Distinguishing between donors and their relatives in complex DNA mixtures with binary models

While likelihood ratio calculations were until the recent past limited to the evaluation of mixtures in which all alleles of all donors are present in the DNA mixture profile, more recent methods are able to deal with allelic dropout and drop-in. This opens up the possibility to obtain likelihood ratios for mixtures where this was not previously possible, but it also means that a full match between the alleged contributor and the crime stain is no longer necessary. We investigate in this article what the consequences are for relatives of the actual donors, because they typically share more alleles with the true donor than an unrelated individual. We do this with a semi-continuous binary approach, where the likelihood ratios are based on the observed alleles and the dropout probabilities for each donor, but not on the peak heights themselves. These models are widespread in the forensic community. Since in many cases a simple model is used where a uniform dropout probability is assumed for all (or for all unknown) contributors, we explore the extent to which this alters the false positive probabilities for relatives of donors, compared to what would have been obtained with the correct probabilities of dropout for each donor.