Statistical Methods for the Analysis of Forensic DNA Mixtures

Abstract

Forensic DNA mixtures are often interpreted statistically using a likelihood ratio. These ratios are of the form, "The evidence is LR times more likely when assuming the prosecution's hypothesis than when assuming the defense hypothesis." The likelihood ratio calculations rest on the allelic frequencies, yet these frequencies are estimated from only a small portion of the population. Therefore, because of sampling error, the likelihood ratio is an estimate, a random variable. In Chapter 2 the use of a confidence interval to report the variation of likelihood ratios is proposed. The formula for the confidence interval is herein explained and a computer program has been made available.

In Chapter 3, a maximum likelihood method is given for the inclusion of peak intensities in forensic DNA mixture likelihood ratio calculations. Observed peak intensities are the result of the underlying composition of the mixture: the amount contributed, and the genotypes of the contributors. This chapter proposes the use of the maximum likelihood method to weight each possible genotype combination by the likelihood of the genotype given the peak intensities. Models based on the Normal and Dirichlet distributions are described. Both models tend to weight more correct genotypes higher, though the Normal model puts much more emphasis on the best model(s) than the Dirichlet. This method can also be applied to certain cases of allele drop out.

In the final chapter, several different situations are explored. Four standard cases are considered: single-contributor evidence, two-contributor evidence, the paternity index, and the consideration of relationship by pedigree. These four standard cases are used as an introduction to basic concepts, which are in turn used to discuss more complicated cases later in the chapter. The more complicated cases discussed include analysis of a paternity index from a mixture, relatives and mixtures, consideration of relatives in the presence of population substructure, and a case of canine parentage under varying degrees of relatedness.