Relationship inference based on DNA mixtures

Today, there exists a number of tools for solving kinship cases. But what happens when information comes from a mixture? DNA mixtures are in general rarely seen in kinship cases, but in a case presented to the Norwegian Institute of Public Health, sample DNA was obtained after a rape case that resulted in an unwanted pregnancy and abortion. The only available DNA from the fetus came in form of a mixture with the mother, and it was of interest to find the father of the fetus. The mother (the victim), however, refused to give her reference data and so commonly used methods for paternity testing were no longer applicable. As this case illustrates, kinship cases involving mixtures and missing reference profiles do occur and make the use of existing methods rather inconvenient. We here present statistical methods that may handle general relationship inference based on DNA mixtures. The basic idea is that likelihood calculations for mixtures can be decomposed into a series of kinship problems. This formulation of the problem facilitates the use of kinship software. We present the freely available R package relMix which extends on the R version of Familias. Complicating factors like mutations, silent alleles, and θ-correction are then easily handled for quite general family relationships, and are included in the statistical methods we develop in this paper. The methods and their implementations are exemplified on the data from the rape case.