Mod-phi convergence I: Normality zones and precise deviations

In this paper, we use the framework of mod-$\phi$ convergence to prove precise large or moderate deviations for quite general sequences of real valued random variables $(X_{n})_{n \in \mathbb{N}}$, which can be lattice or non-lattice distributed. We establish precise estimates of the fluctuations $P[X_{n} \in t_{n}B]$, instead of the usual estimates for the rate of exponential decay $\log( P[X_{n}\in t_{n}B])$. Our approach provides us with a systematic way to characterise the normality zone, that is the zone in which the Gaussian approximation for the tails is still valid. Besides, the residue function measures the extent to which this approximation fails to hold at the edge of the normality zone. The first sections of the article are devoted to a proof of these abstract results and comparisons with existing results. We then propose new examples covered by this theory and coming from various areas of mathematics: classical probability theory, number theory (statistics of additive arithmetic functions), combinatorics (statistics of random permutations), random matrix theory (characteristic polynomials of random matrices in compact Lie groups), graph theory (number of subgraphs in a random Erd\H{o}s-R\'enyi graph), and non-commutative probability theory (asymptotics of random character values of symmetric groups). In particular, we complete our theory of precise deviations by a concrete method of cumulants and dependency graphs, which applies to many examples of sums of "weakly dependent" random variables. The large number as well as the variety of examples hint at a universality class for second order fluctuations.Comment: 103 pages. New (final) version: multiple small improvements ; a new section on mod-Gaussian convergence coming from the factorization of the generating function ; the multi-dimensional results have been moved to a forthcoming paper ; and the introduction has been reworke

Impact of nutraceuticals on markers of systemic inflammation: Potential relevance to cardiovascular diseases – A position paper from the International Lipid Expert Panel (ILEP)

Inflammation is a marker of arterial disease stemming from cholesterol-dependent to -independent molecular mechanisms. In recent years, the role of inflammation in atherogenesis has been underpinned by pharmacological approaches targeting systemic inflammation that have led to a significant reduction in cardiovascular disease (CVD) risk. Although the use of nutraceuticals to prevent CVD has largely focused on lipid-lowering (e.g, red-yeast rice and omega-3 fatty acids), there is growing interest and need, especially now in the time of coronavirus pandemic, in the use of nutraceuticals to reduce inflammatory markers, and potentially the inflammatory CVD burden, however, there is still not enough evidence to confirm this. Indeed, diet is an important lifestyle determinant of health and can influence both systemic and vascular inflammation, to varying extents, according to the individual nutraceutical constituents. Thus, the aim of this Position Paper is to provide the first attempt at recommendations on the use of nutraceuticals with effective anti-inflammatory properties

Efficacy and safety of bempedoic acid for the treatment of hypercholesterolemia: A systematic review and meta-analysis

Background Bempedoic acid is a first-in-class lipid-lowering drug recommended by guidelines for the treatment of hypercholesterolemia. Our objective was to estimate its average effect on plasma lipids in humans and its safety profile. Methods and findings We carried out a systematic review and meta-analysis of phase II and III randomized controlled trials on bempedoic acid (PROSPERO: CRD42019129687). PubMed (Medline), Scopus, Google Scholar, and Web of Science databases were searched, with no language restriction, from inception to 5 August 2019. We included 10 RCTs (n = 3,788) comprising 26 arms (active arm [n = 2,460]; control arm [n = 1,328]). Effect sizes for changes in lipids and high-sensitivity C-reactive protein (hsCRP) serum concentration were expressed as mean differences (MDs) and 95% confidence intervals (CIs). For safety analyses, odds ratios (ORs) and 95% CIs were calculated using the Mantel–Haenszel method. Bempedoic acid significantly reduced total cholesterol (MD −14.94%; 95% CI −17.31%, −12.57%; p < 0.001), non-high-density lipoprotein cholesterol (MD −18.17%; 95% CI −21.14%, −15.19%; p < 0.001), low-density lipoprotein cholesterol (MD −22.94%; 95% CI −26.63%, −19.25%; p < 0.001), low-density lipoprotein particle number (MD −20.67%; 95% CI −23.84%, −17.48%; p < 0.001), apolipoprotein B (MD −15.18%; 95% CI −17.41%, −12.95%; p < 0.001), high-density lipoprotein cholesterol (MD −5.83%; 95% CI −6.14%, −5.52%; p < 0.001), high-density lipoprotein particle number (MD −3.21%; 95% CI −6.40%, −0.02%; p = 0.049), and hsCRP (MD −27.03%; 95% CI −31.42%, −22.64%; p < 0.001). Bempedoic acid did not significantly modify triglyceride level (MD −1.51%; 95% CI −3.75%, 0.74%; p = 0.189), verylow-density lipoprotein particle number (MD 3.79%; 95% CI −9.81%, 17.39%; p = 0.585), and apolipoprotein A-1 (MD −1.83%; 95% CI −5.23%, 1.56%; p = 0.290). Treatment with bempedoic acid was positively associated with an increased risk of discontinuation of treatment (OR 1.37; 95% CI 1.06, 1.76; p = 0.015), elevated serum uric acid (OR 3.55; 95% CI 1.03, 12.27; p = 0.045), elevated liver enzymes (OR 4.28; 95% CI 1.34, 13.71; p = 0.014), and elevated creatine kinase (OR 3.79; 95% CI 1.06, 13.51; p = 0.04), though it was strongly associated with a decreased risk of new onset or worsening diabetes (OR 0.59; 95% CI 0.39, 0.90; p = 0.01). The main limitation of this meta-analysis is related to the relatively small number of individuals involved in the studies, which were often short or middle term in length. Conclusions Our results show that bempedoic acid has favorable effects on lipid profile and hsCRP levels and an acceptable safety profile. Further well-designed studies are needed to explore its longer-term safety

The impact of type of dietary protein, animal versus vegetable, in modifying cardiometabolic risk factors: A position paper from the International Lipid Expert Panel (ILEP)

Proteins play a crucial role in metabolism, in maintaining fluid and acid-base balance and antibody synthesis. Dietary proteins are important nutrients and are classified into: 1) animal proteins (meat, fish, poultry, eggs and dairy), and, 2) plant proteins (legumes, nuts and soy). Dietary modification is one of the most important lifestyle changes that has been shown to significantly decrease the risk of cardiovascular (CV) disease (CVD) by attenuating related risk factors. The CVD burden is reduced by optimum diet through replacement of unprocessed meat with low saturated fat, animal proteins and plant proteins. In view of the available evidence, it has become acceptable to emphasize the role of optimum nutrition to maintain arterial and CV health. Such healthy diets are thought to increase satiety, facilitate weight loss, and improve CV risk. Different studies have compared the benefits of omnivorous and vegetarian diets. Animal protein related risk has been suggested to be greater with red or processed meat over and above poultry, fish and nuts, which carry a lower risk for CVD. In contrast, others have shown no association of red meat intake with CVD. The aim of this expert opinion recommendation was to elucidate the different impact of animal vs vegetable protein on modifying cardiometabolic risk factors. Many observational and interventional studies confirmed that increasing protein intake, especially plant-based proteins and certain animal-based proteins (poultry, fish, unprocessed red meat low in saturated fats and low-fat dairy products) have a positive effect in modifying cardiometabolic risk factors. Red meat intake correlates with increased CVD risk, mainly because of its non-protein ingredients (saturated fats). However, the way red meat is cooked and preserved matters. Thus, it is recommended to substitute red meat with poultry or fish in order to lower CVD risk. Specific amino acids have favourable results in modifying major risk factors for CVD, such as hypertension. Apart from meat, other animal-source proteins, like those found in dairy products (especially whey protein) are inversely correlated to hypertension, obesity and insulin resistance

Effects of alirocumab on types of myocardial infarction: insights from the ODYSSEY OUTCOMES trial

Aims  The third Universal Definition of Myocardial Infarction (MI) Task Force classified MIs into five types: Type 1, spontaneous; Type 2, related to oxygen supply/demand imbalance; Type 3, fatal without ascertainment of cardiac biomarkers; Type 4, related to percutaneous coronary intervention; and Type 5, related to coronary artery bypass surgery. Low-density lipoprotein cholesterol (LDL-C) reduction with statins and proprotein convertase subtilisin–kexin Type 9 (PCSK9) inhibitors reduces risk of MI, but less is known about effects on types of MI. ODYSSEY OUTCOMES compared the PCSK9 inhibitor alirocumab with placebo in 18 924 patients with recent acute coronary syndrome (ACS) and elevated LDL-C (≥1.8 mmol/L) despite intensive statin therapy. In a pre-specified analysis, we assessed the effects of alirocumab on types of MI. Methods and results  Median follow-up was 2.8 years. Myocardial infarction types were prospectively adjudicated and classified. Of 1860 total MIs, 1223 (65.8%) were adjudicated as Type 1, 386 (20.8%) as Type 2, and 244 (13.1%) as Type 4. Few events were Type 3 (n = 2) or Type 5 (n = 5). Alirocumab reduced first MIs [hazard ratio (HR) 0.85, 95% confidence interval (CI) 0.77–0.95; P = 0.003], with reductions in both Type 1 (HR 0.87, 95% CI 0.77–0.99; P = 0.032) and Type 2 (0.77, 0.61–0.97; P = 0.025), but not Type 4 MI. Conclusion  After ACS, alirocumab added to intensive statin therapy favourably impacted on Type 1 and 2 MIs. The data indicate for the first time that a lipid-lowering therapy can attenuate the risk of Type 2 MI. Low-density lipoprotein cholesterol reduction below levels achievable with statins is an effective preventive strategy for both MI types.For complete list of authors see http://dx.doi.org/10.1093/eurheartj/ehz299</p

Nutraceutical approaches to non-alcoholic fatty liver disease (NAFLD): A position paper from the International Lipid Expert Panel (ILEP)

Non-Alcoholic Fatty Liver Disease (NAFLD) is a common condition affecting around 10–25% of the general adult population, 15% of children, and even > 50% of individuals who have type 2 diabetes mellitus. It is a major cause of liver-related morbidity, and cardiovascular (CV) mortality is a common cause of death. In addition to being the initial step of irreversible alterations of the liver parenchyma causing cirrhosis, about 1/6 of those who develop NASH are at risk also developing CV disease (CVD). More recently the acronym MAFLD (Metabolic Associated Fatty Liver Disease) has been preferred by many European and US specialists, providing a clearer message on the metabolic etiology of the disease. The suggestions for the management of NAFLD are like those recommended by guidelines for CVD prevention. In this context, the general approach is to prescribe physical activity and dietary changes the effect weight loss. Lifestyle change in the NAFLD patient has been supplemented in some by the use of nutraceuticals, but the evidence based for these remains uncertain. The aim of this Position Paper was to summarize the clinical evidence relating to the effect of nutraceuticals on NAFLD-related parameters. Our reading of the data is that whilst many nutraceuticals have been studied in relation to NAFLD, none have sufficient evidence to recommend their routine use; robust trials are required to appropriately address efficacy and safety

Effect of alirocumab on mortality after acute coronary syndromes. An analysis of the ODYSSEY OUTCOMES randomized clinical trial

Background: Previous trials of PCSK9 (proprotein convertase subtilisin-kexin type 9) inhibitors demonstrated reductions in major adverse cardiovascular events, but not death. We assessed the effects of alirocumab on death after index acute coronary syndrome. Methods: ODYSSEY OUTCOMES (Evaluation of Cardiovascular Outcomes After an Acute Coronary Syndrome During Treatment With Alirocumab) was a double-blind, randomized comparison of alirocumab or placebo in 18 924 patients who had an ACS 1 to 12 months previously and elevated atherogenic lipoproteins despite intensive statin therapy. Alirocumab dose was blindly titrated to target achieved low-density lipoprotein cholesterol (LDL-C) between 25 and 50 mg/dL. We examined the effects of treatment on all-cause death and its components, cardiovascular and noncardiovascular death, with log-rank testing. Joint semiparametric models tested associations between nonfatal cardiovascular events and cardiovascular or noncardiovascular death. Results: Median follow-up was 2.8 years. Death occurred in 334 (3.5%) and 392 (4.1%) patients, respectively, in the alirocumab and placebo groups (hazard ratio [HR], 0.85; 95% CI, 0.73 to 0.98; P=0.03, nominal P value). This resulted from nonsignificantly fewer cardiovascular (240 [2.5%] vs 271 [2.9%]; HR, 0.88; 95% CI, 0.74 to 1.05; P=0.15) and noncardiovascular (94 [1.0%] vs 121 [1.3%]; HR, 0.77; 95% CI, 0.59 to 1.01; P=0.06) deaths with alirocumab. In a prespecified analysis of 8242 patients eligible for ≥3 years follow-up, alirocumab reduced death (HR, 0.78; 95% CI, 0.65 to 0.94; P=0.01). Patients with nonfatal cardiovascular events were at increased risk for cardiovascular and noncardiovascular deaths (P<0.0001 for the associations). Alirocumab reduced total nonfatal cardiovascular events (P<0.001) and thereby may have attenuated the number of cardiovascular and noncardiovascular deaths. A post hoc analysis found that, compared to patients with lower LDL-C, patients with baseline LDL-C ≥100 mg/dL (2.59 mmol/L) had a greater absolute risk of death and a larger mortality benefit from alirocumab (HR, 0.71; 95% CI, 0.56 to 0.90; Pinteraction=0.007). In the alirocumab group, all-cause death declined wit h achieved LDL-C at 4 months of treatment, to a level of approximately 30 mg/dL (adjusted P=0.017 for linear trend). Conclusions: Alirocumab added to intensive statin therapy has the potential to reduce death after acute coronary syndrome, particularly if treatment is maintained for ≥3 years, if baseline LDL-C is ≥100 mg/dL, or if achieved LDL-C is low. Clinical Trial Registration: URL: https://www.clinicaltrials.gov. Unique identifier: NCT01663402

Step‐by‐step diagnosis and management of the nocebo/drucebo effect in statin‐associated muscle symptoms patients: a position paper from the International Lipid Expert Panel (ILEP)

Statin intolerance is a clinical syndrome whereby adverse effects (AEs) associated with statin therapy [most commonly statin-associated muscle symptoms (SAMS)] result in the discontinuation of therapy and consequently increase the risk of adverse cardiovascular outcomes. However, complete statin intolerance occurs in only a small minority of treated patients (estimated prevalence of only 3–5%). Many perceived AEs are misattributed (e.g. physical musculoskeletal injury and inflammatory myopathies), and subjective symptoms occur as a result of the fact that patients expect them to do so when taking medicines (the nocebo/drucebo effect)—what might be truth even for over 50% of all patients with muscle weakness/pain. Clear guidance is necessary to enable the optimal management of plasma in real-world clinical practice in patients who experience subjective AEs. In this Position Paper of the International Lipid Expert Panel (ILEP), we present a step-by-step patient-centred approach to the identification and management of SAMS with a particular focus on strategies to prevent and manage the nocebo/drucebo effect and to improve long-term compliance with lipid-lowering therapy