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BACKGROUND: Medulloblastoma is associated with rare hereditary cancer predisposition syndromes; however, consensus medulloblastoma predisposition genes have not been defined and screening guidelines for genetic counselling and testing for paediatric patients are not available. We aimed to assess and define these genes to provide evidence for future screening guidelines. METHODS: In this international, multicentre study, we analysed patients with medulloblastoma from retrospective cohorts (International Cancer Genome Consortium [ICGC] PedBrain, Medulloblastoma Advanced Genomics International Consortium [MAGIC], and the CEFALO series) and from prospective cohorts from four clinical studies (SJMB03, SJMB12, SJYC07, and I-HIT-MED). Whole-genome sequences and exome sequences from blood and tumour samples were analysed for rare damaging germline mutations in cancer predisposition genes. DNA methylation profiling was done to determine consensus molecular subgroups: WNT (MBWNT), SHH (MBSHH), group 3 (MBGroup3), and group 4 (MBGroup4). Medulloblastoma predisposition genes were predicted on the basis of rare variant burden tests against controls without a cancer diagnosis from the Exome Aggregation Consortium (ExAC). Previously defined somatic mutational signatures were used to further classify medulloblastoma genomes into two groups, a clock-like group (signatures 1 and 5) and a homologous recombination repair deficiency-like group (signatures 3 and 8), and chromothripsis was investigated using previously established criteria. Progression-free survival and overall survival were modelled for patients with a genetic predisposition to medulloblastoma. FINDINGS: We included a total of 1022 patients with medulloblastoma from the retrospective cohorts (n=673) and the four prospective studies (n=349), from whom blood samples (n=1022) and tumour samples (n=800) were analysed for germline mutations in 110 cancer predisposition genes. In our rare variant burden analysis, we compared these against 53 105 sequenced controls from ExAC and identified APC, BRCA2, PALB2, PTCH1, SUFU, and TP53 as consensus medulloblastoma predisposition genes according to our rare variant burden analysis and estimated that germline mutations accounted for 6% of medulloblastoma diagnoses in the retrospective cohort. The prevalence of genetic predispositions differed between molecular subgroups in the retrospective cohort and was highest for patients in the MBSHH subgroup (20% in the retrospective cohort). These estimates were replicated in the prospective clinical cohort (germline mutations accounted for 5% of medulloblastoma diagnoses, with the highest prevalence [14%] in the MBSHH subgroup). Patients with germline APC mutations developed MBWNT and accounted for most (five [71%] of seven) cases of MBWNT that had no somatic CTNNB1 exon 3 mutations. Patients with germline mutations in SUFU and PTCH1 mostly developed infant MBSHH. Germline TP53 mutations presented only in childhood patients in the MBSHH subgroup and explained more than half (eight [57%] of 14) of all chromothripsis events in this subgroup. Germline mutations in PALB2 and BRCA2 were observed across the MBSHH, MBGroup3, and MBGroup4 molecular subgroups and were associated with mutational signatures typical of homologous recombination repair deficiency. In patients with a genetic predisposition to medulloblastoma, 5-year progression-free survival was 52% (95% CI 40-69) and 5-year overall survival was 65% (95% CI 52-81); these survival estimates differed significantly across patients with germline mutations in different medulloblastoma predisposition genes. INTERPRETATION: Genetic counselling and testing should be used as a standard-of-care procedure in patients with MBWNT and MBSHH because these patients have the highest prevalence of damaging germline mutations in known cancer predisposition genes. We propose criteria for routine genetic screening for patients with medulloblastoma based on clinical and molecular tumour characteristics. FUNDING: German Cancer Aid; German Federal Ministry of Education and Research; German Childhood Cancer Foundation (Deutsche Kinderkrebsstiftung); European Research Council; National Institutes of Health; Canadian Institutes for Health Research; German Cancer Research Center; St Jude Comprehensive Cancer Center; American Lebanese Syrian Associated Charities; Swiss National Science Foundation; European Molecular Biology Organization; Cancer Research UK; Hertie Foundation; Alexander and Margaret Stewart Trust; V Foundation for Cancer Research; Sontag Foundation; Musicians Against Childhood Cancer; BC Cancer Foundation; Swedish Council for Health, Working Life and Welfare; Swedish Research Council; Swedish Cancer Society; the Swedish Radiation Protection Authority; Danish Strategic Research Council; Swiss Federal Office of Public Health; Swiss Research Foundation on Mobile Communication; Masaryk University; Ministry of Health of the Czech Republic; Research Council of Norway; Genome Canada; Genome BC; Terry Fox Research Institute; Ontario Institute for Cancer Research; Pediatric Oncology Group of Ontario; The Family of Kathleen Lorette and the Clark H Smith Brain Tumour Centre; Montreal Children's Hospital Foundation; The Hospital for Sick Children: Sonia and Arthur Labatt Brain Tumour Research Centre, Chief of Research Fund, Cancer Genetics Program, Garron Family Cancer Centre, MDT's Garron Family Endowment; BC Childhood Cancer Parents Association; Cure Search Foundation; Pediatric Brain Tumor Foundation; Brainchild; and the Government of Ontario.