Finite time and asymptotic behaviour of the maximal excursion of a random walk

We evaluate the limit distribution of the maximal excursion of a random walk in any dimension for homogeneous environments and for self-similar supports under the assumption of spherical symmetry. This distribution is obtained in closed form and is an approximation of the exact distribution comparable to that obtained by real space renormalization methods. Then we focus on the early time behaviour of this quantity. The instantaneous diffusion exponent $\nu_n$ exhibits a systematic overshooting of the long time exponent. Exact results are obtained in one dimension up to third order in $n^{-1/2}$. In two dimensions, on a regular lattice and on the Sierpi\'nski gasket we find numerically that the analytic scaling $\nu_n \simeq \nu+A n^{-\nu}$ holds.Comment: 9 pages, 4 figures, accepted J. Phys.

Multicenter International Study of the Consensus Immunoscore for the Prediction of Relapse and Survival in Early-Stage Colon Cancer.

BACKGROUND The prognostic value of Immunoscore was evaluated in Stage II/III colon cancer (CC) patients, but it remains unclear in Stage I/II, and in early-stage subgroups at risk. An international Society for Immunotherapy of Cancer (SITC) study evaluated the pre-defined consensus Immunoscore in tumors from 1885 AJCC/UICC-TNM Stage I/II CC patients from Canada/USA (Cohort 1) and Europe/Asia (Cohort 2). METHODS Digital-pathology is used to quantify the densities of CD3+ and CD8+ T-lymphocyte in the center of tumor (CT) and the invasive margin (IM). The time to recurrence (TTR) was the primary endpoint. Secondary endpoints were disease-free survival (DFS), overall survival (OS), prognosis in Stage I, Stage II, Stage II-high-risk, and microsatellite-stable (MSS) patients. RESULTS High-Immunoscore presented with the lowest risk of recurrence in both cohorts. In Stage I/II, recurrence-free rates at 5 years were 78.4% (95%-CI, 74.4-82.6), 88.1% (95%-CI, 85.7-90.4), 93.4% (95%-CI, 91.1-95.8) in low, intermediate and high Immunoscore, respectively (HR (Hi vs. Lo) = 0.27 (95%-CI, 0.18-0.41); p < 0.0001). In Cox multivariable analysis, the association of Immunoscore to outcome was independent (TTR: HR (Hi vs. Lo) = 0.29, (95%-CI, 0.17-0.50); p < 0.0001) of the patient's gender, T-stage, sidedness, and microsatellite instability-status (MSI). A significant association of Immunoscore with survival was found for Stage II, high-risk Stage II, T4N0 and MSS patients. The Immunoscore also showed significant association with TTR in Stage-I (HR (Hi vs. Lo) = 0.07 (95%-CI, 0.01-0.61); P = 0.016). The Immunoscore had the strongest (69.5%) contribution χ2 for influencing survival. Patients with a high Immunoscore had prolonged TTR in T4N0 tumors even for patients not receiving chemotherapy, and the Immunoscore remained the only significant parameter in multivariable analysis. CONCLUSION In early CC, low Immunoscore reliably identifies patients at risk of relapse for whom a more intensive surveillance program or adjuvant treatment should be considered

Ovarian Cancer Pathology Characteristics as Predictors of Variant Pathogenicity in BRCA1 and BRCA2

BACKGROUND: The distribution of ovarian tumour characteristics differs between germline BRCA1 and BRCA2 pathogenic variant carriers and non-carriers. In this study, we assessed the utility of ovarian tumour characteristics as predictors of BRCA1 and BRCA2 variant pathogenicity, for application using the American College of Medical Genetics and the Association for Molecular Pathology (ACMG/AMP) variant classification system. METHODS: Data for 10,373 ovarian cancer cases, including carriers and non-carriers of BRCA1 or BRCA2 pathogenic variants, were collected from unpublished international cohorts and consortia and published studies. Likelihood ratios (LR) were calculated for the association of ovarian cancer histology and other characteristics, with BRCA1 and BRCA2 variant pathogenicity. Estimates were aligned to ACMG/AMP code strengths (supporting, moderate, strong). RESULTS: No histological subtype provided informative ACMG/AMP evidence in favour of BRCA1 and BRCA2 variant pathogenicity. Evidence against variant pathogenicity was estimated for the mucinous and clear cell histologies (supporting) and borderline cases (moderate). Refined associations are provided according to tumour grade, invasion and age at diagnosis. CONCLUSIONS: We provide detailed estimates for predicting BRCA1 and BRCA2 variant pathogenicity based on ovarian tumour characteristics. This evidence can be combined with other variant information under the ACMG/AMP classification system, to improve classification and carrier clinical management

Estrogen Receptor Status Oppositely Modifies Breast Cancer Prognosis in BRCA1/BRCA2 Mutation Carriers Versus Non-Carriers

Breast cancer (BC) prognosis in BRCA1 and BRCA2 mutation carriers has been reported contradictorily, and the significance of variables influencing prognosis in sporadic BC is not established in BC patients with hereditary BRCA1/BRCA2 mutations. In this retrospective cohort study, we analyzed the effect of clinicopathological characteristics on BC prognosis (disease-free survival [DFS] and disease-specific survival [DSS]) in hereditary BRCA1/BRCA2 mutation carriers. We enrolled 234 BRCA1/BRCA2 mutation carriers and 899 non-carriers, of whom 191 carriers and 680 non-carriers, with complete data, were available for survival analyses. We found that patients with ER-positive tumors developed disease recurrence 2.3-times more likely when they carried a BRCA1/BRCA2 mutation (23/60; 38.3% ER-positive carriers vs. 74/445; 16.6% ER-positive non-carriers; p < 0.001). ER-positive mutation carriers also had a 3.4-times higher risk of death due to BC compared with ER-positive non-carriers (13/60; 21.7% vs. 28/445; 6.3%; p < 0.001). Moreover, prognosis in ER-negative BRCA1/BRCA2 mutation carriers was comparable with that in ER-positive non-carriers. Our study demonstrates that ER-positivity worsens BC prognosis in BRCA1/BRCA2 mutation carriers, while prognosis for carriers with ER-negative tumors (including early-onset) is significantly better and comparable with that in ER-positive, older BC non-carriers. These observations indicate that BRCA1/BRCA2 mutation carriers with ER-positive BC represent high-risk patients