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HLA class I molecules sit at the center of a trade-off: the same allele that helps T cells kill a tumor may also raise autoimmune risk. We built engageability — a new, validated, sequence-derived measure of how permissively an HLA allele's TCR-facing surface engages diverse T-cell receptors — and used it to show that immune "potency" is not one number but several independent axes. When public data proved structurally unable to answer the germline cancer-vs-autoimmunity trade-off (which we prove with an identifiability argument and a blind power analysis), we followed the statistical power to somatic immune escape across ~50,000 tumors. There the pipeline recovers the known B2M loss-of-function control and surfaces a novel, reproducible finding: a locus-wide HLA-B loss/retention hierarchy under HLA loss-of-heterozygosity, with HLA-B*58:01 the one allele individually singled out as preferentially lost (FDR 0.003) — pointing to the alleles tumors keep as escape-durable targets for TCR-based therapy.

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