The comparison of DNA mixture profiles with multiple persons of interest

When we compare a DNA mixture profile to a single person of interest, there are often just two competing explanations considered, and the comparison of how likely these are to lead to the observed mixture is summarized by a likelihood ratio. However, in more complex cases this does not suffice, e.g., when there are multiple persons of interest. One can then compute several likelihood ratios, corresponding to several pairs of hypotheses, and subsequently decide which one(s) to report. This may lead to the computation of a rather large number of such likelihood ratios. In this article we advocate a systematic approach that starts by describing all relevant hypotheses. For each hypothesis, we then compute its likelihood (i.e., the probability to see the genetic data if the hypothesis is true). Based on the likelihoods of all considered hypotheses, one can then make a summary of the findings to report. This may be on the level of the considered hypotheses and/or with likelihood ratios per person of interest. We illustrate with several examples how this approach assists interpretation. The likelihoods summarize how the trace can help to distinguish between the considered hypotheses, in the sense that they transform the prior odds on them into posterior odds, without having to assign prior probabilities on the hypotheses for the calculation of the likelihoods themselves. On the other hand likelihood ratios (LR's) for individual PoI's cannot be obtained without these priors. In many cases these LR's will be quite insensitive to the choice of prior probabilities but in other cases they will be; we give examples of both.We argue that the table of likelihoods of the considered hypotheses is a more natural analog of the LR provided in the simple case with one PoI and two considered hypotheses, compared to the computation of a LR per PoI. We end with a discussion of the choice of prior probabilities, of the existing recommendations for this situation, and on reporting.