Long Memory in a Linear Stochastic Volterra Differential Equation

In this paper we consider a linear stochastic Volterra equation which has a stationary solution. We show that when the kernel of the fundamental solution is regularly varying at infinity with a log-convex tail integral, then the autocovariance function of the stationary solution is also regularly varying at infinity and its exact pointwise rate of decay can be determined. Moreover, it can be shown that this stationary process has either long memory in the sense that the autocovariance function is not integrable over the reals or is subexponential. Under certain conditions upon the kernel, even arbitrarily slow decay rates of the autocovariance function can be achieved. Analogous results are obtained for the corresponding discrete equation

Fine-Scale Mapping of the 4q24 Locus Identifies Two Independent Loci Associated with Breast Cancer Risk

Background: A recent association study identified a common variant (rs9790517) at 4q24 to be associated with breast cancer risk. Independent association signals and potential functional variants in this locus have not been explored. Methods: We conducted a fine-mapping analysis in 55,540 breast cancer cases and 51,168 controls from the Breast Cancer Association Consortium. Results: Conditional analyses identified two independent association signals among women of European ancestry, represented by rs9790517 [conditional P = 2.51 × 10−4; OR, 1.04; 95% confidence interval (CI), 1.02–1.07] and rs77928427 (P = 1.86 × 10−4; OR, 1.04; 95% CI, 1.02–1.07). Functional annotation using data from the Encyclopedia of DNA Elements (ENCODE) project revealed two putative functional variants, rs62331150 and rs73838678 in linkage disequilibrium (LD) with rs9790517 (r2 ≥ 0.90) residing in the active promoter or enhancer, respectively, of the nearest gene, TET2. Both variants are located in DNase I hypersensitivity and transcription factor–binding sites. Using data from both The Cancer Genome Atlas (TCGA) and Molecular Taxonomy of Breast Cancer International Consortium (METABRIC), we showed that rs62331150 was associated with level of expression of TET2 in breast normal and tumor tissue. Conclusion: Our study identified two independent association signals at 4q24 in relation to breast cancer risk and suggested that observed association in this locus may be mediated through the regulation of TET2. Impact: Fine-mapping study with large sample size warranted for identification of independent loci for breast cancer risk

Asymptotic Properties of Fractional Delay Differential Equations

In this paper we study the asymptotic properties of d-dimensional linear fractional differential equations with time delay. First results on existence and uniqueness of solutions are presented. Then we propose necessary and sufficient conditions for asymptotic stability of equations of this type using the inverse Laplace transform method

Minimal Entropy Martingale Measure for Lévy Processes

Let X be a real-valued Lévy process under P in its natural filtration. The minimal entropy martingale measure is defined as an absolutely continuous martingale measure that minimizes the relative entropy with respect to P. We show in this paper that the sufficient conditions for its existence, known in literature, are also necessary and give an explicit formula for the infimum of the relative entropy

A Black--Scholes Model with Long Memory

This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stationary and possesses long memory are characterised. Connections with the class of ARCH($\infty$) processes are sketched.

Efficacy and safety of two neutralising monoclonal antibody therapies, sotrovimab and BRII-196 plus BRII-198, for adults hospitalised with COVID-19 (TICO): a randomised controlled trial

We aimed to assess the efficacy and safety of two neutralising monoclonal antibody therapies (sotrovimab [Vir Biotechnology and GlaxoSmithKline] and BRII-196 plus BRII-198 [Brii Biosciences]) for adults admitted to hospital for COVID-19 (hereafter referred to as hospitalised) with COVID-19. In this multinational, double-blind, randomised, placebo-controlled, clinical trial (Therapeutics for Inpatients with COVID-19 [TICO]), adults (aged ≥18 years) hospitalised with COVID-19 at 43 hospitals in the USA, Denmark, Switzerland, and Poland were recruited. Patients were eligible if they had laboratory-confirmed SARS-CoV-2 infection and COVID-19 symptoms for up to 12 days. Using a web-based application, participants were randomly assigned (2:1:2:1), stratified by trial site pharmacy, to sotrovimab 500 mg, matching placebo for sotrovimab, BRII-196 1000 mg plus BRII-198 1000 mg, or matching placebo for BRII-196 plus BRII-198, in addition to standard of care. Each study product was administered as a single dose given intravenously over 60 min. The concurrent placebo groups were pooled for analyses. The primary outcome was time to sustained clinical recovery, defined as discharge from the hospital to home and remaining at home for 14 consecutive days, up to day 90 after randomisation. Interim futility analyses were based on two seven-category ordinal outcome scales on day 5 that measured pulmonary status and extrapulmonary complications of COVID-19. The safety outcome was a composite of death, serious adverse events, incident organ failure, and serious coinfection up to day 90 after randomisation. Efficacy and safety outcomes were assessed in the modified intention-to-treat population, defined as all patients randomly assigned to treatment who started the study infusion. This study is registered with ClinicalTrials.gov, NCT04501978. Between Dec 16, 2020, and March 1, 2021, 546 patients were enrolled and randomly assigned to sotrovimab (n=184), BRII-196 plus BRII-198 (n=183), or placebo (n=179), of whom 536 received part or all of their assigned study drug (sotrovimab n=182, BRII-196 plus BRII-198 n=176, or placebo n=178; median age of 60 years [IQR 50–72], 228 [43%] patients were female and 308 [57%] were male). At this point, enrolment was halted on the basis of the interim futility analysis. At day 5, neither the sotrovimab group nor the BRII-196 plus BRII-198 group had significantly higher odds of more favourable outcomes than the placebo group on either the pulmonary scale (adjusted odds ratio sotrovimab 1·07 [95% CI 0·74–1·56]; BRII-196 plus BRII-198 0·98 [95% CI 0·67–1·43]) or the pulmonary-plus complications scale (sotrovimab 1·08 [0·74–1·58]; BRII-196 plus BRII-198 1·00 [0·68–1·46]). By day 90, sustained clinical recovery was seen in 151 (85%) patients in the placebo group compared with 160 (88%) in the sotrovimab group (adjusted rate ratio 1·12 [95% CI 0·91–1·37]) and 155 (88%) in the BRII-196 plus BRII-198 group (1·08 [0·88–1·32]). The composite safety outcome up to day 90 was met by 48 (27%) patients in the placebo group, 42 (23%) in the sotrovimab group, and 45 (26%) in the BRII-196 plus BRII-198 group. 13 (7%) patients in the placebo group, 14 (8%) in the sotrovimab group, and 15 (9%) in the BRII-196 plus BRII-198 group died up to day 90. Neither sotrovimab nor BRII-196 plus BRII-198 showed efficacy for improving clinical outcomes among adults hospitalised with COVID-19. US National Institutes of Health and Operation Warp Spee