Exploratory data analysis for the interpretation of low template DNA mixtures

The interpretation of DNA mixtures has proven to be a complex problem in forensic genetics. In particular, low template DNA samples, where alleles can be missing (allele drop-out), or where alleles unrelated to the crime-sample are amplified (allele drop-in), cannot be analysed with classical approaches such as random man not excluded or random match probability. Drop-out, drop-in, stutters and other PCR-related stochastic effects, create uncertainty about the composition of the crime-sample, making it difficult to attach a weight of evidence when (a) reference sample(s) is (are) compared to the crime-sample. In this paper, we use a probabilistic model to calculate likelihood ratios when there is uncertainty about the composition of the crime-sample. This model is essentially exploratory in the sense that it allows the exploration of LRs when two key-parameters, drop-out and drop-in are varied within their plausible ranges of variation. We build on the work of Curran et al., and improve their probabilistic model to allow more flexibility in the way the model parameters are applied. Two new main modifications are brought to their model: (i) different drop-out probabilities can be applied to different contributors, and (ii) different parameters can be used under the prosecution and the defence hypotheses. We illustrate how the LRs can be explored when the drop-out and drop-in parameters are varied, and suggest the use of Monte Carlo simulations to derive plausible ranges for the probability of drop-out. Although the model is suited for both high and low template samples, we illustrate the advantages of the exploratory approach through two DNA mixtures (involving two and at least three individuals) with low template components.