Complex mixtures: a critical examination of a paper by Homer et al.

DNA evidence in criminal cases may be challenging to interpret if several individuals have contributed to a DNA-mixture. The genetic markers conventionally used for forensic applications may be insufficient to resolve cases where there is a small fraction of DNA (say less than 10%) from some contributors or where there are several (say more than 4) contributors. Recently methods have been proposed that claim to substantially improve on existing approaches. The basic idea is to use high-density single nucleotide polymorphism (SNP) genotyping arrays including as many as 500,000 markers or more and explicitly exploit raw allele intensity measures. It is claimed that trace fractions of less than 0.1% can be reliably detected in mixtures with a large number of contributors. Specific forensic issues pertaining to the amount and quality of DNA are not discussed in the paper and will not be addressed here. Rather our paper critically examines the statistical methods and the validity of the conclusions drawn in Homer et al. (2008). We provide a mathematical argument showing that the suggested statistical approach will give misleading results for important cases. For instance, for a two person mixture an individual contributing less than 33% is expected to be declared a non-contributor. The quoted threshold 33% applies when all relative allele frequencies are 0.5. Simulations confirmed the mathematical findings and also provide results for more complex cases. We specified several scenarios for the number of contributors, the mixing proportions and allele frequencies and simulated as many as 500,000 SNPs. A controlled, blinded experiment was performed using the Illumina GoldenGate(®) 360 SNP test panel. Twenty-five mixtures were created from 2 to 5 contributors with proportions ranging from 0.01 to 0.99. The findings were consistent with the mathematical result and the simulations. We conclude that it is not possible to reliably infer the presence of minor contributors to mixtures following the approach suggested in Homer et al. (2008). The basic problem is that the method fails to account for mixing proportions.