Precision Through Frequency-Aware Prioritization: Introducing the Bouziane Similarity Index (BSI) for Rare Variants.

Current genetic similarity metrics, including Identity-by-State (IBS) and Kinship coefficients, treat all alleles equally, ignoring allele frequency differences and partial genetic sharing (Purcell et al., 2007; Speed & Balding, 2015). Despite the recognized biological importance of rare variants (Lee et al., 2012), no widely adopted similarity metric prioritizes rare variant sharing in relationship inference. We introduce two novel metrics: the Bouziane Similarity Index (BSI), a frequency-weighted score emphasizing rare variant matches, and BSI-VAR, a variant that integrates allele dosage and inverse variance weighting to capture partial allele sharing and amplify rare variant signals. To evaluate these metrics, we first performed unsupervised principal component analysis (PCA) on simulated genotype similarity matrices, showing that BSI and BSI-VAR provide clearer genetic structure compared to IBS. We then conducted controlled simulations involving Parent-Child, Sibling, and Random genetic pairs to quantify discriminative performance. Through all evaluations, BSI and especially BSI-VAR consistently outperformed IBS in distinguishing genetic relationships. These findings establish BSI and BSI-VAR as robust, interpretable, and rare-variant-aware alternatives for modern genetic similarity analysis, with potential applications in population genetics, ancestry inference, and precision medicine (Ashley, 2016; Manolio et al., 2009).