The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

A coding variant in RARG confers susceptibility to anthracycline-induced cardiotoxicity in childhood cancer

Anthracyclines are used in over 50% of childhood cancer treatment protocols, but their clinical usefulness is limited by anthracycline-induced cardiotoxicity (ACT) manifesting as asymptomatic cardiac dysfunction and congestive heart failure in up to 57% and 16% of patients, respectively. Candidate gene studies have reported genetic associations with ACT, but these studies have in general lacked robust patient numbers, independent replication or functional validation. Thus, the individual variability in ACT susceptibility remains largely unexplained. We performed a genome-wide association study in 280 patients of European ancestry treated for childhood cancer, with independent replication in similarly treated cohorts of 96 European and 80 non-European patients. We identified a nonsynonymous variant (rs2229774, p.Ser427Leu) in RARG highly associated with ACT (P = 5.9 × 10(-8), odds ratio (95% confidence interval) = 4.7 (2.7-8.3)). This variant alters RARG function, leading to derepression of the key ACT genetic determinant Top2b, and provides new insight into the pathophysiology of this severe adverse drug reaction.

Bivalirudin Versus Heparin Anticoagulation in Transcatheter Aortic Valve Replacement: The Randomized BRAVO-3 Trial.

BACKGROUND Anticoagulation is required during transcatheter aortic valve replacement (TAVR) procedures. Although an optimal regimen has not been determined, heparin is mainly used. Direct thrombin inhibition with bivalirudin may be an effective alternative to heparin as the procedural anticoagulant agent in this setting. OBJECTIVES The goal of this study was to determine whether bivalirudin offers an alternative to heparin as the procedural anticoagulant agent in patients undergoing TAVR. METHODS A total of 802 patients with aortic stenosis were randomized to undergo transfemoral TAVR with bivalirudin versus unfractionated heparin during the procedure. The 2 primary endpoints were major bleeding within 48 h or before hospital discharge (whichever occurred first) and 30-day net adverse clinical events, defined as the combination of major adverse cardiovascular events (all-cause mortality, myocardial infarction, or stroke) and major bleeding. RESULTS Anticoagulation with bivalirudin versus heparin did not meet superiority because it did not result in significantly lower rates of major bleeding at 48 h (6.9% vs. 9.0%; relative risk: 0.77; 95% confidence interval [CI]: 0.48 to 1.23; p = 0.27) or net adverse cardiovascular events at 30 days (14.4% vs. 16.1%; relative risk: 0.89; 95% CI: 0.64 to 1.24; risk difference: -1.72; 95% CI: -6.70 to 3.25; p = 0.50); regarding the latter, the prespecified noninferiority hypothesis was met (pnoninferiority < 0.01). Rates of major adverse cardiovascular events at 48 h were not significantly different (3.5% vs. 4.8%; relative risk: 0.73; 95% CI: 0.37 to 1.43; p = 0.35). At 48 h, the bivalirudin group had significantly fewer myocardial infarctions but more acute kidney injury events than the heparin group; at 30 days, these differences were no longer significant. CONCLUSIONS In this randomized trial of TAVR procedural pharmacotherapy, bivalirudin did not reduce rates of major bleeding at 48 h or net adverse cardiovascular events within 30 days compared with heparin. Although superiority was not shown, the noninferiority hypothesis was met with respect to the latter factor. Given the lower cost, heparin should remain the standard of care, and bivalirudin can be an alternative anticoagulant option in patients unable to receive heparin in TAVR. (International, Multi-center, Open-label, Randomized Controlled Trial in Patients Undergoing TAVR to Determine the Treatment Effect [Both Safety and Efficacy] of Using Bivalirudin Instead of UFH [BRAVO-2/3]; NCT01651780).

Steiner’s formula in the Heisenberg group

Steiner’s tube formula states that the volume of an ϵ-neighborhood of a smooth regular domain in Rn is a polynomial of degree n in the variable ϵ whose coefficients are curvature integrals (also called quermassintegrals). We prove a similar result in the sub-Riemannian setting of the first Heisenberg group. In contrast to the Euclidean setting, we find that the volume of an ϵ-neighborhood with respect to the Heisenberg metric is an analytic function of ϵ that is generally not a polynomial. The coefficients of the series expansion can be explicitly written in terms of integrals of iteratively defined canonical polynomials of just five curvature terms.

CPRPLOT2: Stata module to graph component-plus-residual plots for transformed regressors

cprplot2 is a variation of official Stata's cprplot and is used for graphing component-plus-residual plots (a.k.a. partial residual plots). Additional features (compared to cprplot): (1) cprplot2 can handle variables that enter the model repeatedly via different transformations (for example, polynomials). (2) cprplot2 can display component-plus-residual plots using the original units for transformed variables in the model. (3) A wrapper is provided to quickly display several component-plus-residual plots in a single image.

Recommendations for Genetic Testing to Reduce the Incidence of Anthracycline-induced Cardiotoxicity

AIM Anthracycline-induced cardiotoxicity (ACT) occurs in 57% of treated patients and remains an important limitation of anthracycline-based chemotherapy. In various genetic association studies, potential genetic risk markers for ACT have been identified. Therefore, we developed evidence-based clinical practice recommendations for pharmacogenomic testing to further individualize therapy based on ACT risk. METHODS We followed a standard guideline development process; including a systematic literature search, evidence synthesis and critical appraisal, and the development of clinical practice recommendations with an international expert group. RESULTS RARG rs2229774, SLC28A3 rs7853758 and UGT1A6 rs17863783 variants currently have the strongest and the most consistent evidence for association with ACT. Genetic variants in ABCC1, ABCC2, ABCC5, ABCB1, ABCB4, CBR3, RAC2, NCF4, CYBA, GSTP1, CAT, SULT2B1, POR, HAS3, SLC22A7, SCL22A17, HFE and NOS3 have also been associated with ACT, but require additional validation. We recommend pharmacogenomic testing for the RARG rs2229774 (S427L), SLC28A3 rs7853758 (L461L) and UGT1A6*4 rs17863783 (V209V) variants in childhood cancer patients with an indication for doxorubicin or daunorubicin therapy (Level B - moderate). Based on an overall risk stratification, taking into account genetic and clinical risk factors, we recommend a number of management options including increased frequency of echocardiogram monitoring, follow-up, as well as therapeutic options within the current standard of clinical practice. CONCLUSIONS Existing evidence demonstrates that genetic factors have the potential to improve the discrimination between individuals at higher and lower risk of ACT. Genetic testing may therefore support both patient care decisions and evidence development for an improved prevention of ACT.