Fuzzy Paraopen Sets and Maps in Fuzzy Topological Spaces

The purpose of this article is to study the concepts of fuzzy para open and fuzzy para closet sets in fuzzy topological spaces Further, we introduce a few classes of fuzzy maps namely fuzzy part continuous, fuzzy part continuous, fuzzy para irresolute, fuzzy minimal part continuous, fuzzy maximal part continuous mappings and study their properties

Natural History of Geographic Atrophy Secondary to Age-Related Macular Degeneration: Results from the Prospective Proxima A and B Clinical Trials.

Abstract Purpose To better characterize visual function decline and geographic atrophy (GA) progression secondary to age-related macular degeneration (AMD). Design Proxima A (NCT02479386) and Proxima B (NCT02399072) were global, prospective, non-interventional, observational clinical trials. Participants Eligible patients were aged ≥50 years. Patients in Proxima A had bilateral GA without choroidal neovascularization (CNV) in either eye (N=295). Patients in Proxima B had GA with no CNV in the study eye and CNV±GA in the fellow eye (fellow eye CNV cohort, n=168); or GA with no CNV in the study eye, without CNV/GA in the fellow eye (fellow eye intermediate AMD cohort, n=32). Methods Changes in visual function and imaging/anatomic parameters were evaluated over time using a Mixed Model for Repeated Measurement (MMRM) accounting for key baseline characteristics. Main Outcome Measures Pre-specified endpoints included change in GA area from baseline, best corrected visual acuity (BCVA) score assessed by ETDRS, and BCVA under low-luminance conditions (LLVA). Results At 24 months, the adjusted mean (standard error; SE) change in GA lesion area from baseline was 3.87 (0.15) mm2 in participants with bilateral GA (Proxima A), 3.55 (0.16) mm2 in the fellow eye CNV cohort (Proxima B), and 2.96 (0.25) mm2 in the fellow eye intermediate AMD cohort (Proxima B). GA progression was greater in patients with baseline non-subfoveal (vs. subfoveal) GA lesions, and tended to increase as baseline low-luminance deficit increased (Proxima A; Proxima B, all patients). Conversion to GA or CNV in the fellow eye occurred in 30% and 6.7% of participants, respectively, in the Proxima B intermediate AMD cohort at month 12. Adjusted mean (SE) changes in BCVA and LLVA (ETDRS letters) in the study eye from baseline to 24 months: −13.88 (1.40) and −7.64 (1.20) in Proxima A, −9.49 (1.29) and −7.57 (1.26) in the Proxima B fellow eye CNV cohort, −11.48 (3.39) and −8.37 (3.02) in the Proxima B fellow eye intermediate AMD cohort, respectively. Conclusions The prospective Proxima A and B studies highlight the severe functional impact of GA and the rapid rate of GA lesion progression over a 2-year period, including in patients with unilateral GA at baseline

Embolic strokes of undetermined source: prevalence and patient features in the ESUS Global Registry

Background: Recent evidence supports that most non-lacunar cryptogenic strokes are embolic. Accordingly, these strokes have been designated as embolic strokes of undetermined source (ESUS). Aims: We undertook an international survey to characterize the frequency and clinical features of ESUS patients across global regions. Methods: Consecutive patients hospitalized for ischemic stroke were retrospectively surveyed from 19 stroke research centers in 19 different countries to collect patients meeting criteria for ESUS. Results: Of 2144 patients with recent ischemic stroke, 351 (16%, 95% CI 15% to 18%) met ESUS criteria, similar across global regions (range 16% to 21%), and an additional 308 (14%) patients had incomplete evaluation required for ESUS diagnosis. The mean age of ESUS patients (62 years; SD = 15) was significantly lower than the 1793 non-ESUS ischemic stroke patients (68 years, p ≤ 0.001). Excluding patients with atrial fibrillation (n = 590, mean age = 75 years), the mean age of the remaining 1203 non-ESUS ischemic stroke patients was 64 years (p = 0.02 vs. ESUS patients). Among ESUS patients, hypertension, diabetes, and prior stroke were present in 64%, 25%, and 17%, respectively. Median NIHSS score was 4 (interquartile range 2–8). At discharge, 90% of ESUS patients received antiplatelet therapy and 7% received anticoagulation. Conclusions: This cross-sectional global sample of patients with recent ischemic stroke shows that one-sixth met criteria for ESUS, with additional ESUS patients likely among those with incomplete diagnostic investigation. ESUS patients were relatively young with mild strokes. Antiplatelet therapy was the standard antithrombotic therapy for secondary stroke prevention in all global regions

Global survey of the frequency of atrial fibrillation-associated stroke: embolic stroke of undetermined source global registry

Background and Purpose—Atrial fibrillation (AF) is increasingly recognized as the single most important cause of disabling ischemic stroke in the elderly. We undertook an international survey to characterize the frequency of AF-associated stroke, methods of AF detection, and patient features. Methods—Consecutive patients hospitalized for ischemic stroke in 2013 to 2014 were surveyed from 19 stroke research centers in 19 different countries. Data were analyzed by global regions and World Bank income levels. Results—Of 2144 patients with ischemic stroke, 590 (28%; 95% confidence interval, 25.6–29.5) had AF-associated stroke, with highest frequencies in North America (35%) and Europe (33%) and lowest in Latin America (17%). Most had a history of AF before stroke (15%) or newly detected AF on electrocardiography (10%); only 2% of patients with ischemic stroke had unsuspected AF detected by poststroke cardiac rhythm monitoring. The mean age and 30-day mortality rate of patients with AF-associated stroke (75 years; SD, 11.5 years; 10%; 95% confidence interval, 7.6–12.6, respectively) were substantially higher than those of patients without AF (64 years; SD, 15.58 years; 4%; 95% confidence interval, 3.3–5.4; P<0.001 for both comparisons). There was a strong positive correlation between the mean age and the frequency of AF (r=0.76; P=0.0002). Conclusions—This cross-sectional global sample of patients with recent ischemic stroke shows a substantial frequency of AF-associated stroke throughout the world in proportion to the mean age of the stroke population. Most AF is identified by history or electrocardiography; the yield of conventional short-duration cardiac rhythm monitoring is relatively low. Patients with AF-associated stroke were typically elderly (>75 years old) and more often women

Rivaroxaban or aspirin for patent foramen ovale and embolic stroke of undetermined source: a prespecified subgroup analysis from the NAVIGATE ESUS trial

Background: Patent foramen ovale (PFO) is a contributor to embolic stroke of undetermined source (ESUS). Subgroup analyses from previous studies suggest that anticoagulation could reduce recurrent stroke compared with antiplatelet therapy. We hypothesised that anticoagulant treatment with rivaroxaban, an oral factor Xa inhibitor, would reduce the risk of recurrent ischaemic stroke compared with aspirin among patients with PFO enrolled in the NAVIGATE ESUS trial. Methods: NAVIGATE ESUS was a double-blinded, randomised, phase 3 trial done at 459 centres in 31 countries that assessed the efficacy and safety of rivaroxaban versus aspirin for secondary stroke prevention in patients with ESUS. For this prespecified subgroup analysis, cohorts with and without PFO were defined on the basis of transthoracic echocardiography (TTE) and transoesophageal echocardiography (TOE). The primary efficacy outcome was time to recurrent ischaemic stroke between treatment groups. The primary safety outcome was major bleeding, according to the criteria of the International Society of Thrombosis and Haemostasis. The primary analyses were based on the intention-to-treat population. Additionally, we did a systematic review and random-effects meta-analysis of studies in which patients with cryptogenic stroke and PFO were randomly assigned to receive anticoagulant or antiplatelet therapy. Findings: Between Dec 23, 2014, and Sept 20, 2017, 7213 participants were enrolled and assigned to receive rivaroxaban (n=3609) or aspirin (n=3604). Patients were followed up for a mean of 11 months because of early trial termination. PFO was reported as present in 534 (7·4%) patients on the basis of either TTE or TOE. Patients with PFO assigned to receive aspirin had a recurrent ischaemic stroke rate of 4·8 events per 100 person-years compared with 2·6 events per 100 person-years in those treated with rivaroxaban. Among patients with known PFO, there was insufficient evidence to support a difference in risk of recurrent ischaemic stroke between rivaroxaban and aspirin (hazard ratio [HR] 0·54; 95% CI 0·22–1·36), and the risk was similar for those without known PFO (1·06; 0·84–1·33; pinteraction=0·18). The risks of major bleeding with rivaroxaban versus aspirin were similar in patients with PFO detected (HR 2·05; 95% CI 0·51–8·18) and in those without PFO detected (HR 2·82; 95% CI 1·69–4·70; pinteraction=0·68). The random-effects meta-analysis combined data from NAVIGATE ESUS with data from two previous trials (PICSS and CLOSE) and yielded a summary odds ratio of 0·48 (95% CI 0·24–0·96; p=0·04) for ischaemic stroke in favour of anticoagulation, without evidence of heterogeneity. Interpretation: Among patients with ESUS who have PFO, anticoagulation might reduce the risk of recurrent stroke by about half, although substantial imprecision remains. Dedicated trials of anticoagulation versus antiplatelet therapy or PFO closure, or both, are warranted. Funding: Bayer and Janssen

Rivaroxaban or aspirin for patent foramen ovale and embolic stroke of undetermined source: a prespecified subgroup analysis from the NAVIGATE ESUS trial

Background: Patent foramen ovale (PFO) is a contributor to embolic stroke of undetermined source (ESUS). Subgroup analyses from previous studies suggest that anticoagulation could reduce recurrent stroke compared with antiplatelet therapy. We hypothesised that anticoagulant treatment with rivaroxaban, an oral factor Xa inhibitor, would reduce the risk of recurrent ischaemic stroke compared with aspirin among patients with PFO enrolled in the NAVIGATE ESUS trial. Methods: NAVIGATE ESUS was a double-blinded, randomised, phase 3 trial done at 459 centres in 31 countries that assessed the efficacy and safety of rivaroxaban versus aspirin for secondary stroke prevention in patients with ESUS. For this prespecified subgroup analysis, cohorts with and without PFO were defined on the basis of transthoracic echocardiography (TTE) and transoesophageal echocardiography (TOE). The primary efficacy outcome was time to recurrent ischaemic stroke between treatment groups. The primary safety outcome was major bleeding, according to the criteria of the International Society of Thrombosis and Haemostasis. The primary analyses were based on the intention-to-treat population. Additionally, we did a systematic review and random-effects meta-analysis of studies in which patients with cryptogenic stroke and PFO were randomly assigned to receive anticoagulant or antiplatelet therapy. Findings: Between Dec 23, 2014, and Sept 20, 2017, 7213 participants were enrolled and assigned to receive rivaroxaban (n=3609) or aspirin (n=3604). Patients were followed up for a mean of 11 months because of early trial termination. PFO was reported as present in 534 (7·4%) patients on the basis of either TTE or TOE. Patients with PFO assigned to receive aspirin had a recurrent ischaemic stroke rate of 4·8 events per 100 person-years compared with 2·6 events per 100 person-years in those treated with rivaroxaban. Among patients with known PFO, there was insufficient evidence to support a difference in risk of recurrent ischaemic stroke between rivaroxaban and aspirin (hazard ratio [HR] 0·54; 95% CI 0·22–1·36), and the risk was similar for those without known PFO (1·06; 0·84–1·33; pinteraction=0·18). The risks of major bleeding with rivaroxaban versus aspirin were similar in patients with PFO detected (HR 2·05; 95% CI 0·51–8·18) and in those without PFO detected (HR 2·82; 95% CI 1·69–4·70; pinteraction=0·68). The random-effects meta-analysis combined data from NAVIGATE ESUS with data from two previous trials (PICSS and CLOSE) and yielded a summary odds ratio of 0·48 (95% CI 0·24–0·96; p=0·04) for ischaemic stroke in favour of anticoagulation, without evidence of heterogeneity. Interpretation: Among patients with ESUS who have PFO, anticoagulation might reduce the risk of recurrent stroke by about half, although substantial imprecision remains. Dedicated trials of anticoagulation versus antiplatelet therapy or PFO closure, or both, are warranted. Funding: Bayer and Janssen

Characterization of patients with embolic strokes of undetermined source in the NAVIGATE ESUS randomized trial

Background: The New Approach Rivaroxaban Inhibition of Factor Xa in a Global Trial vs. ASA to Prevent Embolism in Embolic Stroke of Undetermined Source (NAVIGATE-ESUS) trial is a randomized phase-III trial comparing rivaroxaban versus aspirin in patients with recent ESUS. Aims: We aimed to describe the baseline characteristics of this large ESUS cohort to explore relationships among key subgroups. Methods: We enrolled 7213 patients at 459 sites in 31 countries. Prespecified subgroups for primary safety and efficacy analyses included age, sex, race, global region, stroke or transient ischemic attack prior to qualifying event, time to randomization, hypertension, and diabetes mellitus. Results: Mean age was 66.9 ± 9.8 years; 24% were under 60 years. Older patients had more hypertension, coronary disease, and cancer. Strokes in older subjects were more frequently cortical and accompanied by radiographic evidence of prior infarction. Women comprised 38% of participants and were older than men. Patients from East Asia were oldest whereas those from Latin America were youngest. Patients in the Americas more frequently were on aspirin prior to the qualifying stroke. Acute cortical infarction was more common in the United States, Canada, and Western Europe, whereas prior radiographic infarctions were most common in East Asia. Approximately forty-five percent of subjects were enrolled within 30 days of the qualifying stroke, with earliest enrollments in Asia and Eastern Europe. Conclusions: NAVIGATE-ESUS is the largest randomized trial comparing antithrombotic strategies for secondary stroke prevention in patients with ESUS. The study population encompasses a broad array of patients across multiple continents and these subgroups provide ample opportunities for future research

Modeling sequential event times using family data

In genetic epidemiology, families harboring certain genetic mutations are predisposed to successive cancers in their lifetime. This thesis aims to provide reliable estimates of relative risk and age-dependent cumulative risks (penetrance) associated with the mutated gene for successive cancers. We develop a statistical framework for modeling sequential event times arising from family data. A shared frailty model is employed to incorporate the dependence between the two event times. Because families are ascertained through non-random sampling, an ascertainment-corrected retrospective likelihood approach is proposed to account for the non-ignorable sampling design. Simulation studies demonstrate that our proposed method provides unbiased and reliable estimates of disease risks associated with a mutated gene. The frailty approach is also compared to an independent model that ignores the dependence between the events. Finally, we illustrate our approach using 12 Lynch syndrome families and provide penetrance estimates for developing first and second colorectal cancer

Fuzzy paraopen sets and maps in fuzzy topological spaces

<p>The purpose of this article is to study the concepts of fuzzy paraopen and fuzzy paraclosed sets in fuzzy topological spaces Further, we introduce few class of fuzzy maps namely fuzzy paracontinuous, ∗-fuzzy paracontinuous, fuzzy parairresolute, fuzzy minimal paracontinuous, fuzzy maximal paracontinuous mappings and study their prpoerties. </p&gt

Ophthalmol Sci

PURPOSE: To describe the design and rationale of the phase 3 TENAYA (ClinicalTrials.gov identifier, NCT03823287) and LUCERNE (ClinicalTrials.gov identifier, NCT03823300) trials that aimed to assess efficacy, safety, and durability of faricimab, the first bispecific antibody for intraocular use, which independently binds and neutralizes both angiopoietin-2 and vascular endothelial growth factor-A (VEGF-A) versus aflibercept in patients with neovascular age-related macular degeneration (nAMD). DESIGN: Identical, global, double-masked, randomized, controlled, phase 3 clinical trials. PARTICIPANTS: Adults with treatment-naïve nAMD. METHODS: These trials were designed to evaluate patients randomized to receive faricimab 6.0 mg up to every 16 weeks after 4 initial every-4-week doses or aflibercept 2.0 mg every 8 weeks after 3 initial every-4-week doses. The initial doses in the faricimab arm were followed by individualized fixed treatment intervals up to week 60, based on disease activity assessment at weeks 20 and 24, guided by central subfield thickness, best-corrected visual acuity (BCVA), and investigator assessment. The primary efficacy end point was BCVA change from baseline averaged over weeks 40, 44, and 48. Secondary end points included the proportion of patients receiving every-8-week, every-12-week, and every-16-week faricimab and anatomic outcomes. Safety outcomes included incidence and severity of ocular and nonocular adverse events. From week 60, faricimab-treated patients followed a personalized treatment interval (PTI), a novel protocol-driven treat-and-extend regimen with interval adjustment from every 8 weeks to every 16 weeks based on individualized treatment response measured by anatomic criteria, functional criteria, and investigator assessment of patients' disease activity. MAIN OUTCOME MEASURES: Rationale for trial design and PTI approach. RESULTS: The TENAYA and LUCERNE trials were the first registrational trials in nAMD to test fixed dosing regimens up to every 16 weeks based on patients' disease activity in year 1 and incorporate a PTI paradigm during year 2. The PTI approach was designed to tailor treatment intervals to individual patient needs, to reflect clinical practice treatment practice, and to reduce treatment burden. CONCLUSIONS: The innovative trial design rationale for the TENAYA and LUCERNE trials included maximizing the benefits of angiopoietin-2 blockade through dosing up to every 16 weeks and PTI regimens based on patients' disease activity while fulfilling health authority requirements for potential registrational efforts