Accurate assessment of the weight of evidence for DNA mixtures by integrating the likelihood ratio.

Several methods exist for weight of evidence calculations on DNA mixtures. Especially if dropout is a possibility, it may be difficult to estimate mixture specific parameters needed for the evaluation. For semi-continuous models, the LR for a person to have contributed to a mixture depends on the specified number of contributors and the probability of dropout for each. We show here that, for the semi-continuous model that we consider, the weight of evidence can be accurately obtained by applying the standard statistical technique of integrating the likelihood ratio against the parameter likelihoods obtained from the mixture data. This method takes into account all likelihood ratios belonging to every choice of parameters, but LR's belonging to parameters that provide a better explanation to the mixture data put in more weight into the final result. We therefore avoid having to estimate the number of contributors or their probabilities of dropout, and let the whole evaluation depend on the mixture data and the allele frequencies, which is a practical advantage as well as a gain in objectivity. Using simulated mixtures, we compare the LR obtained in this way with the best informed LR, i.e., the LR using the parameters that were used to generate the data, and show that results obtained by integration of the LR approximate closely these ideal values. We investigate both contributors and non-contributors for mixtures with various numbers of contributors. For contributors we always obtain a result close to the best informed LR whereas non-contributors are excluded more strongly if a smaller dropout probability is imposed for them. The results therefore naturally lead us to reconsider what we mean by a contributor, or by the number of contributors.