Interpretation of complex DNA proﬁles using empirical models and a method to measure their robustness Peter Gill a, * , James Curran b , Cedric Neumann a , Amanda Kirkham a , Tim Clayton c , Jonathan Whitaker c , Jim Lambert c a Forensic Science Service, Trident Court, 2960 Solihull Parkway, Solihull B37 7YN, UK b Department of Statistics, The University of Auckland, Private Bag 92019, Auckland, New Zealand c Forensic Science Service, Sandbeck Way, Audby Lane, West Yorkshire LS22 7DN, UK Received 3 May 2007; received in revised form 3 September 2007; accepted 9 October 2007 Abstract A new methodology is presented in order to report complex DNA proﬁles. We have brought together a number of different theories in order to devise a new protocol to interpret complex cases using likelihood ratios. The calculations are designed to be highly conservative and are widely applicable. We apply a low copy number (LCN) interpretation framework, which includes the probabilities of dropout and contamination, to ‘conventional’ DNA cases. In conventional casework, stutters often compromise calculations when they are observed with the same height as a minor contributor to a mixture. Stutters cannot be distinguished from minor alleles. We compensate by treating them as real alleles and including them in the calculation. By increasing the number of potential contributors to the DNA proﬁle, we can account for the extra alleles that result. We propose that the likelihood ratio is qualiﬁed with additional robustness parameters to indicate the probability of misleading evidence in favour of the prosecution, under the assumption that a random man was a contributor instead of the suspect. To do this we apply a new kind of case-speciﬁc ‘Tippett’ test. Although the method is complex, we suggest a ‘user-friendly’ way to explain the results to a court. The method is easily extended to carry out ranked likelihood ratio (LR) searches for suspects in national DNA databases. # 2007 Elsevier Ireland Ltd. All rights reserved. Keywords: Mixtures; Low copy number; Tippett test; Expert system; LoComatioN; Likelihood ratio 1. Introduction 1.1. Elimination of the ‘inconclusive’ DNA proﬁle Using traditional methods, it is only possible to report a DNA proﬁle that actually matches the suspect in whole or in part. Consequently, the probative value given always has a likelihood ratio (LR) greater than one. However, DNA proﬁles are often ambiguous—they may be partial, with alleles missing under prosecution (H p ) propositions; they may be mixtures; stutters may interfere with the interpretation. Every DNA scientist will routinely make decisions on whether to report a proﬁle in the context of missing alleles, or additional alleles in the proﬁle that do not match the suspect. Expert opinion is used to carry out the assessment, but this can lead to reporting inconsistencies where some scientists may apply a probative value to a result, whereas others may be more ‘cautious’ and provide an inconclusive result that neither includes nor excludes the suspect. For complex proﬁles, this means that a traditional calculation can only be carried out provided that simplifying assumptions are made—for example, if the proﬁle is partial then we must assume that dropout has occurred under the prosecution hypothesis. But, if the suspect genotype is ab and the crime stain proﬁle is a, then the numerator probability is less than one, and a traditional LR calculation may not be conservative [1,2], especially if the peak in the crime stain is sufﬁciently large such that the probability of dropout is effectively zero (Pr(D)  0) [2]. If the DNA proﬁle is complex, or if there are several bands that do not match the suspect reference proﬁle, then extra contributors or contamination (probabilistically measured by Pr(C) [1]) must also be considered. The judgement ‘call’ may be to report the DNA proﬁle as ‘inconclusive’, using a phrase such as ‘‘no meaningful www.elsevier.com/locate/fsig Available online at www.sciencedirect.com Forensic Science International: Genetics 2 (2008) 91–103 * Corresponding author. E-mail address: dnapgill@compuserve.com (P. Gill). 1872-4973/$ – see front matter # 2007 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.fsigen.2007.10.160