Wronskian Formulation of the Spectrum of Curvature Perturbations

We present a new formulation for the evaluation of the primordial spectrum of curvature perturbations generated during inflation, using the fact that the Wronskian of the scalar field perturbation equation is constant. In the literature, there are many works on the same issue focusing on a few specific aspects or effects. Here we deal with the general multi-component scalar field, and show that our new formalism gives a method to evaluate the final amplitude of the curvature perturbation systematically and economically. The advantage of the new method is that one only has to solve a single mode of the scalar field perturbation equation backward in time from the end of inflation to the stage at which the perturbation is within the Hubble horizon, at which the initial values of the scalar field perturbations are given. We also clarify the relation of the new method with the new delta N formalism recently developed in Lee et al.(2005).Comment: 13 pages, 1 figures, submitted to JCAP, Minor corrections have been mad

Impact of primary kidney disease on the effects of empagliflozin in patients with chronic kidney disease: secondary analyses of the EMPA-KIDNEY trial

Background: The EMPA KIDNEY trial showed that empagliflozin reduced the risk of the primary composite outcome of kidney disease progression or cardiovascular death in patients with chronic kidney disease mainly through slowing progression. We aimed to assess how effects of empagliflozin might differ by primary kidney disease across its broad population. Methods: EMPA-KIDNEY, a randomised, controlled, phase 3 trial, was conducted at 241 centres in eight countries (Canada, China, Germany, Italy, Japan, Malaysia, the UK, and the USA). Patients were eligible if their estimated glomerular filtration rate (eGFR) was 20 to less than 45 mL/min per 1·73 m2, or 45 to less than 90 mL/min per 1·73 m2 with a urinary albumin-to-creatinine ratio (uACR) of 200 mg/g or higher at screening. They were randomly assigned (1:1) to 10 mg oral empagliflozin once daily or matching placebo. Effects on kidney disease progression (defined as a sustained ≥40% eGFR decline from randomisation, end-stage kidney disease, a sustained eGFR below 10 mL/min per 1·73 m2, or death from kidney failure) were assessed using prespecified Cox models, and eGFR slope analyses used shared parameter models. Subgroup comparisons were performed by including relevant interaction terms in models. EMPA-KIDNEY is registered with ClinicalTrials.gov, NCT03594110. Findings: Between May 15, 2019, and April 16, 2021, 6609 participants were randomly assigned and followed up for a median of 2·0 years (IQR 1·5–2·4). Prespecified subgroupings by primary kidney disease included 2057 (31·1%) participants with diabetic kidney disease, 1669 (25·3%) with glomerular disease, 1445 (21·9%) with hypertensive or renovascular disease, and 1438 (21·8%) with other or unknown causes. Kidney disease progression occurred in 384 (11·6%) of 3304 patients in the empagliflozin group and 504 (15·2%) of 3305 patients in the placebo group (hazard ratio 0·71 [95% CI 0·62–0·81]), with no evidence that the relative effect size varied significantly by primary kidney disease (pheterogeneity=0·62). The between-group difference in chronic eGFR slopes (ie, from 2 months to final follow-up) was 1·37 mL/min per 1·73 m2 per year (95% CI 1·16–1·59), representing a 50% (42–58) reduction in the rate of chronic eGFR decline. This relative effect of empagliflozin on chronic eGFR slope was similar in analyses by different primary kidney diseases, including in explorations by type of glomerular disease and diabetes (p values for heterogeneity all >0·1). Interpretation: In a broad range of patients with chronic kidney disease at risk of progression, including a wide range of non-diabetic causes of chronic kidney disease, empagliflozin reduced risk of kidney disease progression. Relative effect sizes were broadly similar irrespective of the cause of primary kidney disease, suggesting that SGLT2 inhibitors should be part of a standard of care to minimise risk of kidney failure in chronic kidney disease. Funding: Boehringer Ingelheim, Eli Lilly, and UK Medical Research Council

Rivaroxaban with or without aspirin in stable cardiovascular disease

BACKGROUND: We evaluated whether rivaroxaban alone or in combination with aspirin would be more effective than aspirin alone for secondary cardiovascular prevention. METHODS: In this double-blind trial, we randomly assigned 27,395 participants with stable atherosclerotic vascular disease to receive rivaroxaban (2.5 mg twice daily) plus aspirin (100 mg once daily), rivaroxaban (5 mg twice daily), or aspirin (100 mg once daily). The primary outcome was a composite of cardiovascular death, stroke, or myocardial infarction. The study was stopped for superiority of the rivaroxaban-plus-aspirin group after a mean follow-up of 23 months. RESULTS: The primary outcome occurred in fewer patients in the rivaroxaban-plus-aspirin group than in the aspirin-alone group (379 patients [4.1%] vs. 496 patients [5.4%]; hazard ratio, 0.76; 95% confidence interval [CI], 0.66 to 0.86; P<0.001; z=−4.126), but major bleeding events occurred in more patients in the rivaroxaban-plus-aspirin group (288 patients [3.1%] vs. 170 patients [1.9%]; hazard ratio, 1.70; 95% CI, 1.40 to 2.05; P<0.001). There was no significant difference in intracranial or fatal bleeding between these two groups. There were 313 deaths (3.4%) in the rivaroxaban-plus-aspirin group as compared with 378 (4.1%) in the aspirin-alone group (hazard ratio, 0.82; 95% CI, 0.71 to 0.96; P=0.01; threshold P value for significance, 0.0025). The primary outcome did not occur in significantly fewer patients in the rivaroxaban-alone group than in the aspirin-alone group, but major bleeding events occurred in more patients in the rivaroxaban-alone group. CONCLUSIONS: Among patients with stable atherosclerotic vascular disease, those assigned to rivaroxaban (2.5 mg twice daily) plus aspirin had better cardiovascular outcomes and more major bleeding events than those assigned to aspirin alone. Rivaroxaban (5 mg twice daily) alone did not result in better cardiovascular outcomes than aspirin alone and resulted in more major bleeding events

Effects of empagliflozin on progression of chronic kidney disease: a prespecified secondary analysis from the empa-kidney trial

Background: Sodium–glucose co-transporter-2 (SGLT2) inhibitors reduce progression of chronic kidney disease and the risk of cardiovascular morbidity and mortality in a wide range of patients. However, their effects on kidney disease progression in some patients with chronic kidney disease are unclear because few clinical kidney outcomes occurred among such patients in the completed trials. In particular, some guidelines stratify their level of recommendation about who should be treated with SGLT2 inhibitors based on diabetes status and albuminuria. We aimed to assess the effects of empagliflozin on progression of chronic kidney disease both overall and among specific types of participants in the EMPA-KIDNEY trial. Methods: EMPA-KIDNEY, a randomised, controlled, phase 3 trial, was conducted at 241 centres in eight countries (Canada, China, Germany, Italy, Japan, Malaysia, the UK, and the USA), and included individuals aged 18 years or older with an estimated glomerular filtration rate (eGFR) of 20 to less than 45 mL/min per 1·73 m2, or with an eGFR of 45 to less than 90 mL/min per 1·73 m2 with a urinary albumin-to-creatinine ratio (uACR) of 200 mg/g or higher. We explored the effects of 10 mg oral empagliflozin once daily versus placebo on the annualised rate of change in estimated glomerular filtration rate (eGFR slope), a tertiary outcome. We studied the acute slope (from randomisation to 2 months) and chronic slope (from 2 months onwards) separately, using shared parameter models to estimate the latter. Analyses were done in all randomly assigned participants by intention to treat. EMPA-KIDNEY is registered at ClinicalTrials.gov, NCT03594110. Findings: Between May 15, 2019, and April 16, 2021, 6609 participants were randomly assigned and then followed up for a median of 2·0 years (IQR 1·5–2·4). Prespecified subgroups of eGFR included 2282 (34·5%) participants with an eGFR of less than 30 mL/min per 1·73 m2, 2928 (44·3%) with an eGFR of 30 to less than 45 mL/min per 1·73 m2, and 1399 (21·2%) with an eGFR 45 mL/min per 1·73 m2 or higher. Prespecified subgroups of uACR included 1328 (20·1%) with a uACR of less than 30 mg/g, 1864 (28·2%) with a uACR of 30 to 300 mg/g, and 3417 (51·7%) with a uACR of more than 300 mg/g. Overall, allocation to empagliflozin caused an acute 2·12 mL/min per 1·73 m2 (95% CI 1·83–2·41) reduction in eGFR, equivalent to a 6% (5–6) dip in the first 2 months. After this, it halved the chronic slope from –2·75 to –1·37 mL/min per 1·73 m2 per year (relative difference 50%, 95% CI 42–58). The absolute and relative benefits of empagliflozin on the magnitude of the chronic slope varied significantly depending on diabetes status and baseline levels of eGFR and uACR. In particular, the absolute difference in chronic slopes was lower in patients with lower baseline uACR, but because this group progressed more slowly than those with higher uACR, this translated to a larger relative difference in chronic slopes in this group (86% [36–136] reduction in the chronic slope among those with baseline uACR &lt;30 mg/g compared with a 29% [19–38] reduction for those with baseline uACR ≥2000 mg/g; ptrend&lt;0·0001). Interpretation: Empagliflozin slowed the rate of progression of chronic kidney disease among all types of participant in the EMPA-KIDNEY trial, including those with little albuminuria. Albuminuria alone should not be used to determine whether to treat with an SGLT2 inhibitor. Funding: Boehringer Ingelheim and Eli Lilly

Impact of primary kidney disease on the effects of empagliflozin in patients with chronic kidney disease: secondary analyses of the EMPA-KIDNEY trial

Background: The EMPA-KIDNEY trial showed that empagliflozin reduced the risk of the primary composite outcome of kidney disease progression or cardiovascular death in patients with chronic kidney disease mainly through slowing progression. We aimed to assess how effects of empagliflozin might differ by primary kidney disease across its broad population. Methods: EMPA-KIDNEY, a randomised, controlled, phase 3 trial, was conducted at 241 centres in eight countries (Canada, China, Germany, Italy, Japan, Malaysia, the UK, and the USA). Patients were eligible if their estimated glomerular filtration rate (eGFR) was 20 to less than 45 mL/min per 1·73 m2, or 45 to less than 90 mL/min per 1·73 m2 with a urinary albumin-to-creatinine ratio (uACR) of 200 mg/g or higher at screening. They were randomly assigned (1:1) to 10 mg oral empagliflozin once daily or matching placebo. Effects on kidney disease progression (defined as a sustained ≥40% eGFR decline from randomisation, end-stage kidney disease, a sustained eGFR below 10 mL/min per 1·73 m2, or death from kidney failure) were assessed using prespecified Cox models, and eGFR slope analyses used shared parameter models. Subgroup comparisons were performed by including relevant interaction terms in models. EMPA-KIDNEY is registered with ClinicalTrials.gov, NCT03594110. Findings: Between May 15, 2019, and April 16, 2021, 6609 participants were randomly assigned and followed up for a median of 2·0 years (IQR 1·5–2·4). Prespecified subgroupings by primary kidney disease included 2057 (31·1%) participants with diabetic kidney disease, 1669 (25·3%) with glomerular disease, 1445 (21·9%) with hypertensive or renovascular disease, and 1438 (21·8%) with other or unknown causes. Kidney disease progression occurred in 384 (11·6%) of 3304 patients in the empagliflozin group and 504 (15·2%) of 3305 patients in the placebo group (hazard ratio 0·71 [95% CI 0·62–0·81]), with no evidence that the relative effect size varied significantly by primary kidney disease (pheterogeneity=0·62). The between-group difference in chronic eGFR slopes (ie, from 2 months to final follow-up) was 1·37 mL/min per 1·73 m2 per year (95% CI 1·16–1·59), representing a 50% (42–58) reduction in the rate of chronic eGFR decline. This relative effect of empagliflozin on chronic eGFR slope was similar in analyses by different primary kidney diseases, including in explorations by type of glomerular disease and diabetes (p values for heterogeneity all &gt;0·1). Interpretation: In a broad range of patients with chronic kidney disease at risk of progression, including a wide range of non-diabetic causes of chronic kidney disease, empagliflozin reduced risk of kidney disease progression. Relative effect sizes were broadly similar irrespective of the cause of primary kidney disease, suggesting that SGLT2 inhibitors should be part of a standard of care to minimise risk of kidney failure in chronic kidney disease. Funding: Boehringer Ingelheim, Eli Lilly, and UK Medical Research Council

Impact of primary kidney disease on the effects of empagliflozin in patients with chronic kidney disease: secondary analyses of the EMPA-KIDNEY trial

Background: The EMPA-KIDNEY trial showed that empagliflozin reduced the risk of the primary composite outcome of kidney disease progression or cardiovascular death in patients with chronic kidney disease mainly through slowing progression. We aimed to assess how effects of empagliflozin might differ by primary kidney disease across its broad population. Methods: EMPA-KIDNEY, a randomised, controlled, phase 3 trial, was conducted at 241 centres in eight countries (Canada, China, Germany, Italy, Japan, Malaysia, the UK, and the USA). Patients were eligible if their estimated glomerular filtration rate (eGFR) was 20 to less than 45 mL/min per 1·73 m2, or 45 to less than 90 mL/min per 1·73 m2 with a urinary albumin-to-creatinine ratio (uACR) of 200 mg/g or higher at screening. They were randomly assigned (1:1) to 10 mg oral empagliflozin once daily or matching placebo. Effects on kidney disease progression (defined as a sustained ≥40% eGFR decline from randomisation, end-stage kidney disease, a sustained eGFR below 10 mL/min per 1·73 m2, or death from kidney failure) were assessed using prespecified Cox models, and eGFR slope analyses used shared parameter models. Subgroup comparisons were performed by including relevant interaction terms in models. EMPA-KIDNEY is registered with ClinicalTrials.gov, NCT03594110. Findings: Between May 15, 2019, and April 16, 2021, 6609 participants were randomly assigned and followed up for a median of 2·0 years (IQR 1·5-2·4). Prespecified subgroupings by primary kidney disease included 2057 (31·1%) participants with diabetic kidney disease, 1669 (25·3%) with glomerular disease, 1445 (21·9%) with hypertensive or renovascular disease, and 1438 (21·8%) with other or unknown causes. Kidney disease progression occurred in 384 (11·6%) of 3304 patients in the empagliflozin group and 504 (15·2%) of 3305 patients in the placebo group (hazard ratio 0·71 [95% CI 0·62-0·81]), with no evidence that the relative effect size varied significantly by primary kidney disease (pheterogeneity=0·62). The between-group difference in chronic eGFR slopes (ie, from 2 months to final follow-up) was 1·37 mL/min per 1·73 m2 per year (95% CI 1·16-1·59), representing a 50% (42-58) reduction in the rate of chronic eGFR decline. This relative effect of empagliflozin on chronic eGFR slope was similar in analyses by different primary kidney diseases, including in explorations by type of glomerular disease and diabetes (p values for heterogeneity all >0·1). Interpretation: In a broad range of patients with chronic kidney disease at risk of progression, including a wide range of non-diabetic causes of chronic kidney disease, empagliflozin reduced risk of kidney disease progression. Relative effect sizes were broadly similar irrespective of the cause of primary kidney disease, suggesting that SGLT2 inhibitors should be part of a standard of care to minimise risk of kidney failure in chronic kidney disease. Funding: Boehringer Ingelheim, Eli Lilly, and UK Medical Research Council

Effects of empagliflozin on progression of chronic kidney disease: a prespecified secondary analysis from the empa-kidney trial

Background: Sodium-glucose co-transporter-2 (SGLT2) inhibitors reduce progression of chronic kidney disease and the risk of cardiovascular morbidity and mortality in a wide range of patients. However, their effects on kidney disease progression in some patients with chronic kidney disease are unclear because few clinical kidney outcomes occurred among such patients in the completed trials. In particular, some guidelines stratify their level of recommendation about who should be treated with SGLT2 inhibitors based on diabetes status and albuminuria. We aimed to assess the effects of empagliflozin on progression of chronic kidney disease both overall and among specific types of participants in the EMPA-KIDNEY trial. Methods: EMPA-KIDNEY, a randomised, controlled, phase 3 trial, was conducted at 241 centres in eight countries (Canada, China, Germany, Italy, Japan, Malaysia, the UK, and the USA), and included individuals aged 18 years or older with an estimated glomerular filtration rate (eGFR) of 20 to less than 45 mL/min per 1·73 m2, or with an eGFR of 45 to less than 90 mL/min per 1·73 m2 with a urinary albumin-to-creatinine ratio (uACR) of 200 mg/g or higher. We explored the effects of 10 mg oral empagliflozin once daily versus placebo on the annualised rate of change in estimated glomerular filtration rate (eGFR slope), a tertiary outcome. We studied the acute slope (from randomisation to 2 months) and chronic slope (from 2 months onwards) separately, using shared parameter models to estimate the latter. Analyses were done in all randomly assigned participants by intention to treat. EMPA-KIDNEY is registered at ClinicalTrials.gov, NCT03594110. Findings: Between May 15, 2019, and April 16, 2021, 6609 participants were randomly assigned and then followed up for a median of 2·0 years (IQR 1·5-2·4). Prespecified subgroups of eGFR included 2282 (34·5%) participants with an eGFR of less than 30 mL/min per 1·73 m2, 2928 (44·3%) with an eGFR of 30 to less than 45 mL/min per 1·73 m2, and 1399 (21·2%) with an eGFR 45 mL/min per 1·73 m2 or higher. Prespecified subgroups of uACR included 1328 (20·1%) with a uACR of less than 30 mg/g, 1864 (28·2%) with a uACR of 30 to 300 mg/g, and 3417 (51·7%) with a uACR of more than 300 mg/g. Overall, allocation to empagliflozin caused an acute 2·12 mL/min per 1·73 m2 (95% CI 1·83-2·41) reduction in eGFR, equivalent to a 6% (5-6) dip in the first 2 months. After this, it halved the chronic slope from -2·75 to -1·37 mL/min per 1·73 m2 per year (relative difference 50%, 95% CI 42-58). The absolute and relative benefits of empagliflozin on the magnitude of the chronic slope varied significantly depending on diabetes status and baseline levels of eGFR and uACR. In particular, the absolute difference in chronic slopes was lower in patients with lower baseline uACR, but because this group progressed more slowly than those with higher uACR, this translated to a larger relative difference in chronic slopes in this group (86% [36-136] reduction in the chronic slope among those with baseline uACR <30 mg/g compared with a 29% [19-38] reduction for those with baseline uACR ≥2000 mg/g; ptrend<0·0001). Interpretation: Empagliflozin slowed the rate of progression of chronic kidney disease among all types of participant in the EMPA-KIDNEY trial, including those with little albuminuria. Albuminuria alone should not be used to determine whether to treat with an SGLT2 inhibitor. Funding: Boehringer Ingelheim and Eli Lilly