Compound and Conditioned Likelihood Ratio Behavior within a Probabilistic Genotyping Context

Abstract

In cases where multiple questioned individuals are separately supported as contributors to a mixed DNA profile, guidance documents recommend performing a comparison to see if there is support for their joint contribution. Anecdotal observations suggest the summed log of the individual likelihood ratios (LR), termed the simple LR product, should be roughly equivalent to or less than the log(LR) for the joint likelihood ratio, termed the compound LR. To assist casework analysts in evaluating statistical weights applied to a case at hand, this study assessed how consistently compound LRs conform to an additive behavior when compared to the simple LR product counterparts. Two-, three-, and four-person DNA mixture data, of various mixture proportions and DNA inputs, were interpreted by STRmix® version 2.8 Probabilistic Genotyping Software. Relative magnitudes of LR increases were found to be dependent on both template level and mixture composition. The distribution of log(LR) differences between all compound/simple LR comparisons was ~−2.7 to ~28.3. This level of information gain was similar to that for compound LR comparisons, with and without interpretation conditioning (~−3.2 to ~27.7). In both scenarios, the probability density peaked at approximately 0.5, indicating the information gain from constrained genotype combinations has a comparable impact on the outcome of LR calculations whether the restriction is applied before or after interpretation.

Keywords

• likelihood ratio
• sub-source propositions
• conditioning
• compound LR
• additive behavior