Calculating likelihoods and likelihood ratios at SNPs-based mixtures. A reappraisal of the binomial inference, as applied to forensic identity tests

Single nucleotide polymorphisms (SNPs) are useful forensic markers. When a SNPs-based forensic protocol targets a body fluid stain, it returns elementary evidence regardless of the number of individuals that might have contributed to the stain deposition. Therefore, drawing inference from a mixed stain with SNPs is different than drawing it while using multinomial polymorphisms. We here revisit this subject, with a view to contribute to a fresher insight into it. First, we manage to model conditional semi-continuous likelihoods in terms of matrices of genotype permutations vs number of contributors (NTZsc). Secondly, we redefine some algebraic formulas to approach the semi-continuous calculation. To address allelic dropouts, we introduce a peak height ratio index ( h, or: the minor read divided by the major read at any NGS-based typing result) into the semi-continuous formulas, for they to act as an acceptable proxy of the split drop (Haned et al, 2012) model of calculation. Secondly, we introduce a new, empirical method to deduct the expected quantitative ratio at which the contributors of a mixture have originally mixed and the observed ratio generated by each genotype combination at each locus. Compliance between observed and expected quantity ratios is measured in terms of (1-{chi}2) values at each state of a locus deconvolution. These probability values are multiplied, along with the h index, to the relevant population probabilities to weigh the overall plausibility of each combination according to the quantitative perspective. We compare calculation performances of our empirical procedure (NITZq) with those of the EUROFORMIX software ver. 3.0.3. NITZq generates LR values a few orders of magnitude lower than EUROFORMIX when true contributors are used as POIs, but much lower LR values when false contributors are used as POIs. NITZ calculation routines may be useful, especially in combination with mass genomics typing protocols.