Weighted median algorithms for L1 approximation

Background: Several studies showed that life course adiposity was associated with Alzheimer’s disease (AD). However, the underlying causality remains unclear. Objective: We aimed to examine the causal relationship between life course adiposity and AD using Mendelian randomization (MR) analysis. Methods: Instrumental variants were obtained from large genome-wide association studies (GWAS) for life course adiposity, including birth weight (BW), childhood body mass index (BMI), adult BMI, waist circumference (WC), waist-to-hip ratio (WHR), and body fat percentage (BFP). A meta-analysis of GWAS for AD including 71,880 cases and 383,378 controls was used in this study. MR analyses were performed using inverse variance weighted (IVW), weighted median, and MR-Egger regression methods. We calculated odds ratios (ORs) per genetically predicted standard deviation (1-SD) unit increase in each trait for AD. Results: Genetically predicted 1-SD increase in adult BMI was significantly associated with higher risk of AD (IVW: OR = 1.03, 95% confidence interval [CI] = 1.01–1.05, p = 2.7×10–3) after Bonferroni correction. The weighted median method indicated a significant association between BW and AD (OR = 0.94, 95% CI = 0.90–0.98, p = 1.8×10–3). We also found suggestive associations of AD with WC (IVW: OR = 1.03, 95% CI = 1.00–1.07, p = 0.048) and WHR (weighted median: OR = 1.04, 95% CI = 1.00–1.07, p = 0.029). No association was detected of AD with childhood BMI and BFP. Conclusion: Our study demonstrated that lower BW and higher adult BMI had causal effects on increased AD risk.

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Novel finite point approach for solving time-fractional convection-dominated diffusion equations

Advances in Difference Equations ◽

10.1186/s13662-020-03178-8 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Xiaomin Liu ◽

Muhammad Abbas ◽

Honghong Yang ◽

Xinqiang Qin ◽

Tahir Nazir

Keyword(s):

Variable Coefficients ◽

Numerical Dispersion ◽

Discrete Equation ◽

Finite Point ◽

Spatial Direction ◽

Convection Diffusion ◽

Convection Diffusion Equation ◽

Tailored Finite Point Method ◽

L1 Approximation ◽

The Stability

AbstractIn this paper, a stabilized numerical method with high accuracy is proposed to solve time-fractional singularly perturbed convection-diffusion equation with variable coefficients. The tailored finite point method (TFPM) is adopted to discrete equation in the spatial direction, while the time direction is discreted by the G-L approximation and the L1 approximation. It can effectively eliminate non-physical oscillation or excessive numerical dispersion caused by convection dominant. The stability of the scheme is verified by theoretical analysis. Finally, one-dimensional and two-dimensional numerical examples are presented to verify the efficiency of the method.

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A Mendelian randomization analysis of the relationship between cardioembolic risk factors and ischemic stroke

Scientific Reports ◽

10.1038/s41598-021-93979-y ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Danyang Tian ◽

Linjing Zhang ◽

Zhenhuang Zhuang ◽

Tao Huang ◽

Dongsheng Fan

Keyword(s):

Risk Factors ◽

Ischemic Stroke ◽

Mendelian Randomization ◽

P Wave ◽

Cardioembolic Stroke ◽

Large Artery ◽

Weighted Analysis ◽

Inverse Variance ◽

Weighted Median ◽

Genetically Determined

AbstractObservational studies have shown that several risk factors are associated with cardioembolic stroke. However, whether such associations reflect causality remains unknown. We aimed to determine whether established and provisional cardioembolic risk factors are causally associated with cardioembolic stroke. Genetic instruments for atrial fibrillation (AF), myocardial infarction (MI), electrocardiogram (ECG) indices and N-terminal pro-brain natriuretic peptide (NT-pro BNP) were obtained from large genetic consortiums. Summarized data of ischemic stroke and its subtypes were extracted from the MEGASTROKE consortium. Causal estimates were calculated by applying inverse-variance weighted analysis, weighted median analysis, simple median analysis and Mendelian randomization (MR)-Egger regression. Genetically predicted AF was significantly associated with higher odds of ischemic stroke (odds ratio (OR): 1.20, 95% confidence intervals (CI): 1.16–1.24, P = 6.53 × 10–30) and cardioembolic stroke (OR: 1.95, 95% CI: 1.85–2.06, P = 8.81 × 10–125). Suggestive associations were found between genetically determined resting heart rate and higher odds of ischemic stroke (OR: 1.01, 95% CI: 1.00–1.02, P = 0.005), large-artery atherosclerotic stroke (OR: 1.02, 95% CI: 1.00–1.04, P = 0.026) and cardioembolic stroke (OR: 1.02, 95% CI: 1.00–1.04, P = 0.028). There was no causal association of P‐wave terminal force in the precordial lead V1 (PTFVI), P-wave duration (PWD), NT-pro BNP or PR interval with ischemic stroke or any subtype.

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