Forensic Population Genetics - Research Paper| Volume 52, 102481, May 2021
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# Comparing multiple POI to DNA mixtures

Published:February 09, 2021

## Highlights

• Propositions used to assess DNA comparisons should be functionally exhaustive.
• We combine various propositions so that collectively they are exhaustive.
• The LR formed given these exhaustive propositions is termed LRE.
• LRE is, in most cases, well approximated by assuming the other POI(s) is a donor.
• Advice is given when pairs of donors individually have LR > 1 but together LR = 0.

## Abstract

In casework, laboratories may be asked to compare DNA mixtures to multiple persons of interest (POI). Guidelines on forensic DNA mixture interpretation recommend that analysts consider several pairs of propositions; however, it is unclear if several likelihood ratios (LRs) per person should be reported or not. The propositions communicated to the court should not depend on the value of the LR. As such, we suggest that the propositions should be functionally exhaustive. This implies that all propositions with a non-zero prior probability need to be considered, at least initially. Those that have a significant posterior probability need to be used in the final evaluation. Using standard probability theory we combine various propositions so that collectively they are exhaustive. This involves a prior probability that the sub-proposition is true, given that the primary proposition is true. Imagine a case in which there are two possible donors: i and j. We focus our analysis first on donor i so that the primary proposition is that i is one of the sources of the DNA. In this example, given that i is a donor, we would further consider that j is either a donor or not. In practice, the prior weights for these sub-propositions may be difficult to assign. However, the LR is often linearly related to these priors and its behaviour is predictable. We also believe that these priors are unavoidable and are hidden in alternative methods.
We term the likelihood ratio formed from these context-exhaustive propositions $L R i / i ¯$.
$L R i / i ¯$ is trialed in a set of two- and three-person mixtures. For two-person mixtures, $L R i / i ¯$ is often well approximated by LRij/ja, where the subscript ij describes the proposition that i and j are the donors and ja describes the proposition that j and an alternate, unknown individual (a), who is unrelated to both i and j, are the donors. For three-person mixtures, $L R i / i ¯$ is often well approximated by LRijk/jka where the subscript ijk describes the proposition that i, j, and k are the donors and jka describes the proposition that j, k, and an unknown, unrelated (to i, j, and k) individual (a) are the donors. In our simulations, LRij/ja had fewer inclusionary LRs for non-contributors than the unconditioned LR (LRia/aa).

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