not be omitted from consideration.

The interpretation of mixed DNA profiles from a mother, father, and child trio.

We report the interpretation of three-person mixed DNA profiles constructed from DNA from one mother, father, and child trio using the probabilistic genotyping software STRmix™. A total of 40 mixtures were examined, with varying total template and mixture proportions of the three contributors. In addition, mixtures were artificially degraded at four different rates to test the effects of degradation on the interpretation of mother, father and child trios. A total of 560 STRmix™ analyses were undertaken, examining four different interpretation strategies. Reasonable results were only achieved by conditioning on one parent as an assumed donor and applying a user-informed prior to the mixture proportion of both parents. For each of the 40 amplified mixtures, 10,000 non-donors were compared, conditioning on one parent and applying a user-informed prior to the mixture proportion of both parents. This leads to 800,000 non-donor tests.

Testing whether stutter and low-level DNA peaks are additive.

Peaks in an electropherogram could represent alleles, stutter product, or a combination of allele and stutter. Continuous probabilistic genotyping (PG) systems model the heights of peaks in an additive manner: for a shared or composite peak, PG models assume that the peak height is the sum of the allelic component and the stutter component. In this work we examine the assumption that the heights of overlapping alleles from a minor contributor and stutter peaks from a major contributor are additive. Any peak below the analytical threshold is considered unobserved; hence, in any dataset and particularly in low-template DNA profiles, some or many peaks may be unobserved or missing. Using simulation and empirical data, we show that an additive model can explain the heights of overlapping alleles from a minor contributor and stutter peaks from a major contributor as long as missing data are carefully considered. We use a naive method of imputation for the missing data which appears to perform adequately in this case. If missing data are ignored then the sum of stutter and allelic peaks is expected to be an overestimate of the average height of the composite peaks, as was observed in this study.