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In this trial, women between the ages of 60 and 90 with low bone mineral density received twice-yearly subcutaneous injections of denosumab, a fully human monoclonal antibody against the receptor activator of nuclear factor-κB ligand, which inhibits the development and activity of osteoclasts, or placebo. Denosumab was associated with a reduced risk of vertebral, nonvertebral, and hip fractures. Women between the ages of 60 and 90 with low bone mineral density received twice-yearly subcutaneous injections of denosumab, which inhibits the development and activity of osteoclasts, or placebo. Denosumab was associated with a reduced risk of vertebral, nonvertebral, and hip fractures. Fractures are a major cause of disability and health care costs. 1 , 2 The use of denosumab is a novel approach to fracture prevention. It is a fully human monoclonal antibody against the receptor activator of nuclear factor-κB ligand (RANKL), a cytokine that is essential for the formation, function, and survival of osteoclasts. 3 By binding RANKL, denosumab prevents the interaction of RANKL with its receptor, RANK, on osteoclasts and osteoclast precursors and reversibly inhibits osteoclast-mediated bone resorption. 4 In previous trials, the subcutaneous administration of 60 mg of denosumab every 6 months reduced bone turnover and increased bone mineral density. 5 – 8 We . . .

Men receiving androgen-deprivation therapy for nonmetastatic prostate cancer are at high risk for bone loss and fractures. This placebo-controlled study investigated the effects of denosumab, a fully human monoclonal antibody against the receptor activator of nuclear factor-κB ligand, on bone mineral density and fractures in such men. Use of denosumab was associated with increased bone mineral density at all sites and reduction in the incidence of new vertebral fractures. This study investigated the effects of denosumab on bone mineral density and fractures in men receiving androgen-deprivation therapy for prostate cancer. Use of denosumab was associated with increased bone mineral density at all sites and reduction in the incidence of new vertebral fractures. Prostate cancer is the most common newly diagnosed cancer in men worldwide. 1 In the United States, prostate cancer accounts for approximately 25% of all new cancer diagnoses and 10% of all deaths from cancer. 2 Androgen-deprivation therapy, through bilateral orchiectomy or treatment with gonadotropin-releasing hormone (GnRH) agonists, is the standard first-line therapy for metastatic prostate cancer. 3 , 4 GnRH agonists are also frequently used to treat men with nonmetastatic prostate cancer. 5 Androgen-deprivation therapy improves disease-free and overall survival in various clinical settings, such as when used as adjuvant treatment in men with locally advanced prostate cancer who are undergoing radiation therapy 6 , . . .

Bone metastases are a major cause of morbidity and mortality in men with prostate cancer. Preclinical studies suggest that osteoclast inhibition might prevent bone metastases. We assessed denosumab, a fully human anti-RANKL monoclonal antibody, for prevention of bone metastasis or death in non-metastatic castration-resistant prostate cancer. In this phase 3, double-blind, randomised, placebo-controlled study, men with non-metastatic castration-resistant prostate cancer at high risk of bone metastasis (prostate-specific antigen [PSA] ≥8·0 μg/L or PSA doubling time ≤10·0 months, or both) were enrolled at 319 centres from 30 countries. Patients were randomly assigned (1:1) via an interactive voice response system to receive subcutaneous denosumab 120 mg or subcutaneous placebo every 4 weeks. Randomisation was stratified by PSA eligibility criteria and previous or ongoing chemotherapy for prostate cancer. Patients, investigators, and all people involved in study conduct were masked to treatment allocation. The primary endpoint was bone-metastasis-free survival, a composite endpoint determined by time to first occurrence of bone metastasis (symptomatic or asymptomatic) or death from any cause. Efficacy analysis was by intention to treat. The masked treatment phase of the trial has been completed. This trial was registered at ClinicalTrials.gov, number NCT00286091. 1432 patients were randomly assigned to treatment groups (716 denosumab, 716 placebo). Denosumab significantly increased bone-metastasis-free survival by a median of 4·2 months compared with placebo (median 29·5 [95% CI 25·4–33·3] vs 25·2 [22·2–29·5] months; hazard ratio [HR] 0·85, 95% CI 0·73–0·98, p=0·028). Denosumab also significantly delayed time to first bone metastasis (33·2 [95% CI 29·5–38·0] vs 29·5 [22·4–33·1] months; HR 0·84, 95% CI 0·71–0·98, p=0·032). Overall survival did not differ between groups (denosumab, 43·9 [95% CI 40·1–not estimable] months vs placebo, 44·8 [40·1–not estimable] months; HR 1·01, 95% CI 0·85–1·20, p=0·91). Rates of adverse events and serious adverse events were similar in both groups, except for osteonecrosis of the jaw and hypocalcaemia. 33 (5%) patients on denosumab developed osteonecrosis of the jaw versus none on placebo. Hypocalcaemia occurred in 12 (2%) patients on denosumab and two (<1%) on placebo. This large randomised study shows that targeting of the bone microenvironment can delay bone metastasis in men with prostate cancer. Amgen Inc.

Bone metastases are a major burden in men with advanced prostate cancer. We compared denosumab, a human monoclonal antibody against RANKL, with zoledronic acid for prevention of skeletal-related events in men with bone metastases from castration-resistant prostate cancer. In this phase 3 study, men with castration-resistant prostate cancer and no previous exposure to intravenous bisphosphonate were enrolled from 342 centres in 39 countries. An interactive voice response system was used to assign patients (1:1 ratio), according to a computer-generated randomisation sequence, to receive 120 mg subcutaneous denosumab plus intravenous placebo, or 4 mg intravenous zoledronic acid plus subcutaneous placebo, every 4 weeks until the primary analysis cutoff date. Randomisation was stratified by previous skeletal-related event, prostate-specific antigen concentration, and chemotherapy for prostate cancer within 6 weeks before randomisation. Supplemental calcium and vitamin D were strongly recommended. Patients, study staff, and investigators were masked to treatment assignment. The primary endpoint was time to first on-study skeletal-related event (pathological fracture, radiation therapy, surgery to bone, or spinal cord compression), and was assessed for non-inferiority. The same outcome was further assessed for superiority as a secondary endpoint. Efficacy analysis was by intention to treat. This study is registered with ClinicalTrials.gov, number NCT00321620, and has been completed. 1904 patients were randomised, of whom 950 assigned to denosumab and 951 assigned to receive zoledronic acid were eligible for the efficacy analysis. Median duration on study at primary analysis cutoff date was 12·2 months (IQR 5·9–18·5) for patients on denosumab and 11·2 months (IQR 5·6–17·4) for those on zoledronic acid. Median time to first on-study skeletal-related event was 20·7 months (95% CI 18·8–24·9) with denosumab compared with 17·1 months (15·0–19·4) with zoledronic acid (hazard ratio 0·82, 95% CI 0·71–0·95; p=0·0002 for non-inferiority; p=0·008 for superiority). Adverse events were recorded in 916 patients (97%) on denosumab and 918 patients (97%) on zoledronic acid, and serious adverse events were recorded in 594 patients (63%) on denosumab and 568 patients (60%) on zoledronic acid. More events of hypocalcaemia occurred in the denosumab group (121 [13%]) than in the zoledronic acid group (55 [6%]; p<0·0001). Osteonecrosis of the jaw occurred infrequently (22 [2%] vs 12 [1%]; p=0·09). Denosumab was better than zoledronic acid for prevention of skeletal-related events, and potentially represents a novel treatment option in men with bone metastases from castration-resistant prostate cancer. Amgen.

Receptor activator of nuclear factor-kappa B (RANK) ligand (RANKL) binds RANK on the surface of osteoclast precursors to trigger osteoclastogenesis. Recent studies have indicated that osteocytic RANKL has an important role in osteoclastogenesis during bone remodelling; however, the role of osteoblastic RANKL remains unclear. Here we show that vesicular RANK, which is secreted from the maturing osteoclasts, binds osteoblastic RANKL and promotes bone formation by triggering RANKL reverse signalling, which activates Runt-related transcription factor 2 (Runx2). The proline-rich motif in the RANKL cytoplasmic tail is required for reverse signalling, and a RANKL(Pro29Ala) point mutation reduces activation of the reverse signalling pathway. The coupling of bone resorption and formation is disrupted in RANKL(Pro29Ala) mutant mice, indicating that osteoblastic RANKL functions as a coupling signal acceptor that recognizes vesicular RANK. RANKL reverse signalling is therefore a potential pharmacological target for avoiding the reduced bone formation associated with inhibition of osteoclastogenesis. Osteoclasts secrete small extracellular vesicles that stimulate osteoblasts, promoting bone formation via receptor activator of nuclear factor-kappa B ligand (RANKL), thereby linking bone formation and resorption.

A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer product of vectors. A rank-1 order-$k$ tensor is the outer product of $k$ nonzero vectors. Any symmetric tensor can be decomposed into a linear combination of rank-1 tensors, each of which is symmetric or not. The rank of a symmetric tensor is the minimal number of rank-1 tensors that is necessary to reconstruct it. The symmetric rank is obtained when the constituting rank-1 tensors are imposed to be themselves symmetric. It is shown that rank and symmetric rank are equal in a number of cases and that they always exist in an algebraically closed field. We will discuss the notion of the generic symmetric rank, which, due to the work of Alexander and Hirschowitz [J. Algebraic Geom., 4 (1995), pp. 201-222], is now known for any values of dimension and order. We will also show that the set of symmetric tensors of symmetric rank at most $r$ is not closed unless $r=1$.

The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has to be fixed a priori. In this paper, we consider the optimization problem on the set of bounded-rank matrices. We propose a Riemannian rank-adaptive method, which consists of fixed-rank optimization, rank increase step and rank reduction step. We explore its performance applied to the low-rank matrix completion problem. Numerical experiments on synthetic and real-world datasets illustrate that the proposed rank-adaptive method compares favorably with state-of-the-art algorithms. In addition, it shows that one can incorporate each aspect of this rank-adaptive framework separately into existing algorithms for the purpose of improving performance.

Denosumab increased lumbar spine bone mineral density (BMD) versus placebo in a 2-year, randomized, placebo-controlled, phase 3 study of patients with hormone-receptor-positive, non-metastatic breast cancer and low bone mass who were receiving adjuvant aromatase inhibitor therapy. In subgroup analyses at 12 and 24 months, we evaluated factors (duration and type of aromatase inhibitor, tamoxifen use, age, time since menopause, body mass index, T-score) that might influence BMD at the lumbar spine, total hip, femoral neck, and 1/3 radius. Patients were randomized to receive placebo (n = 125) or 60 mg denosumab (n = 127) subcutaneously every 6 months. In all subgroups, 12 or 24 months' treatment with denosumab was associated with larger BMD gains than placebo across multiple skeletal sites. Most increases were statistically significant (P < 0.05). Twice-yearly administration of denosumab, regardless of patient subgroup or skeletal site, resulted in consistent increases in BMD versus placebo at 12 and 24 months.

Denosumab is a human IgG2 monoclonal antibody against receptor activator of nuclear factor kappa‐B ligand (RANKL) for the treatment of osteoporosis and bone loss. HLX14 is a proposed biosimilar of denosumab. This randomized, parallel‐group, two‐part, phase I study aimed to compare the pharmacokinetics, pharmacodynamics, safety, and immunogenicity of HLX14 with reference denosumab in Chinese healthy adult male participants. In Part 1, participants were randomized 1:1 and given HLX14 or reference denosumab sourced from the European Union (EU). In double‐blind Part 2, participants were randomized 1:1:1:1 to receive HLX14 or denosumab sourced from the United States, EU, or China. All study drugs were administered via subcutaneous injection at a single dose of 60 mg. The primary endpoints were area under the serum drug concentration–time curve from time 0 to the last concentration‐quantifiable time t (AUC0–t), maximum serum drug concentration (Cmax), and area under the serum drug concentration–time curve from time 0 to infinity (AUC0–inf). Twenty‐four participants were randomized in Part 1 and 228 in Part 2. The 90% confidence intervals of geometric mean ratio of AUC0–t, Cmax, and AUC0–inf between HLX14 and denosumab from different sources fell within the pre‐specified similarity margins of 0.80–1.25 (AUC0–t, 0.91–1.13; Cmax, 0.91–1.13; AUC0–inf, 0.91–1.12), demonstrating pharmacokinetic similarity. No notable difference was observed among treatment groups in pharmacodynamics, safety, or immunogenicity. HLX14 demonstrated highly similar pharmacokinetic characteristics with comparable pharmacodynamics, safety, and immunogenicity to denosumab, supporting its further investigation as a potential denosumab biosimilar.

The estimation of large covariance and precision matrices is fundamental in modern multivariate analysis. However, problems arise from the statistical analysis of large panel economic and financial data. The covariance matrix reveals marginal correlations between variables, while the precision matrix encodes conditional correlations between pairs of variables given the remaining variables. In this paper, we provide a selective review of several recent developments on the estimation of large covariance and precision matrices. We focus on two general approaches: a rank-based method and a factor-model-based method. Theories and applications of both approaches are presented. These methods are expected to be widely applicable to the analysis of economic and financial data.