ERM and RERM are optimal estimators for regression problems when malicious outliers corrupt the labels

We study Empirical Risk Minimizers (ERM) and Regularized Empirical Risk Minimizers (RERM) for regression problems with convex and $L$-Lipschitz loss functions. We consider a setting where |\cO| malicious outliers contaminate the labels. In that case, under a local Bernstein condition, we show that the $L_2$-error rate is bounded by r_N + AL |\cO|/N, where $N$ is the total number of observations, $r_N$ is the $L_2$-error rate in the non-contaminated setting and $A$ is a parameter coming from the local Bernstein condition. When $r_N$ is minimax-rate-optimal in a non-contaminated setting, the rate r_N + AL|\cO|/N is also minimax-rate-optimal when |\cO| outliers contaminate the label. The main results of the paper can be used for many non-regularized and regularized procedures under weak assumptions on the noise. We present results for Huber's M-estimators (without penalization or regularized by the $\ell_1$-norm) and for general regularized learning problems in reproducible kernel Hilbert spaces when the noise can be heavy-tailed.Comment: 2 figure

Who Is In Charge, and Who Should Be? The Disciplinary Role of the Commander in Military Justice Systems

BackgroundStandard therapy for newly diagnosed glioblastoma is radiotherapy plus temozolomide. In this phase 3 study, we evaluated the effect of the addition of bevacizumab to radiotherapy-temozolomide for the treatment of newly diagnosed glioblastoma. MethodsWe randomly assigned patients with supratentorial glioblastoma to receive intravenous bevacizumab (10 mg per kilogram of body weight every 2 weeks) or placebo, plus radiotherapy (2 Gy 5 days a week; maximum, 60 Gy) and oral temozolomide (75 mg per square meter of body-surface area per day) for 6 weeks. After a 28-day treatment break, maintenance bevacizumab (10 mg per kilogram intravenously every 2 weeks) or placebo, plus temozolomide (150 to 200 mg per square meter per day for 5 days), was continued for six 4-week cycles, followed by bevacizumab monotherapy (15 mg per kilogram intravenously every 3 weeks) or placebo until the disease progressed or unacceptable toxic effects developed. The coprimary end points were investigator-assessed progression-free survival and overall survival. ResultsA total of 458 patients were assigned to the bevacizumab group, and 463 patients to the placebo group. The median progression-free survival was longer in the bevacizumab group than in the placebo group (10.6 months vs. 6.2 months; stratified hazard ratio for progression or death, 0.64; 95% confidence interval [CI], 0.55 to 0.74; P<0.001). The benefit with respect to progression-free survival was observed across subgroups. Overall survival did not differ significantly between groups (stratified hazard ratio for death, 0.88; 95% CI, 0.76 to 1.02; P=0.10). The respective overall survival rates with bevacizumab and placebo were 72.4% and 66.3% at 1 year (P=0.049) and 33.9% and 30.1% at 2 years (P=0.24). Baseline health-related quality of life and performance status were maintained longer in the bevacizumab group, and the glucocorticoid requirement was lower. More patients in the bevacizumab group than in the placebo group had grade 3 or higher adverse events (66.8% vs. 51.3%) and grade 3 or higher adverse events often associated with bevacizumab (32.5% vs. 15.8%). ConclusionsThe addition of bevacizumab to radiotherapy-temozolomide did not improve survival in patients with glioblastoma. Improved progression-free survival and maintenance of baseline quality of life and performance status were observed with bevacizumab; however, the rate of adverse events was higher with bevacizumab than with placebo.

Use of metformin and outcome of patients with newly diagnosed glioblastoma: Pooled analysis

Metformin has been linked to improve survival of patients with various cancers. There is little information on survival of glioblastoma patients after use of metformin. We assessed the association between metformin use and survival in a pooled analysis of patient data from 1,731 individuals from the randomized AVAglio, CENTRIC and CORE trials. We performed multivariate Cox analyses for overall survival (OS) and progression-free survival (PFS) comparing patients' use of metformin at baseline and/or during concomitant radiochemotherapy (TMZ/RT). Further exploratory analyses investigated the effect of metformin with a history of diabetes and nonfasting glucose levels in relation to OS or PFS of glioblastoma patients. Metformin alone or in any combination was not significantly associated with OS or PFS (at baseline, hazard ratio [HR] for OS = 0.87; 95% confidence interval [CI] = 0.65-1.16; HR for PFS = 0.84; 95% CI = 0.64-1.10; during TMZ/RT HR for OS = 0.97; 95% CI = 0.68-1.38; HR for PFS = 1.02; 95% CI = 0.74-1.41). We found a statistically nonsignificant association of metformin monotherapy with glioblastoma survival at baseline (HR for OS = 0.68; 95% CI = 0.42-1.10; HR for PFS = 0.57; 95% CI = 0.36-0.91), but not during the TMZ/RT period (HR for OS = 0.90; 95% CI = 0.51-1.56; HR for PFS = 1.05; 95% CI = 0.64-1.73). Diabetes mellitus or increased nonfasting glucose levels were not associated with a difference in OS or PFS in our selected study population. Metformin did not prolong survival of patients with newly diagnosed glioblastoma in our analysis. Additional studies may identify patients with specific tumor characteristics that are associated with potential benefit from treatment with metformin, possibly due to metabolic vulnerabilities

End-binding 1 protein overexpression correlates with glioblastoma progression and sensitizes to <i>Vinca</i>-alkaloids <i>in vitro</i> and <i>in vivo</i>

International audienceEnd-binding 1 protein (EB1) is a key player in the regulation of microtubule (MT) dynamics. Here, we investigated the role of EB1 in glioblastoma (GBM) tumor progression and its potential predictive role for response to Vinca-alkaloid chemotherapy. Immunohistological analysis of the 109 human GBM cases revealed that EB1 overexpression correlated with poor outcome including progression-free survival and overall survival. Downregulation of EB1 by shRNA inhibited cell migration and proliferation in vitro. Conversely, EB1 overexpression promoted them and accelerated tumor growth in orthotopically-transplanted nude mice. Furthermore, EB1 was largely overexpressed in stem-like GBM6 that display in vivo a higher tumorigenicity with a more infiltrative pattern of migration than stem-like GBM9. GBM6 showed strong and EB1-dependent migratory potential. The predictive role of EB1 in the response of GBM cells to chemotherapy was investigated. Vinflunine and vincristine increased survival of EB1-overexpressing U87 bearing mice and were more effective to inhibit cell migration and proliferation in EB1-overexpressing clones than in controls. Vinca inhibited the increase of MT growth rate and growth length induced by EB1 overexpression. Altogether, our results show that EB1 expression level has a prognostic value in GBM, and that Vinca-alkaloid chemotherapy could improve the treatment of GBM patients with EB1-overexpressing tumor

Associations of levetiracetam use with the safety and tolerability profile of chemoradiotherapy for patients with newly diagnosed glioblastoma

Background Levetiracetam (LEV) is one of the most frequently used antiepileptic drugs (AED) for brain tumor patients with seizures. We hypothesized that toxicity of LEV and temozolomide-based chemoradiotherapy may overlap. Methods Using a pooled cohort of patients with newly diagnosed glioblastoma included in clinical trials prior to chemoradiotherapy (CENTRIC, CORE, AVAglio) or prior to maintenance therapy (ACT-IV), we tested associations of hematologic toxicity, nausea or emesis, fatigue, and psychiatric adverse events during concomitant and maintenance treatment with the use of LEV alone or with other AED versus other AED alone or in combination versus no AED use at the start of chemoradiotherapy and of maintenance treatment. Results Of 1681 and 2020 patients who started concomitant chemoradiotherapy and maintenance temozolomide, respectively, 473 and 714 patients (28.1% and 35.3%) were treated with a LEV-containing regimen, 538 and 475 patients (32.0% and 23.5%) with other AED, and 670 and 831 patients (39.9% and 41.1%) had no AED. LEV was associated with higher risk of psychiatric adverse events during concomitant treatment in univariable and multivariable analyses (RR 1.86 and 1.88, P < .001) while there were no associations with hematologic toxicity, nausea or emesis, or fatigue. LEV was associated with reduced risk of nausea or emesis during maintenance treatment in multivariable analysis (HR = 0.80, P = .017) while there were no associations with hematologic toxicity, fatigue, or psychiatric adverse events. Conclusions LEV is not associated with reduced tolerability of chemoradiotherapy in patients with glioblastoma regarding hematologic toxicity and fatigue. Antiemetic properties of LEV may be beneficial during maintenance temozolomide

MGMT Promoter Methylation Cutoff with Safety Margin for Selecting Glioblastoma Patients into Trials Omitting Temozolomide: A Pooled Analysis of Four Clinical Trials.

The methylation status of the O &lt;sup&gt;6&lt;/sup&gt; -methylguanine DNA methyltransferase (MGMT) gene promoter is predictive for benefit from temozolomide in glioblastoma (GBM). A clinically optimized cutoff was sought allowing patient selection for therapy without temozolomide, while avoiding to withhold it from patients who may potentially benefit.Experimental Design: Quantitative MGMT methylation-specific PCR data were obtained for newly diagnosed patients with GBM screened or treated with standard radiotherapy and temozolomide in four randomized trials. The pooled dataset was randomly split into a training and test dataset. The unsupervised cutoff was obtained at a 50% probability to be (un)methylated. ROC analysis identified an optimal cutoff supervised by overall survival (OS). For 4,041 patients valid MGMT results were obtained, whereof 1,725 were randomized. The unsupervised cutoff in the training dataset was 1.27 (log &lt;sub&gt;2&lt;/sub&gt; [1,000 × (MGMT+1)/ACTB]), separating unmethylated and methylated patients. The optimal supervised cutoff for unmethylated patients was -0.28 (AUC = 0.61), classifying "truly unmethylated" (≤-0.28) and "gray zone" patients (&gt;-0.28, ≤1.27), the latter comprising approximately 10% of cases. In contrast, for patients with MGMT methylation (&gt;1.27) more methylation was not related to better outcome. Both methylated and gray zone patients performed significantly better for OS than truly unmethylated patients [HR = 0.35, 95% confidence interval (CI), 0.27-0.45, P &lt; 0.0001; HR = 0.58, 95% CI, 0.43-0.78, P &lt; 0.001], validated in the test dataset. The MGMT assay was highly reproducible upon retesting of 218 paired samples (R &lt;sup&gt;2&lt;/sup&gt; = 0.94). Low MGMT methylation (gray zone) may confer some sensitivity to temozolomide treatment, hence the lower safety margin should be considered for selecting patients with unmethylated GBM into trials omitting temozolomide