{'fraction_non_alphanumeric': 0.03481190342504211, 'fraction_numerical': 0.020774845592363842, 'mean_word_length': 5.1875, 'pattern_counts': {'":': 0, '<': 3, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Potential Misrepresentation of Inherited Breast Cancer Risk by Common Germline Alleles

Hundreds of common variants have been found to confer small but significant differences in breast cancer risk, supporting the polygenic additive model of inherited risk. This widely accepted model is at odds with twin data indicating highly elevated risk in a subgroup of women. Using a novel closed-pattern-mining algorithm, we provide evidence that rare variants or haplotypes may underlie the association of breast cancer risk with common germline alleles. Our method, called Chromosome Overlap, consists in iteratively pairing chromosomes from affected individuals and looking for noncontiguous patterns of shared alleles without exhaustive enumeration. We applied Chromosome Overlap to haplotypes of genotyped SNPs from 9,011 female breast cancer cases from the UK Biobank (UKBB) at three topologically associating domains containing well-established common-allele "hits" for breast cancer. A total of 181,034 UKBB women of "white British" ancestry were used to assess the discovered haplotypes, and 55,346 cases and controls of European ancestry in the Discovery, Biology, and Risk of Inherited Variants in Breast Cancer (DRIVE) case-control study were used for replication. Out of twenty rare (frequency < -0.1%) risk haplotypes of large effect identified in UKBB at P < 1.0 x 10 ^ -5, four (hazard ratio: 4.22-20.2) were subsequently replicated in DRIVE (odds ratio: 2.13-11.9) at P < 0.05. Our results support the genetic heterogeneity and rare-variant/haplotype basis of breast cancer risk and suggest a novel type of "synthetic association" wherein common risk alleles on a rare risk haplotype may misrepresent disease risk through their tagging of many "false positive" haplotypes.