Poisson Distribution

泊松分布
  • 文章类型: Journal Article
    阳泉市疾病预防控制中心,中国,针对卡拉-阿扎尔疫情日益增多的趋势,采取了一系列的防控措施。作为回应,我们提出了一个新的模型来更科学地评估这些干预措施的有效性.
    我们从阳泉市疾病预防控制中心(CDC)获得了2017年至2021年Kala-Azar的发病率数据。我们构建了泊松分段回归模型,谐波泊松分段回归模型,和改进的谐波泊松分段回归模型,并使用这三种模型来解释干预效果,分别。最后,通过比较三种模型的拟合效果,选择最优模型。
    初步分析显示干预前Kala-Azar有潜在的上升趋势[发生率比(IRR):1.045,95%置信区间(CI):1.027-1.063,p<0.001]。就长期影响而言,干预后Kala-Azar的上升显着放缓(IRR:0.960,95CI:0.927-0.995,p=0.026),干预后每增加一个月,Kala-Azar的风险增加0.3%(β1β3=0.003,IRR=1.003)。模型拟合效果的结果表明,改进的谐波泊松分段回归模型拟合效果最好,和MSE的值,MAE,RMSE最低,分别为0.017、0.101和0.130。
    从长远来看,阳泉市疾控中心采取的干预措施可以很好地遏制Kala-Azar的上升趋势。改进的谐波泊松分段回归模型具有更高的拟合性能,为季节性传染病干预效果的评价提供一定的科学参考。
    UNASSIGNED: The Centre for Disease Control and Prevention in Yangquan, China, has taken a series of preventive and control measures in response to the increasing trend of Kala-Azar. In response, we propose a new model to more scientifically evaluate the effectiveness of these interventions.
    UNASSIGNED: We obtained the incidence data of Kala-Azar from 2017 to 2021 from the Centre for Disease Control and Prevention (CDC) in Yangquan. We constructed Poisson segmented regression model, harmonic Poisson segmental regression model, and improved harmonic Poisson segmented regression model, and used the three models to explain the intervention effect, respectively. Finally, we selected the optimal model by comparing the fitting effects of the three models.
    UNASSIGNED: The primary analysis showed an underlying upward trend of Kala-Azar before intervention [incidence rate ratio (IRR): 1.045, 95% confidence interval (CI): 1.027-1.063, p < 0.001]. In terms of long-term effects, the rise of Kala-Azar slowed down significantly after the intervention (IRR:0.960, 95%CI:0.927-0.995, p = 0.026), and the risk of Kala-Azar increased by 0.3% for each additional month after intervention (β1  + β3  = 0.003, IRR = 1.003). The results of the model fitting effect showed that the improved harmonic Poisson segmental regression model had the best fitting effect, and the values of MSE, MAE, and RMSE were the lowest, which were 0.017, 0.101, and 0.130, respectively.
    UNASSIGNED: In the long term, the intervention measures taken by the Yangquan CDC can well curb the upward trend of Kala-Azar. The improved harmonic Poisson segmented regression model has higher fitting performance, which can provide a certain scientific reference for the evaluation of the intervention effect of seasonal infectious diseases.
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  • 文章类型: Journal Article
    单分子表面增强拉曼光谱(SM-SERS)具有巨大的潜力,可以彻底改变超色光谱的定量分析。然而,由于强烈的强度波动和闪烁特性,实现定量的SM-SERS具有挑战性。在这项研究中,我们揭示了SERS光谱中统计SERS概率P与微观平均分子数α之间的关系P=1-e-α,这为实现SM-SERS定量的统计途径奠定了物理基础。利用SERS概率校准,我们实现了具有批次间稳健性的定量SERS分析,浓度检测范围极广,涵盖9个数量级,和超低的检测极限远低于单分子水平。这些结果表明了通过统计途径进行稳健SERS定量的物理可行性,并且无疑为在各种应用场景中实现SERS作为实用分析工具开辟了新途径。
    Single-molecule surface-enhanced Raman spectroscopy (SM-SERS) holds great potential to revolutionize ultratrace quantitative analysis. However, achieving quantitative SM-SERS is challenging because of strong intensity fluctuation and blinking characteristics. In this study, we reveal the relation P = 1 - e-α between the statistical SERS probability P and the microscopic average molecule number α in SERS spectra, which lays the physical foundation for a statistical route to implement SM-SERS quantitation. Utilizing SERS probability calibration, we achieve quantitative SERS analysis with batch-to-batch robustness, extremely wide detection range of concentration covering 9 orders of magnitude, and ultralow detection limit far below the single-molecule level. These results indicate the physical feasibility of robust SERS quantitation through statistical route and certainly open a new avenue for implementing SERS as a practical analysis tool in various application scenarios.
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  • 文章类型: Journal Article
    基于液滴的单细胞测序技术依赖于每个液滴封装单个细胞的基本假设,实现单个细胞组学分析。然而,多胞胎不可避免的问题,两个或多个细胞被包裹在一个液滴中,可能导致虚假的细胞类型注释和模糊的真实生物学发现。多重染色体的问题在单细胞多重组学设置中加剧,其中,集成用于聚类的跨模态信息可能会无意中促进多个聚类的聚合,并增加错误细胞类型注释的风险。这里,我们提出了一种基于复合泊松模型的单细胞多体组数据多重检测框架.利用实验细胞散列结果作为多重状态的真相,我们进行了三模态DOGMA-seq实验,并从两个组织中生成了17个基准数据集,共涉及280,123个液滴。我们证明了所提出的方法是集成跨模态多重信号的重要工具,有效消除单细胞多组学数据中的多重簇-基准单组学方法被证明是不充分的任务。
    Droplet-based single-cell sequencing techniques rely on the fundamental assumption that each droplet encapsulates a single cell, enabling individual cell omics profiling. However, the inevitable issue of multiplets, where two or more cells are encapsulated within a single droplet, can lead to spurious cell type annotations and obscure true biological findings. The issue of multiplets is exacerbated in single-cell multiomics settings, where integrating cross-modality information for clustering can inadvertently promote the aggregation of multiplet clusters and increase the risk of erroneous cell type annotations. Here, we propose a compound Poisson model-based framework for multiplet detection in single-cell multiomics data. Leveraging experimental cell hashing results as the ground truth for multiplet status, we conducted trimodal DOGMA-seq experiments and generated 17 benchmarking datasets from two tissues, involving a total of 280,123 droplets. We demonstrated that the proposed method is an essential tool for integrating cross-modality multiplet signals, effectively eliminating multiplet clusters in single-cell multiomics data-a task at which the benchmarked single-omics methods proved inadequate.
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  • 文章类型: Journal Article
    当前的泊松因子模型通常假设因子未知,它忽略了某些可观察协变量的解释潜力。本研究侧重于高维设置,其中计数响应变量和/或协变量的数量可以随着样本大小的增加而发散。提出了协变量增强的过分散泊松因子模型,以联合执行高维泊松因子分析,并估计过分散计数数据的大系数矩阵。提供了一组可识别性条件,从理论上保证了计算可识别性。通过在大系数矩阵上施加低秩约束,我们将响应变量和协变量的相互依赖性结合起来。为了解决非线性带来的计算挑战,两个高维潜在矩阵,和低秩约束,我们提出了一种结合Laplace和Taylor近似的变分估计方案。我们还开发了一个基于奇异值比率的标准来确定因子的数量和系数矩阵的秩。综合仿真研究表明,所提出的方法在估计精度和计算效率方面优于最先进的方法。通过对CITE-seq数据集的应用证明了我们方法的实用性。在R包COAP中可以灵活地实现我们提出的方法。
    The current Poisson factor models often assume that the factors are unknown, which overlooks the explanatory potential of certain observable covariates. This study focuses on high dimensional settings, where the number of the count response variables and/or covariates can diverge as the sample size increases. A covariate-augmented overdispersed Poisson factor model is proposed to jointly perform a high-dimensional Poisson factor analysis and estimate a large coefficient matrix for overdispersed count data. A group of identifiability conditions is provided to theoretically guarantee computational identifiability. We incorporate the interdependence of both response variables and covariates by imposing a low-rank constraint on the large coefficient matrix. To address the computation challenges posed by nonlinearity, two high-dimensional latent matrices, and the low-rank constraint, we propose a novel variational estimation scheme that combines Laplace and Taylor approximations. We also develop a criterion based on a singular value ratio to determine the number of factors and the rank of the coefficient matrix. Comprehensive simulation studies demonstrate that the proposed method outperforms the state-of-the-art methods in estimation accuracy and computational efficiency. The practical merit of our method is demonstrated by an application to the CITE-seq dataset. A flexible implementation of our proposed method is available in the R package COAP.
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  • 文章类型: Journal Article
    在复杂的混合物中,各种分子在极低浓度下的定量检测一直是许多科学和工程领域的主要目标。从致癌诱变剂和早期疾病标志物的检测到环境污染物和生物恐怖剂1-5。此外,无需外部标记或修饰即可检测这些分析物的技术非常有价值,通常更受欢迎6。在这方面,表面增强拉曼光谱可以仅根据其固有和独特的振动信号检测复杂混合物中的分子种类7。然而,迄今为止,由于不可控制的信号异质性和低分析物浓度下较差的再现性,为此目的开发表面增强拉曼光谱一直具有挑战性8。这里,作为概念的证明,我们证明,使用数字(纳米)胶体增强拉曼光谱,在非常低的浓度下,广泛的目标分子的可重复定量可以通过单分子计数常规实现,仅限于测量过程的泊松噪声。作为增强这些振动特征的金属胶体纳米颗粒,包括羟胺还原的银胶体,可以在常规条件下大规模制造,我们预计,数字(纳米)胶体增强拉曼光谱将成为各种分析物的可靠和超灵敏检测的首选技术,包括那些对人类健康非常重要的。
    Quantitative detection of various molecules at very low concentrations in complex mixtures has been the main objective in many fields of science and engineering, from the detection of cancer-causing mutagens and early disease markers to environmental pollutants and bioterror agents1-5. Moreover, technologies that can detect these analytes without external labels or modifications are extremely valuable and often preferred6. In this regard, surface-enhanced Raman spectroscopy can detect molecular species in complex mixtures on the basis only of their intrinsic and unique vibrational signatures7. However, the development of surface-enhanced Raman spectroscopy for this purpose has been challenging so far because of uncontrollable signal heterogeneity and poor reproducibility at low analyte concentrations8. Here, as a proof of concept, we show that, using digital (nano)colloid-enhanced Raman spectroscopy, reproducible quantification of a broad range of target molecules at very low concentrations can be routinely achieved with single-molecule counting, limited only by the Poisson noise of the measurement process. As metallic colloidal nanoparticles that enhance these vibrational signatures, including hydroxylamine-reduced-silver colloids, can be fabricated at large scale under routine conditions, we anticipate that digital (nano)colloid-enhanced Raman spectroscopy will become the technology of choice for the reliable and ultrasensitive detection of various analytes, including those of great importance for human health.
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  • 文章类型: Journal Article
    细颗粒物(PM2.5)是心血管疾病的危险因素。PM2.5成分与心血管疾病之间的关联是一个特别感兴趣的点,但不一致。本研究旨在探讨PM2.5中重金属(类)成分对心血管的影响。死亡率数据,安阳市大气污染物和气象因素,收集了2017年至2021年的中国。每月对PM2.5中的重金属(类)进行监测和检查。将案例交叉设计应用于估计数据集。镉(Cd)的四分位数间距增加,滞后1的锑(Sb)和砷(As)与8.1%的增量相关(95%CI:3.3,13.2),4.8%(95%CI:0.2,9.5)和3.5%(95%CI:1.1,6.0)心血管死亡率。滞后2期硒与脑血管死亡率呈负相关(RR=0.92095%CI:0.862,0.983)。当日铝暴露与缺血性心脏病死亡率呈正相关(RR=1.08395%CI:1.001,1.172)。分层分析表明性别,年龄和季节改变了As对心血管的影响(P<0.05)。我们的研究表明,重金属(类)在PM2.5的不利影响中起关键作用。Cd,Sb和As是心血管死亡的重要危险因素。这些发现对准确控制和管理空气污染物以改善公共卫生效益具有潜在意义。
    Fine particulate matter (PM2.5) is a risk factor of cardiovascular disease. Associations between PM2.5 compositions and cardiovascular disease are a point of special interest but inconsistent. This study aimed to explore the cardiovascular effects of heavy metal(loid) compositions in PM2.5. Data for mortality, air pollutants and meteorological factors in Anyang, China from 2017 to 2021 were collected. Heavy metal(loid) in PM2.5 were monitored and examined monthly. A Case-crossover design was applied to the estimated data set. The interquartile range increase in cadmium (Cd), antimony (Sb) and arsenic (As) at lag 1 was associated with increment of 8.1% (95% CI: 3.3, 13.2), 4.8% (95% CI: 0.2, 9.5) and 3.5% (95% CI: 1.1, 6.0) cardiovascular mortality. Selenium in lag 2 was inversely associated with cerebrovascular mortality (RR = 0.920 95% CI: 0.862, 0.983). Current-day exposure of aluminum was positively associated with mortality from ischemic heart disease (RR = 1.083 95% CI: 1.001, 1.172). Stratified analysis indicated sex, age and season modified the cardiovascular effects of As (P < 0.05). Our study reveals that heavy metal(loid) play key roles in adverse effects of PM2.5. Cd, Sb and As were significant risk factors of cardiovascular mortality. These findings have potential implications for accurate air pollutants control and management to improve public health benefits.
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  • 文章类型: Journal Article
    在生物医学和公共卫生的情况下,通常会观察到多变量计数数据中的过零。为了更好地分析这类数据,我们首先建立了一个边缘化的多元零膨胀泊松(MZIP)回归模型,以直接解释总体暴露对边际均值的影响.然后,通过同时考虑异质性和相关性,我们为新开发的MZIP回归模型定义了多个Pearson残差。此外,提出了一种新的基于多个皮尔逊残差的模型平均预测方法,证明了该模型平均预测的渐近最优性。仿真和医学中的两个经验应用用于说明所提出方法的有效性。
    Excessive zeros in multivariate count data are often observed in scenarios of biomedicine and public health. To provide a better analysis on this type of data, we first develop a marginalized multivariate zero-inflated Poisson (MZIP) regression model to directly interpret the overall exposure effects on marginal means. Then, we define a multiple Pearson residual for our newly developed MZIP regression model by simultaneously taking heterogeneity and correlation into consideration. Furthermore, a new model averaging prediction method is introduced based on the multiple Pearson residual, and the asymptotical optimality of this model averaging prediction is proved. Simulations and two empirical applications in medicine are used to illustrate the effectiveness of the proposed method.
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  • 文章类型: Journal Article
    人类微生物组研究由于其在理解人类健康和疾病方面的关键作用而变得越来越重要。在微生物组研究领域,生成的数据通常涉及操作分类单位计数,这往往会带来过度分散和零通胀等挑战。为了解决与分散相关的问题,广义泊松模型提供了一个灵活的解决方案,有效地处理以过度分散为特征的数据,等色散,和分散不足。此外,零膨胀广义泊松模型的领域提供了同时解决过度分散和零膨胀的战略途径。零通胀现象通常源于研究人群的异质性。当特定的微生物类群未能在某些受试者的微生物群落中茁壮成长时,它就会出现,因此导致这些个体一致的零计数。这个子集的主题代表一个潜在的类,它们的零来自真正不存在的微生物类群。在本文中,我们介绍了一种新颖的测试方法,旨在在广义泊松回归模型中发现此类潜在类别。我们建立了闭式检验统计量,并基于估计方程推导了其渐近分布。为了评估其疗效,我们进行了大量的模拟研究,并进一步应用该测试来检测来自Bogalusa心脏研究的人类肠道微生物组数据中的潜在类别。
    Human microbiome research has gained increasing importance due to its critical roles in comprehending human health and disease. Within the realm of microbiome research, the data generated often involves operational taxonomic unit counts, which can frequently present challenges such as over-dispersion and zero-inflation. To address dispersion-related concerns, the generalized Poisson model offers a flexible solution, effectively handling data characterized by over-dispersion, equi-dispersion, and under-dispersion. Furthermore, the realm of zero-inflated generalized Poisson models provides a strategic avenue to simultaneously tackle both over-dispersion and zero-inflation. The phenomenon of zero-inflation frequently stems from the heterogeneous nature of study populations. It emerges when specific microbial taxa fail to thrive in the microbial community of certain subjects, consequently resulting in a consistent count of zeros for these individuals. This subset of subjects represents a latent class, where their zeros originate from the genuine absence of the microbial taxa. In this paper, we introduce a novel testing methodology designed to uncover such latent classes within generalized Poisson regression models. We establish a closed-form test statistic and deduce its asymptotic distribution based on estimating equations. To assess its efficacy, we conduct an extensive array of simulation studies, and further apply the test to detect latent classes in human gut microbiome data from the Bogalusa Heart Study.
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  • 文章类型: Journal Article
    近年来,随着传染病的数量和复杂性的增加,有人提出了使用控制图监测公共卫生和疾病的想法。在本文中,我们研究了多变量控制图,用于监视具有双变量泊松分布的双变量整数值自相关过程,并通过比较控制图的性能来选择最优控制方案。此外,以澳大利亚两个州的脑膜炎球菌患者事件为例说明这些方法的应用.结果表明,D指数加权移动平均控制方案能够更快地检测到均值的变化,这是一个显著的优势。
    In recent years, with the increasing number and complexity of infectious diseases, the idea of using control charts to monitor public health and disease has been proposed. In this paper, we study multivariate control charts for monitoring a bivariate integer-valued autocorrelation process with bivariate Poisson distribution and select the optimal control scheme by comparing the performance of control charts. Furthermore, the meningococcal patient event in two states in Australia serves as an example to illustrate the application of these methods. The results show that the D exponentially weighted moving average control scheme can detect the changes in the mean value faster, which is a significant advantage.
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  • 文章类型: Journal Article
    事实证明,基于废水的流行病学可用于监测社区中的COVID-19感染动态。然而,在低患病率地区,废水中低浓度的SARS-CoV-2RNA使这变得困难。这里,我们在2020年10月至2022年12月期间使用实时逆转录PCR(RT-qPCR)监测废水中的SARS-CoV-2RNA,第四,第五,第六,第七,以及日本爆发的第八波COVID-19。在第三波和第四波中,病毒RNA在所有样品中都低于检测限。然而,通过计算每个样品的qPCR阳性重复数,我们发现,废水中所有重复的阳性率与第三次症状发作日期的临床确诊病例数显著相关,第四,第五波时间步长分析表明,2天任一方的症状发作,COVID-19患者在粪便中排泄了大量废水监测可以检测到的病毒。我们还证明了废水中的病毒基因组拷贝数,根据SARSA-CoV-2RNA的阳性率估计,与临床确诊病例数相关。因此,阳性计数方法可用于追踪低流行地区的COVID-19动态。
    Wastewater-based epidemiology has proved useful for monitoring the COVID-19 infection dynamics in communities. However, in regions of low prevalence, low concentrations of SARS-CoV-2 RNA in wastewater make this difficult. Here, we used real-time reverse-transcription PCR (RT-qPCR) to monitor SARS-CoV-2 RNA in wastewater from October 2020 to December 2022 during the third, fourth, fifth, sixth, seventh, and eighth waves of the COVID-19 outbreak in Japan. Viral RNA was below the limit of detection in all samples during the third and fourth waves. However, by counting the number of positive replicates in qPCR of each sample, we found that the positive ratio to all replicates in wastewater was significantly correlated with the number of clinically confirmed cases by the date of symptom onset during the third, fourth, and fifth waves. Time-step analysis indicated that, for 2 days either side of symptom onset, COVID-19 patients excreted in their feces large amounts of virus that wastewater surveillance could detect. We also demonstrated that the viral genome copy number in wastewater, as estimated from the positive ratio of SARSA-CoV-2 RNA, was correlated with the number of clinically confirmed cases. The positive count method is thus useful for tracing COVID-19 dynamics in regions of low prevalence.
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