Evaluating the weight of evidence by using quantitative short tandem repeat data in DNA mixtures


Address for Correspondence: Torben Tvedebrink, Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK 9220 Aalborg East, Denmark.
E-mail: tvede@math.aau.dk


Summary.  The evaluation of results from mixtures of deoxyribonucleic acid (DNA) from two or more people in crime case investigations may be improved by taking not only the qualitative but also the quantitative part of the results into consideration. We present a statistical likelihood approach to assess the probability of observed peak heights and peak areas information for a pair of profiles matching the DNA mixture. Furthermore, we demonstrate how to incorporate this probability in the evaluation of the weight of the evidence by a likelihood ratio approach. Our model is based on a multivariate normal distribution of peak areas for assessing the weight of the evidence. On the basis of data from analyses of controlled experiments with mixed DNA samples, we exploited the linear relationship between peak heights and peak areas, and the linear relationships of the means and variances of the measurements. Furthermore, the contribution from one individual's allele to the mean area of this allele is assumed to be proportional to the average of peak height measurements of alleles, where the individual is the only contributor. For shared alleles in mixed DNA samples, it is possible to observe only the cumulative peak heights and areas. Complying with this latent structure, we used the EM algorithm to impute the missing variables on the basis of a compound symmetry model. The measurements were subject to intralocus and interlocus correlations not depending on the actual alleles of the DNA profiles. Owing to factorization of the likelihood, properties of the normal distribution and use of auxiliary variables, an ordinary implementation of the EM algorithm solved the missing data problem.