The analogy between DNA kinship and DNA mixture evaluation, with applications for the interpretation of likelihood ratios produced by possibly imperfect models

Two main applications of forensic DNA analysis are the investigation of possible relatedness and the investigation whether a person left DNA in a trace. Both of these are usually carried out by the calculation of likelihood ratios. In the kinship case, it is standard to let the likelihood ratio express the support in favour of the investigated relatedness versus no relatedness, and in the investigation of traces, one by default compares the hypothesis that the person of interest contributed DNA, versus that he is unrelated to any of the actual contributors. In both cases however, we can also view the probabilistic procedure as an inference of the profile of the person we look for: in other words, in both cases we carry out probabilistic genotyping. In this article we use this general analogy to develop various more specific analogies between kinship and mixture likelihood ratios. These analogies help to understand the concepts that play a role, and also to understand the importance of the statistical modeling needed for DNA mixtures. In this article, we apply our findings to consider what we can and cannot conclude from a likelihood ratio in favour of contribution to a mixed DNA profile, if that is computed by a model whose specifics are not entirely known to us, or where we do not know whether they provide a good description of the stochastic effects involved in the generation of DNA trace profiles. We show that, if unrelated individuals are adequately modeled, we can give bounds on how often LR's coming from certain types of black box models may arise, both for persons who are actual contributors and who are unrelated. In particular we show that no model, provided it satisfies basic requirements, can overestimate the evidence found for actual contributors both often and strongly.