Regression models for DNA-mixtures

This paper deals with the statistical interpretation of DNA mixture evidence. The conventional methods used in forensic casework today use something like 16 STR-markers. Power can be increased by rather using SNP-markers. New statistical methods are then needed, and we present a regression framework. The basic idea is that the traditional forensic hypotheses, commonly denoted HD and HP, are replaced by parametric versions: a person contributes to a mixture if and only if the fraction he contributes is greater than 0. This contributed fraction is a parameter of the regression model. The regression model uses the peak heights directly and there is no need to specify or estimate the number of contributors to the mixture. Also, drop-in and drop-out pose no principal problems. Data from 25 controlled blinded experiments were used to test the model. The number of contributors varied between 2 and 5, and the fractions contributed ranged from 0.01 to 0.99. The fractions were accurately estimated by the regression analyses. There were no false positives (i.e., in no cases were non-contributors declared to contributors). Some false negatives occurred for fractions of 0.1 or lower. Simulations were performed to test the model further. The analyses show that useful estimates can be obtained from a relatively small number of SNP-markers. Reasonable results are achieved using 300 markers which is close to the 313 SNPs in the controlled experiment. Increasing the number of SNPs, the analyses demonstrate that individuals contributing as little as 1% can reliably be detected, which suggests that cases beyond the reach of conventional forensic methods today can be reported.