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A three-way multivariate data analysis: comparison of EU countries’ COVID-19 incidence trajectories from May 2020 to February 2021 三方多变量数据分析:2020年5月至2021年2月欧盟国家新冠肺炎发病轨迹比较
Pub Date : 2021-08-30 DOI: 10.15406/bbij.2021.10.00336
J. Tallon, Paulo Gomes, L. Bacelar-Nicolau, Sérgio Bacelar
Introduction: About a year and a half after the declaration of the COVID-19 pandemic, almost the entire planet has been affected by SARS-CoV-2 coronavirus and its variants, with serious public health consequences and other repercussions not yet thoroughly evaluated or foreseen in terms of economic, financial and social disruption throughout communities. Therefore, it is of utmost importance to understand the geography of the evolution of successive pandemic waves. Particularly in European countries, where, in recent decades, more advanced models for cohesion and competitiveness of a whole with more than 400 million inhabitants have been achieved, with ambitious challenges for horizon 2030 regarding this vast territory’s economic, social, and environmental sustainability. Objective: The main objective of this research is to describe the multivariate trajectories of COVID-19 incidence, mortality, hospital admissions, ICU admissions and testing, over three successive waves, covering all European Union (EU) countries with more than two million inhabitants, over 14-days periods before May 4 2020, until February 22 2021. Methods: This research includes 22 European countries representing about 98.8% of the EU population, described by six epidemiological variables over 43 time periods from the ECDC database: the 14-day notification rate Biometrics & Biostatistics International Journal Research Article Open Access of new cases reported for 100,000 inhabitants; the 14-day notification rate of reported deaths per one million inhabitants; the mean and the rate for 100,000 population of hospital occupancy and ICU occupancy; the testing rate per 100,000 population; and the 14-days percentage of test positivity An exploratory data analysis of each epidemiological variable identified a typology of countries profiles evolution. Multivariate exploratory statistical methods, namely a 3-way data analysis (double principal components and rank principal components analyses), were applied with software R version 4.1.0. Results: The multivariate evolution profile of the COVID-19 pandemic in the EU over the studied period highlighted 3 phases: the first phase over 24 time periods, with a relatively low COVID-19 incidence, hitting only part of EU countries; a second phase at the beginning of the second wave, when COVID-19 spread to most countries, with a higher impact on national health systems; lastly, a third phase coincident with the peak of the second wave and the onset of the third wave, a particularly reactive phase from the public authorities, with intensified testing of the population. These results are clear from the principal component analysis of the centres of gravity of the 43 time periods (interstructure). The multivariate statistical analysis of the global dataset of all countries over the 43 time periods additionally provides the main factorial representation of the trajectories of COVID-19 for each country in direct comparison with the global average rank
在宣布COVID-19大流行大约一年半后,几乎整个地球都受到了SARS-CoV-2冠状病毒及其变种的影响,在整个社区的经济、金融和社会中断方面造成了严重的公共卫生后果和其他影响,尚未得到彻底评估或预见。因此,了解连续大流行波演变的地理位置至关重要。特别是在欧洲国家,近几十年来,在拥有4亿多居民的整体凝聚力和竞争力方面,已经实现了更先进的模式,这一广阔领土的经济、社会和环境可持续性在2030年面临着雄心勃勃的挑战。目的:本研究的主要目的是描述在2020年5月4日至2021年2月22日的14天内,连续三波覆盖所有人口超过200万的欧盟(EU)国家的COVID-19发病率、死亡率、住院率、ICU入院率和检测的多变量轨迹。方法:本研究包括22个欧洲国家,约占欧盟人口的98.8%,由ECDC数据库中43个时间段的6个流行病学变量描述:每10万居民报告的新病例的14天通报率;每100万居民报告死亡的14天通报率;10万人口医院入住率和ICU入住率均值和比率;每10万人的检测率;对每个流行病学变量的探索性数据分析确定了国家概况演变的类型。采用多元探索性统计方法,即三向数据分析(双主成分分析和秩主成分分析),软件R版本4.1.0。结果:在研究期间,欧盟COVID-19大流行的多变量演变概况突出了3个阶段:第一阶段超过24个时间段,COVID-19发病率相对较低,仅影响部分欧盟国家;在第二波疫情开始时进入第二阶段,此时COVID-19传播到大多数国家,对国家卫生系统的影响更大;最后,第三阶段恰逢第二波的高峰和第三波的开始,这是公共当局特别积极的阶段,加强了对人口的检测。从43个时间段(基础结构)重心的主成分分析可以清楚地看出这些结果。对43个时间段内所有国家的全球数据集进行的多变量统计分析还提供了每个国家COVID-19轨迹的主要因子表示,直接与整个研究期间(基础设施)六个流行病学变量达到的全球平均排名值进行比较。这些轨迹使我们能够在连续的大流行病浪潮和反周期行为中确定不同的国家概况,部分原因是欧盟内部应对大流行病的公共政策没有充分协调。
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引用次数: 2
Comparison of quota sampling and stratified random sampling 定额抽样与分层随机抽样的比较
Pub Date : 2021-02-25 DOI: 10.15406/bbij.2021.10.00326
Rufai Iliyasu, I. Etikan
The possibility that researchers should be able to obtain data from all cases is questionable. There is a need; therefore, this article provides a probability and non-probability sampling. In this paper we studied the differences and similarities of the two with approach that is more of fritter away time, cost sufficient with energy required throughout the sample observed. The pair shows the differences and similarities between them, different articles were reviewed to compare the two. Quota sampling and Stratified sampling are close to each other. Both require the division into groups of the target population. The main goal of both methods is to select a representative sample and facilitate sub-group research. There are major variations, however. Stratified sampling uses simple random sampling when the categories are generated; sampling of the quota uses sampling of availability. For stratified sampling, a sampling frame is necessary, but not needed for quota sampling. More specifically, stratified sampling is a method of probability sampling which enables the calculation of the sampling error. For quota samples, this is not possible. Quota sampling is therefore primarily used by market analysts rather than stratified sampling, as it is mostly cost-effective and easy to conduct and has the appealing equity of satisfying population reach. However, it disguises potentially significant bias.
研究人员能够从所有病例中获取数据的可能性值得怀疑。有需要;因此,本文提供了概率抽样和非概率抽样。在本文中,我们研究了这两种方法的异同之处,这种方法更多地消耗了时间,成本足以在整个观察样本中所需的能量。这对展示了他们之间的异同,对不同的文章进行了回顾比较。配额抽样和分层抽样是非常接近的。两者都需要将目标人群划分为不同的群体。这两种方法的主要目的是选择一个有代表性的样本,并促进子群体研究。然而,有一些主要的变化。分层抽样在生成类别时采用简单随机抽样;配额的抽样使用可用性抽样。对于分层抽样,需要一个采样帧,但对于配额抽样则不需要。更具体地说,分层抽样是一种能够计算抽样误差的概率抽样方法。对于配额样本,这是不可能的。因此,配额抽样主要由市场分析师使用,而不是分层抽样,因为它最具成本效益,易于进行,并且具有满足人口覆盖的吸引力。然而,它掩盖了潜在的重大偏见。
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引用次数: 42
A simple graphic method to assess correlation 一个简单的图表方法来评估相关性
Pub Date : 2021-02-05 DOI: 10.15406/BBIJ.2021.10.00324
Othmar W. Winkler
This study explores the correlation between two variables and to demonstrate a simple graphic method to assess their degree of correlation. Following the lead of early English biometricians, it has been tacitly assumed that the studied variables develop in the same direction: when variable A’s measurements are higher from one object to another, the measurements of variable B, also are higher. The customary measure of co-relation relies on a least squares fitted trend line, then assuming that the trend is more real than, and has priority over the individually recorded data. The situation changes when measurements of variables develop in opposite directions: The very first data set I used to perform a correlation analysis was a study of student grades achieved and the percentage of their having missed classes: the more a student was absent from class, the lower were his achieved grades. In that situation the accepted model of correlation analysis – the mathematically fitted straight line and the squared distance of each student’s record from that line - was not appropriate. The usual correlation coefficient contradicted visual evidence of those data because the model underlying that situation treats the individual data as having more reality value than the general trend, but not as deviations or errors. The visual appearance, the graph of that situation, resembles a rectangular triangle, formed by the horizontal and vertical axis as its catheters, and the hypotenuse formed by a line through and representing the highest data points. This image justifies the expression “Triangular correlation”.
本研究探讨了两个变量之间的相关性,并展示了一种简单的图形方法来评估它们的相关程度。在早期英国生物计量学家的领导下,人们默认所研究的变量是朝着同一个方向发展的:当变量A从一个物体到另一个物体的测量值更高时,变量B的测量值也会更高。相互关系的习惯度量依赖于最小二乘拟合的趋势线,然后假设趋势比单独记录的数据更真实,并且优先于单独记录的数据。当变量的测量向相反的方向发展时,情况就发生了变化:我用来进行相关性分析的第一个数据集是对学生成绩和缺课率的研究:学生缺课越多,他的成绩就越低。在这种情况下,公认的相关分析模型——数学上拟合的直线和每个学生的成绩与这条直线的平方距离——是不合适的。通常的相关系数与这些数据的视觉证据相矛盾,因为这种情况下的模型将单个数据视为比总体趋势更具现实价值,而不是偏差或误差。这种情况的图形的视觉外观类似于一个矩形三角形,由水平轴和垂直轴作为其导管组成,斜边由一条穿过并表示最高数据点的线组成。这幅图证明了“三角相关”的说法是正确的。
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引用次数: 0
Forecasting homicides, rapes and counterfeiting currency: A case study in Sri Lanka 预测谋杀、强奸和伪造货币:斯里兰卡的案例研究
Pub Date : 2020-12-31 DOI: 10.15406/BBIJ.2020.09.00322
Chathura B. Wickrama, Ruwan D. Nawarathna, Lakshika S. Nawarathna
Crimes have been disturbing threats to all the Sri Lankans all over the country. Finding the main variables associated with crimes are very vital for policymakers. Our main goal in this study is to forecast of homicides, rapes and counterfeiting currency from 2013 to 2020 using auto-regressive conditional Poisson (ACP) and auto-regressive integrated moving average (ARIMA) models. All the predictions are made assuming that the prevailing conditions in the country affecting crime rates remain unchanged during the period. Moreover, multiple linear regression and Least Absolute Shrinkage and Selection Operator (LASSO) regression analysis were used to identify the key variables associated with crimes. Profiling of districts as safe or unsafe was performed based on the overall total crime rate of Sri Lanka which is to compare with individual district’s crime rates. Data were collected from the Department of Police and Department of Census and Statistics, Sri Lanka. It is observed that there are 14 safe and 11 unsafe districts in Sri Lanka. Moreover, it is found that the total migrant population and percentage of urban population is positively correlated with total crime. Besides, total migrant population, unemployment rate, mean household income and percentage of the urban population are significant variables for total crimes, and total migrant population, Gini index, mean household income and percentage of the urban population are significant variables for homicides. Random K-nearest neighbour (RKNN) algorithm classified districts as safe and unsafe with 84% of prediction accuracy.
犯罪一直是对全国所有斯里兰卡人的令人不安的威胁。找到与犯罪相关的主要变量对政策制定者来说非常重要。本研究的主要目标是使用自回归条件泊松(ACP)和自回归综合移动平均(ARIMA)模型预测2013年至2020年的杀人、强奸和假币。所有这些预测都是假设在这一期间影响犯罪率的国内普遍情况保持不变。此外,多元线性回归和最小绝对收缩和选择算子(LASSO)回归分析用于识别与犯罪相关的关键变量。对安全或不安全地区的概况分析是根据斯里兰卡的总体总犯罪率进行的,这是为了与个别地区的犯罪率进行比较。数据收集自斯里兰卡警察部门和人口普查和统计部门。据观察,斯里兰卡有14个安全区和11个不安全区。此外,研究发现,流动人口总数和城市人口比例与总犯罪率呈正相关。此外,流动人口总数、失业率、家庭平均收入和城市人口比例是总犯罪的显著变量,流动人口总数、基尼系数、家庭平均收入和城市人口比例是凶杀案的显著变量。随机k近邻(RKNN)算法将区域划分为安全区域和不安全区域,预测准确率为84%。
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引用次数: 1
Dynamics of Spruce budworms and single species competition models with bifurcation analysis 云杉芽虫动态与单种竞争模型的分岔分析
Pub Date : 2020-12-30 DOI: 10.15406/BBIJ.2020.09.00323
F. Tasnim, M. Kamrujjaman
Choristoneura Fumiferana is perilous defoliators of forest lands in North America and many countries in Europe. In this study, we consider mathematical models in ecology, epidemiology and bifurcation studies; the spruce budworm model and the population model with harvesting. The study is designed based on bifurcation analysis. In particular, the results support population thresholds necessary for survival in certain cases. In a series of numerical examples, the outcomes are presented graphically to compare with bifurcation results.
Fumiferana是北美和欧洲许多国家森林土地上危险的掠叶动物。在本研究中,我们考虑了生态学、流行病学和分支研究中的数学模型;云杉芽虫模型与种群模型。本研究基于分岔分析进行设计。特别是,结果支持在某些情况下生存所必需的人口阈值。在一系列数值算例中,用图形表示了结果,以便与分岔结果进行比较。
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引用次数: 2
Comparative prevalence of COVID–19 in european countries: a time window at second wave COVID-19在欧洲国家的比较流行:第二波的时间窗口
Pub Date : 2020-12-21 DOI: 10.15406/BBIJ.2020.09.00321
J. Tallon, Paulo Gomes, L. Bacelar-Nicolau
Introduction: The pandemic generated by COVID–19 completely changed people's daily lives, their relationship with family and friends, unexpectedly disrupted their working conditions and enhanced the need for an enduring resilience to face yet a second wave of the disease. It is crucial to keep continuously updating our knowledge about COVID–19 prevalence and incidence evolutions over large connected territories, where the disease is striking in alarming proportions. Objective: The main objective of this research is to identify and describe COVID–19 prevalence, incidence and mortality profiles in EU and EEE/EFTA countries, seven months after the start of the pandemic in Europe, and more recent tendencies, probably associated to the beginning of a second wave. Methods: This COVID–19 study covers thirty–one European countries. Six epidemiological variables where analyzed per 100 000 inhabitants on October 25 2020, two of them evaluated over the seven previous days. A multivariate statistical exploratory analysis based on rank principal components and cluster analysis was applied. Results: A COVID–19 prevalence typology of six country clusters was identified regarding 31 countries (EU, UK and three EEE/EFTA countries). The five epidemiological variables and number of tests revealed a wider dispersion with outlier observations. The rank transformation of data and their multivariate statistical analysis allowed us to construct a rational to better discriminate and describe these clusters, identifying specific behaviours related to the global prevalence from March until the end of October or highlight recent evolutions of COVID–19 incidence in the context of a second wave of pandemic. In fact we pinpointed country clusters where COVID–19 reached alarming levels which persist, or have even worsen, at the beginning of the second wave. Additionally, two other clusters were identified: one with countries that seems to be evolving into a situation under control, and another cluster of countries very weakly struck on the first wave, but are now facing a very complex surge, that will test their health systems capacity and timely response regarding covid and non–covid patients. Finally, the worst and more dramatic situation occurred in countries where the number of deaths per 100 000 inhabitants attained an impressive cumulative score.
由COVID-19引起的大流行彻底改变了人们的日常生活,改变了他们与家人和朋友的关系,出乎意料地破坏了他们的工作条件,并加强了对持久抵御第二波疾病的需求。至关重要的是,要不断更新我们对COVID-19在大面积互联地区流行和发病率演变的认识,在这些地区,这种疾病的发病率惊人。目的:本研究的主要目的是确定和描述在欧洲大流行开始七个月后,欧盟和EEE/EFTA国家的COVID-19流行率、发病率和死亡率概况,以及最近可能与第二波开始有关的趋势。方法:本研究涵盖31个欧洲国家。2020年10月25日,每10万居民分析了6个流行病学变量,其中2个在前7天进行了评估。采用基于秩主成分和聚类分析的多元统计探索性分析。结果:在31个国家(欧盟、英国和3个EEE/EFTA国家)中确定了6个国家群集的COVID-19流行类型。5个流行病学变量和检验次数显示,离群值的差异更大。数据的等级转换及其多变量统计分析使我们能够构建一个合理的方法来更好地区分和描述这些聚集性,确定与3月至10月底全球流行情况相关的具体行为,或强调在第二波大流行背景下COVID-19发病率的最新演变。事实上,我们确定了COVID-19达到惊人水平的国家群,这些水平在第二波浪潮开始时持续存在,甚至恶化。此外,还确定了另外两组:一组国家似乎正在演变成一种得到控制的情况,另一组国家在第一波疫情中受到的打击非常微弱,但现在正面临非常复杂的激增,这将考验它们的卫生系统能力和对covid和非covid患者的及时反应。最后,最糟糕和更严重的情况发生在每10万居民死亡人数达到令人印象深刻的累积分数的国家。
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引用次数: 2
Worldwide statins prescription pattern: is it similar? 世界范围内他汀类药物的处方模式是否相似?
Pub Date : 2020-11-27 DOI: 10.15406/BBIJ.2020.09.00320
Masoud Amiri
Statins are commonly prescribed to prevent or treat of cardiovascular diseases (CVD) worldwide, preventing about 80,000 stroke and heart attack cases annually. Various statins have been initiated with different biologic properties, chemical structure, safety, efficacy and side effects, with no similar prescription pattern in different countries. One of the most common reasons of the changes among different countries, might be due to the behavior of physicians in various continents.
他汀类药物通常用于预防或治疗心血管疾病(CVD),每年可预防约80,000例中风和心脏病发作。各种他汀类药物的生物特性、化学结构、安全性、疗效和副作用各不相同,不同国家的处方模式也不相同。不同国家之间的变化最常见的原因之一,可能是由于不同大陆的医生的行为。
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引用次数: 1
Visual outcomes in diabetic macular edema patients after avastin injection 糖尿病性黄斑水肿患者注射阿瓦斯丁后的视力状况
Pub Date : 2020-11-23 DOI: 10.15406/BBIJ.2020.09.00319
Charles Masih, Kanwal Parveen, Samreen Brohi, Shehar Bano Siyal, Fatima Zia, Shabnam Pari Bhutto, Muhammad Faisal Fahim
Objective: To determine the visual outcome in Diabetic Macular Edema patients after 3rd Avastin injections attending a tertiary eye care hospital. Materials and methods: This was a cross sectional study with Non probability convenient sampling technique. The study was carried out at Diabetic clinic of Al-Ibrahim Eye Hospital, Isra Postgraduate Institute of Ophthalmology, Karachi-Pakistan. Ethical approval was taken from the institutional review board of Institute. Data collection were done retrospectively from January 2017 to June 2019. Data were retrieved for DME patients who have completed three follow-ups with Avastin injection. Inclusion Criteria were patients with age 30 to 60 years, Patient with PDR and NPDR with diabetic macular edema after 3rd injection. Data Analysis was done using SPSS version 23.0. Results: A total of 40 eyes of 40 patients were included in this study after getting information from the record sheet. Analysis were done in 30 eyes of 30 patients because 10 patients were missed their follow-up due to certain reason which were observed from record sheet. Mean age of patients was found to be 41.25±10.24.Pre-operative Avastin injection best corrected visual acuity (BCVA) was noticed by using Log MAR without glasses was 0.49 and with glasses was 0.40. Post-operative best corrected visual acuity Log MAR without glasses 0.51 and with glasses 0.42 after Avastin injection. Improvement of visual acuity was classified as Improved, worsen and Stable. There were 22 (73.33%) patients observed with improvement in visual acuity, 5 (16.66%) patients retained their vision stable and only 3 (10%) patients worsen their visual acuity after all three Avastin injections. Conclusion: The most common cause of diabetic macular edema is non-proliferative diabetic retinopathy and proliferative Diabetic Retinopathy. The Intravitreal injection play vital role, the timely treatment would improve prognosis of visual outcomes in Diabetic macular edema. So the study significantly shows the improvement in best corrected visual acuity before and after three visits.
目的:了解三级眼科医院糖尿病性黄斑水肿患者接受第三次阿瓦斯丁注射后的视力状况。材料与方法:采用非概率方便抽样技术进行横断面研究。该研究在巴基斯坦卡拉奇以色列眼科研究生院Al-Ibrahim眼科医院糖尿病门诊进行。伦理批准由研究所的机构审查委员会采取。回顾性收集2017年1月至2019年6月的数据。数据被检索的DME患者已经完成了阿瓦斯汀注射的三个随访。入选标准为年龄30 ~ 60岁,第3次注射后伴有糖尿病性黄斑水肿的PDR和NPDR患者。数据分析采用SPSS 23.0版本。结果:40例患者共40只眼从病历中获取信息,纳入本研究。对30例患者的30只眼进行了分析,其中10例患者由于某种原因错过了随访,从病历中观察到。患者平均年龄为41.25±10.24岁。术前注射阿瓦斯汀时,不配戴眼镜和配戴眼镜的最佳矫正视力分别为0.49和0.40。注射阿瓦斯汀后,术后最佳矫正视力Log MAR不配戴眼镜0.51,配戴眼镜0.42。视力改善分为改善、恶化和稳定。三次注射阿瓦斯汀后,22例(73.33%)患者视力改善,5例(16.66%)患者视力保持稳定,仅有3例(10%)患者视力恶化。结论:非增殖性糖尿病视网膜病变和增殖性糖尿病视网膜病变是糖尿病黄斑水肿最常见的病因。玻璃体内注射对糖尿病性黄斑水肿患者的视力预后起着至关重要的作用,及时治疗可改善视力预后。因此,该研究显著显示了三次就诊前后最佳矫正视力的改善。
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引用次数: 0
Comparing two quantities by using a ratio 用比率来比较两个量
Pub Date : 2020-10-31 DOI: 10.15406/BBIJ.2020.09.00318
S. Zheng
where nij are sometimes replaced by 0.5 ij n + , when some of the ij n are zero. This result can be derived under the assumption of multinomial sampling by using the Delta Method. When RR is used to compare two quantities, the log transformation is conducted, that is ( ) 1|1 1|2 ˆ ˆ log / π π is often considered instead of ( ) 1|1 1|2 ˆ ˆ / π π , since the former has a sampling distribution which is closer to normal than that of the latter. The estimated asymptotic standard error (ASE) of log(RR):
其中nij有时被0.5 ijn +取代,当某些ijn为零时。这一结果可以在多项式抽样的假设下用Delta方法得到。当使用RR比较两个量时,进行对数变换,即()1|1 1|2↑↑log / π π通常代替()1|1 1|2↑↑/ π π,因为前者的抽样分布比后者更接近正态分布。对数(RR)的估计渐近标准误差(ASE):
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引用次数: 0
Truncated Akash distribution: properties and applications 截断Akash分布:属性和应用
Pub Date : 2020-10-26 DOI: 10.15406/BBIJ.2020.09.00317
K. Shukla
In this paper, Truncated Akash distribution has been proposed. Its mean and variance have been derived. Nature of cumulative distribution and hazard rate functions have been derived and presented graphically. Its moments including Coefficient of Variation, Skenwness, Kurtosis and Index of dispersion have been derived. Maximum likelihood method of estimation has been used to estimate the parameter of proposed model. It has been applied on three data sets and compares its superiority over one parameter exponential, Lindley, Akash, Ishita and truncated Lindley distribution.
本文提出了截断Akash分布。其均值和方差均已导出。推导了累积分布和危险率函数的性质,并用图形表示。推导了其变异系数、偏度、峰度和色散指数等矩。采用极大似然估计法对模型参数进行估计。将其应用于三个数据集,并比较了其相对于单参数指数、Lindley、Akash、Ishita和截断Lindley分布的优越性。
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引用次数: 1
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