零膨胀负二项回归模型在共存疾病影响因素研究中的应用

目的 探讨零膨胀负二项回归模型在居民患有共存疾病及其影响因素研究中的应用。方法 分别用Poisson分布、负二项分布和零膨胀模型来拟合居民共存疾病数量并分析聚集性,筛选出共存疾病的主要影响因素。结果 拟合分布的结果显示,共存疾病数量不符合Poisson分布（χ2=196.419,P<0.001）,符合负二项分布（χ2=6.677,P=0.154）;聚集指数K=1.779,过离散检验统计量O=15.18>1.96,所以资料存在聚集性。零膨胀检验统计量Vuong=6.58,P<0.001,零膨胀模型要优于Poisson或负二项模型。零膨胀负二项回归分析显示:在负二项部分得出,年龄越大、有高强度运动、焦虑程度越高、体质指数越高、糖化血红蛋白（hemoglobin A1c,HbA1c）水平越高、有糖尿病家族史、有高血压史、高收缩压和高水平胆固醇的居民发生共存疾病的数量会增加;在Logit部分得出,年龄越大、焦虑程度越高、体质指数越高、甘油三酯水平越高、空腹血糖（fasting blood glucose,FPG）越高、有高血压家族史和高收缩压的居民发生慢性病的风险较大。结论 居民患共存疾病有聚集性和零计数过多的特点,零膨胀负二项回归模型在拟合具有该类特点的数据中优势明显。     

零膨胀计数资料几种模型方法的比较研究

目的探讨处理零膨胀计数资料的几种模型之间的比较及其应用。方法在R语言中,分别用Poisson回归、负二项回归、零膨胀模型和hurdle模型来拟合66岁以上老年人医疗保健需求的数据,并通过似然比检验、Vuong检验和AIC、BIC的比较,对模型进行评估。结果零膨胀负二项模型和负二项hurdle回归模型对数据的拟合效果优于其他回归模型,负二项hurdle模型的拟合结果与数据更接近,其拟合结果显示老年人住院天数越长、患有慢性病数量越多、受教育年数越久、参加私人保险,其访问医疗诊所的次数越多,而自评健康状况良好、男性的老年人医疗诊所访问的次数较少,即医疗保健需求的次数较少。结论零膨胀负二项回归模型和负二项hurdle模型处理零过多、过离散数据的效果优于一般的计数模型;而在零观测值相对较少的情况下,用负二项hurdle模型可能更合适。     

猩红热的发病率与气象因素的负二项回归分析

目的通过负二项回归模型探讨气象因素与猩红热发病的关系。方法对1985—2005年安徽省某市猩红热月平均发病率和月平均降水量、月平均气压、月平均气温、月平均相对湿度、月平均最低气温5项气象资料的数据进行描述性分析,然后拟合负二项回归模型,并且对2006年每个月份的发病率做一个预测。结果模型的超离散度K=0．41（95％CI：0．32-0．53）,进行似然比）x2检验x2=306．42,P〈0．001,认为发现负二项回归是适合的模型。猩红热的发生与月平均气压、月平均相对湿度和月平均最低气温有统计学意义（均有P〈0．05）。对2006年各个月份的月发病率预测的结果表明（Wilcoxon符号秩和检验,Z=0．24,P=0．814）,预测值与实际值之间差异无统计学意义,提示预测效果比较理想。结论通过拟合负二项回归模型发现,对猩红热的发生和预测,月平均气压、月平均相对湿度和月平均最低气温是不可忽略的气象因素。     

零频数过多模型在亚健康状态研究中的应用

探讨零频数过多(ZI)模型在亚健康症状数研究中的应用.应用Stata 11.0软件拟合ZI模型分析亚健康症状数的危险因素,并用d系数、Vuong检验、O检验、似然比拟合优度检验比较ZI模型与传统负二项回归模型、Poisson回归模型的拟合效果.α=0.939,Vuong检验Z=32.08,P＜0.0001,表明此数据的零频数过多.亚健康症状数的(-x)=2.90,s=3.85,过度离散统计量0=308.011,P＜0.001,s2＞(-x),表明存在过度离散.从4个模型中的拟合优度看,零频数过多的负二项回归(ZINB)模型log likelihood最大,AIC最小,说明ZINB模型的拟合效果最佳.当计数资料中出现过多的零频数时(如亚健康症状数资料),应用ZINB模型能够获得最佳的拟合效果.

Abstract：

To explore the goodness of fit about the zero-inflated (ZI) models in analyzing data related to sub-health symptoms in which the counts are non-negative integers. ZI models are conducted with Stata 11.0. The coefficient of a, Vuong test, O test and likelihood test are used to compare the goodness of fit for ZI models with the common used models such as passion model,negative binomial model. When a is 0.939, and the Z statistic of Vuong test is 32.08, P＜0.0001,which shows that there are too many zeros. The mean number of sub-health symptoms is 2.90, s=3.85, 0=308.011, P＜0.001, s2＞(-x), indicating that the data are over-dispersed. In addition, the optimum goodness of fit is found in zero-inflated negative binomial (ZINB) model with the largest log likelihood and the smallest AIC. ZINB seems the optimal model to study those over-dispersed count data with too many zeros.     

一种空间负二项回归模型及其应用

目的研究用于具有空间相关性资料的一种新的统计分析方法:空间负二项回归。方法构建空间负二项回归模型,利用蒙特卡罗最大似然法进行模型参数估计,并采用钉螺实例,比较常规负二项回归与空间负二项回归的模型拟合与参数估计效果。结果实例分析表明,当资料存在空间相关性时,空间负二项回归可以有效地提高数据拟合精度,改善参数估计。结论空间负二项回归是一种可以用于分析具有空间相关性计数型反应变量的广义线性模型。     

复杂抽样Poisson回归分析方法及应用

目的 本文通过检验45岁及以上的人群体重指数(BMI)与跌倒性伤害发生的联系,详尽地阐述了复杂抽样Poisson回归分析方法及应用的必要性.方法 本报告应用2010年美国德克萨斯州BRFSS数据,分析了跌倒性伤害与体重指数的联系强度.结果 普通Poisson回归分析高估了肥胖、患有心血管疾病、小于25000美元的年收入与跌倒性伤害的联系;低估了中等和差的健康状况、未被雇用、未婚和受教育程度低与跌倒性伤害的联系,但假设检验结果没有变;与复杂抽样负二项回归(NB)分析结果相比,年龄与跌倒性伤害的联系强度没有改变,其统计学检验也保持未变.数据拟合复杂抽样NB回归,离散参数α=8.15,标准误1.68,α的95％ CI=5.44-12.22,表明跌倒性伤害数据的方差是其均数的8.15倍,因此复杂抽样NB回归模型更适合BRFSS数据.结论 普通Poisson回归分析低估了参数估计的方差和标准误,造成了肥胖、患有心血管疾病、小于25000美元的年收入与跌倒性伤害的假关联关系;复杂抽样NB回归调整了模型的参数估计,适合多阶段抽样设计的数据分析.     

重症监护患者呼吸机使用天数影响因素的零截尾计数回归分析

目的 研究零截尾计数模型在临床监测中的应用.方法 零截尾Poisson和负二项回归被应用于一组实际观察到的重症监护患者数据,探索影响其呼吸机使用时间的因素.结果 零截尾负二项模型表明有并发症、气管切开、APACHE得分越高、血中性粒细胞比例增高、伴有肺部炎症等是影响患者呼吸机使用天数增多的主要因素.结论 截尾计数模型可以很好地解决临床监测计数资料零截尾的问题.     

住院病例医疗费用分布及影响因素Logistic回归分析

目的探讨住院病例医疗费用分布及其影响因素.方法用SAS6.12软件对我国南方某市5年来近21万条住院病例进行统计分析,以各分型病例医疗费的上、下四分位数为界,将医疗费分为高、中、低三个等级及高、适度两个等级,用logistic回归分析找出影响费用的因素,并用建模数据和另外6万条数据验证模型预测效果.结果医疗费用的影响因素有:住院日、病人身份、危重病例、手术病例、年龄、医院等级、输血、转归情况(好转)、诊断个数、一级护理等18项.费用分为三个等级的logistic回归模型,对建模病例和验证病例预测符合率分别为63.81%、54.82%;费用分为两个等级的logistic回归模型,预测符合率分别为82.59%、77.32%.结果增加医疗费用划分等级,会增加模型拟合的难度,降低预测结果;利用logistic回归模型判断和预测住院病例医疗费的高低,可以及时地了解费用控制情况,为加强费用管理提供依据.     

Poisson及负二项分布对微核试验数据拟合效果

目的 探讨微核试验数据(每1 000个双核淋巴细胞中具有微核的淋巴细胞数)的统计分布,为微核试验数据的统计分析提供依据.方法 利用东北某大型钢铁公司158名焦炉工和66名非焦炉工微核检测的实例数据,进行矩法估计Poisson分布和二项分布的参数,同时拟合Poisson分布和负二项分布,比较其拟合效果.结果 拟合优度检验显示,焦炉工和非焦炉工微核数据均不服从Poisson分布(P<0.001);焦炉工微核数据服从负二项分布(P=0.545),非焦炉工微核数据虽不服从负二项分布(P<0.001),但该数据似合负二项分布的效果要好于拟合Poisson分布(拟合负二项分布比值3.1<拟合Poisson分布比值20.3).结论 对于具有聚集性趋向(即方差与均数比值较大)的微核数据,相对于拟合Poisson分布,拟合负二项分布是一较好选择.     

传染病链二项分布资料的Poisson回归模型

目的 本文旨在介绍Poisson回归模型在具有链结构的传染病资料分析中的应用。方法 借助极大似然法,对五口之家的普通感冒资料分别拟合五种Poisson回归模型,其中“代数”以亚变量的形式进入模型,而“已感染者数”以连续性指示变量进入模型。结果 本文介绍的模型以Greenwood和Reed—Frost链二项分布模型为特例,Poisson回归模型与相应的链二项分布模型分析结果往往非常近似。结论 用Poisson回归模型处理和分析传染病链二项分布资料更简便易行,必要时可同时分析协变量的作用。     

Performance of the modified Poisson regression approach for estimating relative risks from clustered prospective data

Modified Poisson regression, which combines a log Poisson regression model with robust variance estimation, is a useful alternative to log binomial regression for estimating relative risks. Previous studies have shown both analytically and by simulation that modified Poisson regression is appropriate for independent prospective data. This method is often applied to clustered prospective data, despite a lack of evidence to support its use in this setting. The purpose of this article is to evaluate the performance of the modified Poisson regression approach for estimating relative risks from clustered prospective data, by using generalized estimating equations to account for clustering. A simulation study is conducted to compare log binomial regression and modified Poisson regression for analyzing clustered data from intervention and observational studies. Both methods generally perform well in terms of bias, type I error, and coverage. Unlike log binomial regression, modified Poisson regression is not prone to convergence problems. The methods are contrasted by using example data sets from 2 large studies. The results presented in this article support the use of modified Poisson regression as an alternative to log binomial regression for analyzing clustered prospective data when clustering is taken into account by using generalized estimating equations.     

Estimation of adjusted rate differences using additive negative binomial regression

Rate differences are an important effect measure in biostatistics and provide an alternative perspective to rate ratios. When the data are event counts observed during an exposure period, adjusted rate differences may be estimated using an identity‐link Poisson generalised linear model, also known as additive Poisson regression. A problem with this approach is that the assumption of equality of mean and variance rarely holds in real data, which often show overdispersion. An additive negative binomial model is the natural alternative to account for this; however, standard model‐fitting methods are often unable to cope with the constrained parameter space arising from the non‐negativity restrictions of the additive model. In this paper, we propose a novel solution to this problem using a variant of the expectation–conditional maximisation–either algorithm. Our method provides a reliable way to fit an additive negative binomial regression model and also permits flexible generalisations using semi‐parametric regression functions. We illustrate the method using a placebo‐controlled clinical trial of fenofibrate treatment in patients with type II diabetes, where the outcome is the number of laser therapy courses administered to treat diabetic retinopathy. An R package is available that implements the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Population Heterogeneity in the Salience of Multiple Risk Factors for Adolescent Delinquency

PurposeTo present mixture regression analysis as an alternative to more standard regression analysis for predicting adolescent delinquency. We demonstrate how mixture regression analysis allows for the identification of population subgroups defined by the salience of multiple risk factors.MethodsWe identified population subgroups (i.e., latent classes) of individuals based on their coefficients in a regression model predicting adolescent delinquency from eight previously established risk indices drawn from the community, school, family, peer, and individual levels. The study included N = 37,763 10th-grade adolescents who participated in the Communities That Care Youth Survey. Standard, zero-inflated, and mixture Poisson and negative binomial regression models were considered.ResultsStandard and mixture negative binomial regression models were selected as optimal. The five-class regression model was interpreted based on the class-specific regression coefficients, indicating that risk factors had varying salience across classes of adolescents.ConclusionsStandard regression showed that all risk factors were significantly associated with delinquency. Mixture regression provided more nuanced information, suggesting a unique set of risk factors that were salient for different subgroups of adolescents. Implications for the design of subgroup-specific interventions are discussed.     

Marginalized zero‐inflated negative binomial regression with application to dental caries

The zero‐inflated negative binomial regression model (ZINB) is often employed in diverse fields such as dentistry, health care utilization, highway safety, and medicine to examine relationships between exposures of interest and overdispersed count outcomes exhibiting many zeros. The regression coefficients of ZINB have latent class interpretations for a susceptible subpopulation at risk for the disease/condition under study with counts generated from a negative binomial distribution and for a non‐susceptible subpopulation that provides only zero counts. The ZINB parameters, however, are not well‐suited for estimating overall exposure effects, specifically, in quantifying the effect of an explanatory variable in the overall mixture population. In this paper, a marginalized zero‐inflated negative binomial regression (MZINB) model for independent responses is proposed to model the population marginal mean count directly, providing straightforward inference for overall exposure effects based on maximum likelihood estimation. Through simulation studies, the finite sample performance of MZINB is compared with marginalized zero‐inflated Poisson, Poisson, and negative binomial regression. The MZINB model is applied in the evaluation of a school‐based fluoride mouthrinse program on dental caries in 677 children. Copyright © 2015 John Wiley & Sons, Ltd.     

零膨胀模型在心肌缺血节段数影响因素研究中的应用

目的讨论零膨胀模型在计数资料中的应用。方法应用零膨胀负二项模型分析冠心病患者心肌缺血节段数的影响因素。结果零膨胀负二项模型logit部分结果表明没有家族史、年龄越小、左室收缩末容积越小的患者发生心肌节段缺血的可能性较小;负二项部分结果表明有糖尿病史、有冠心病家族史、左室收缩末容积越大的患者发生心肌缺血节段数越多。结论当计数资料存在过多零计数时,应用零过多模型能够得到很好的拟合效果。     

二分类 Logistic 回归在冠心病危险因素研究中的应用

目的：应用二分类Logistic回归在可能引发冠心病影响因素中筛选危险因素，建立冠心病危险因素“最优”回归方程。方法采取系统抽样方法，对某几所医院心血管内科初诊为冠心病并进行冠脉造影病例，抽取400例30～65岁患者病例作为样本。通过二分类Logistic回归方法分析冠心病与危险因素的相关关系。结果以是否冠心病为因变量，各因素为自变量，筛选影响因素。经相关分析、共线性诊断，筛选出冠心病危险因素为年龄、合并疾病、吸烟、收缩压、血糖、尿酸、低密度脂蛋白、脂蛋白（ a）。结论用二分类Logistic回归找出危险因素，可以有效分析各因素的相对重要性。     

Reducing Monte Carlo error in the Bayesian estimation of risk ratios using log‐binomial regression models

In cohort studies, binary outcomes are very often analyzed by logistic regression. However, it is well known that when the goal is to estimate a risk ratio, the logistic regression is inappropriate if the outcome is common. In these cases, a log‐binomial regression model is preferable. On the other hand, the estimation of the regression coefficients of the log‐binomial model is difficult owing to the constraints that must be imposed on these coefficients. Bayesian methods allow a straightforward approach for log‐binomial regression models and produce smaller mean squared errors in the estimation of risk ratios than the frequentist methods, and the posterior inferences can be obtained using the software WinBUGS. However, Markov chain Monte Carlo methods implemented in WinBUGS can lead to large Monte Carlo errors in the approximations to the posterior inferences because they produce correlated simulations, and the accuracy of the approximations are inversely related to this correlation. To reduce correlation and to improve accuracy, we propose a reparameterization based on a Poisson model and a sampling algorithm coded in R. Copyright © 2015 John Wiley & Sons, Ltd.     

Zero-inflated models for regression analysis of count data: a study of growth and development

Poisson regression is widely used in medical studies, and can be extended to negative binomial regression to allow for heterogeneity. When there is an excess number of zero counts, a useful approach is to used a mixture model with a proportion P of subjects not at risk, and a proportion of 1--P at-risk subjects who take on outcome values following a Poisson or negative binomial distribution. Covariate effects can be incorporated into both components of the models. In child assessment, fine motor development is often measured by test items that involve a process of imitation and a process of fine motor exercise. One such developmental milestone is 'building a tower of cubes'. This study analyses the impact of foetal growth and postnatal somatic growth on this milestone, operationalized as the number of cubes and measured around the age of 22 months. It is shown that the two aspects of early growth may have different implications for imitation and fine motor dexterity. The usual approach of recording and analysing the milestone as a binary outcome, such as whether the child can build a tower of three cubes, may leave out important information.     

Negative binomial distribution versus Poisson in the analysis of recurrent phenomena]

Objective: The aim is to unfold the difficulties likely to arise in risk calculations through aggregated database when the studied phenomenon is recurrent and to display the negative binomial distribution as a valid and simple alternative to analyse this kind of phenomenon.Methods: When the studied phenomenon is recurrent, the analysis by means of the Poisson regression can provoke overdispersion or extra-poisson variance, what leads to underestimating the standard errors in coefficients and may divert into the statistical significance of factors which as a matter of fact are not associated with the phenomenon beforehand. The negative binomial can grasp part of the variance which the Poisson is unable to identify. In order to check this out, the fit of both distributions were compared, based on the number of hospitalizations of individuals aged between 65 and 69, during 1996. This comparison was carried out by means of two different aggregated databases: by individuals and by variables.Results: There were differences in the fitted models by means of both distributions in both databases. By the analysis of the residuals, when using the base by individuals, the negative binomial fits correctly 67.9% of the observations badly fitted by the Poisson. Using the aggregated variables database, the percentage is 50%. In both cases, Poisson estimates four out of the six studied variables as significant. As to the negative binomial, there are two significant based on individuals and one in the variable database.Conclusion: The existence of overdispersion is frequent in recurrent-type phenomena. When this occurs, the negative binomial distribution is more appropiate than the Poisson.