贝叶斯统计在艾滋病疫情估计中的应用

随着艾滋病在世界各国的流行,波及的地域越来越广,人群更多,流行模式更为复杂,对艾滋病疫情估计和预测的方法也需要不断改进与完善。已有的疫情估计中的数理统计模型和计算机软件预测方法各有其优缺点,不同的疫情估计方法相互结合、相互印证有利于艾滋病疫情的综合评估。本文对贝叶斯统计在艾滋病疫情估计中的思想、发展、应用以及注意事项展开综述,为贝叶斯统计在艾滋病疫情估计中的进一步应用提供参考。     

贝叶斯网络模型在体检结果分析中的应用

目的探讨贝叶斯网络在医务人员健康状况分析中的应用,为医务人员健康管理提供方向和思路。方法通过半朴素贝叶斯(TAN)构建年龄、性别、部门(临床/非临床)等基本信息之间的连接,以此为基础建立贝叶斯网络表示各体检指标间的关联关系。结果在2014-2017年某三甲医院医务人员体检数据上,贝叶斯网络以年龄、性别、肝脏为3个中心结点,建立起与其他体检指标的关联。以中心结点肝脏为条件的分组异常检出率统计及贝叶斯网络推断结果同时显示:该院医务人员肝脏与甲状腺、胆囊、肾脏、体重指标之间的关联性差异有统计学意义。结论贝叶斯网络对于建立医务人员体检管理体系具有可参考价值。     

贝叶斯log-binomial回归方法评估患病率比的研究

探讨贝叶斯log-binomial回归估计患病率比的方法及应用。以看护人识别腹泻危险症状与婴幼儿腹泻求医关系为实例,利用Openbugs软件拟合贝叶斯log-binomial回归模型估计看护人识别腹泻危险症状与婴幼儿腹泻求医关系的患病率比（prevalence ratio,PR）。看护人能识别腹泻危险症状可提高大约13%的求医概率。贝叶斯log-binomial回归3个模型均收敛,估计的PR值（95% CI）分别为1.130（1.005～1.265）、1.128（1.001～1.264）、1.132（1.004～1.267）;常规log-binomial回归模型1和模型2收敛,估计的PR值（95% CI）分别为1.130（1.055～1.206）和1.126（1.051～1.203）,但模型3不收敛,用复制方法估计PR值（95% CI）为1.125（1.051～1.200）。贝叶斯log-binomial回归3个模型PR的点估计和区间估计虽与常规log-binomial回归稍有差异,但整体一致性较好。贝叶斯log-binomial回归能有效地估计PR,模型不收敛问题少,与常规log-binomial回归相比在应用上更有优势。     

Logistic 函数模型在预测慢病患病率中的应用

目的探讨不同Logistic函数模型在预测慢性非传染性疾病（慢病）患病率中的应用。方法利用我国建国以来4次大规模高血压抽样调查的数据，分别以年份、人均国内生产总值（gross domestic product，GDP）的对数和老龄化率（65岁以上人群所占比例）作为白变量，患病率作为因变量，并参照美国近50年来的高血压流行状况选取模型的上限，建立Logistic函数模型，对高血压未来的发展趋势进行预估。通过计算各模型的平均绝对误差（MAE）、均方误差（MSE）和决定系数（R^2）比较其拟合效果。结果取40％为Logistic模型的患病率上界，以年份为自变量时，2010年的患病率估计值为20．35％，患病率将在2060年左右趋于稳定（MAE=0．735，MSE=0．704，R^2=0．965）；以人均GDP的对数为自变量时，预计2010年的患病率约为23．80％（MAE=0．896，MSE=0．969，R^2=0．964）；以老龄化率为自变量时，2010年的患病率将达到26．63％（MAE=1．004，MSE=1．659，R^2=0．945）。结论Logistic函数模型在理论上符合人们对未来疾病发展的预估，同时在实际中，可以找到其它国家和地区的疾病流行状况作为现实依托，预测结果较为可靠。其中以GDP和老龄化率作为白变量的模型更注重数据的临床意义。     

Logistic函数模型在预测慢病患病率中的应用

目的探讨不同Logistic函数模型在预测慢性非传染性疾病(慢病)患病率中的应用。方法利用我国建国以来4次大规模高血压抽样调查的数据,分别以年份、人均国内生产总值(gross domestic product,GDP)的对数和老龄化率(65岁以上人群所占比例)作为自变量,患病率作为因变量,并参照美国近50年来的高血压流行状况选取模型的上限,建立Logistic函数模型,对高血压未来的发展趋势进行预估。通过计算各模型的平均绝对误差(MAE)、均方误差(MSE)和决定系数(R2)比较其拟合效果。结果取40%为Logistic模型的患病率上界,以年份为自变量时,2010年的患病率估计值为20.35%,患病率将在2060年左右趋于稳定(MAE=0.735,MSE=0.704,R2=0.963);以人均GDP的对数为自变量时,预计2010年的患病率约为23.80%(MAE=0.896,MSE=0.969,R2=0.964);以老龄化率为自变量时,2010年的患病率将达到26.63%(MAE=1.004,MSE=1.659,R2=0.945)。结论 Logistic函数模型在理论上符合人们对未来疾...     

贝叶斯分层模型在医疗器械临床试验中的应用

贝叶斯方法是基于贝叶斯定理而发展起来的,用于系统阐述和解决统计问题的方法.贝叶斯方法的核心在于参数随机化,在先验概率的基础上通过参数的后验概率进行统计推断.医疗器械往往具备优良的先验信息,贝叶斯方法在器械临床试验中的应用贯穿试验设计和数据分析的各个阶段,贝叶斯方法在正确应用的前提下,临床试验的成本会比频率学派更小.贝叶斯分层模型与经典贝叶斯方法相比,对先验信息的可交换性要求更低,更为灵活的借取“部分”先验信息.本文以一项冠脉支架临床试验为例,应用贝叶斯分层模型方法,对实际结果与传统频率学派方法获得的结果进行比较,并进行相应的讨论.     

贝叶斯时空模型在布鲁氏菌病疫情数据分析中的应用

以2000-2007年内蒙古地区布鲁氏菌病(布病)疫情数据为例,运用空间统计学和传染病流行病学的相关理论,应用贝叶斯理论框架建立时空模型,分析布病在时间和空间上呈现的格局及其演变,以及与之相关联的协变量及其变化,并与传统分析方法进行比较.结果 显示,拟合协变量的贝叶斯时空模型相对较佳(离差信息准则值最小,为2388.000).2000-2007年内蒙古自治区101个旗县的布病疫情呈现较强的空间相关性,时空格局存在较明显的共变现象,每年空间相关性不尽相同,空间相关系数后验中位数位于0.968～0.973之间,总体上随时间变化略呈下降趋势.地区类型和牛羊存栏数量与内蒙古布病流行可能有关,且牛羊存栏数量对布病的影响随年份而变化.与传统描述流行病学分析方法比较,贝叶斯方法对布病发病相对危险度的估计更加稳定.

Abstract：

Based on the number of brucellosis cases reported from the national infectious diseases reporting system in Inner Mongolia from 2000 to 2007, a model was developed. Theories of spatial statistics were used, together with knowledge on infectious disease epidemiology and the frame of Bayesian statistics, before the Bayesian spatio-temporal models were respectively set. The effects of space, time, space-time and the relative covariates were also considered. These models were applied to analyze the brucellosis distribution and time trend in Inner Mongolia during 2000-2007. The results of Bayesian spatio-temporal models was expressed by mapping of the disease and compared to the conventional statistical methods. Results showed that the Bayesian models, under consideration of space-time effect and the relative covariates (deviance information criterion, DIC=2388.000) ,seemed to be the best way to serve the purpose. The county-level spatial correlation of brucellosis epidemics was positive and quite strong in Inner Mongolia. However, the spatial correlation varied with time and the coefficients ranged from 0.968 to 0.973, having a weakening trend during 2000-2007. Types of region and number of stock (cattle and sheep) might be related to the brucellosis epidemics, and the effect on the number of cattle and sheep changed by year. Compared to conventional statistical methods, Bayesian spatio-temporal modeling could precisely estimate the incidence relative risk and was an important tool to analyze the epidemic distribution patterns of infectious diseases and to estimate the incidence relative risk.     

手足口病情层次分析评分及病情分级阈值的拟合分布-贝叶斯修正模型

目的 构建手足口病病情定量评估模型,探索将主观的临床诊疗经验通过客观科学的方式量化为标准化病情分级的方法。方法 提出了基于层次分析法的病情指标权重确定法以及评分模型,基于历史样本数据(训练组123例,验证组70例),进行了病情评分的分布拟合,根据概率密度函数交点得到等级阈值并采用贝叶斯推断对等级阈值进行修正,建立起一个将临床数据分析和专家经验科学融合并标准化的手足口病定量评分分级模型,并进行了三种方法的评价效果比对。结果 训练样本评分的权重层次分析模型ROC曲线的AUC>0.898提示模型构建贴合实际;得到评分模型病情Ⅰ、Ⅱ、Ⅲ等级的具体阈值,对三种方法得到病情等级阈值进行验证得到正确率分别是：分布拟合-贝叶斯推断最优为81%,传统ROC法次之为67%,单一分布拟合最低为64%。结论 本研究提出的基于拟合分布概率密度函数的阈值确定方法较之公认的ROC阈值确定方法结果接近,二者本质思想是一致的,保证了该方法的可信度;其优点在于能够实现和贝叶斯推断的联合,科学融入了专家经验使其正确率明显提升,较好地克服了历史样本代表性不足以及样本量较少的问题。     

贝叶斯统计在率估计与分析中的应用

在疾病流行状况调查中,发病率、患病率和死亡率等这类指标简单而实用,它们在不同人群间的差异可以提示高危人群,对率的空间分布特征和时间变化规律的探讨可以帮助了解疾病的地区差异和变化趋势,提示高危地区,从而指导公共卫生干预措施的制定、实施和监测,因此,正确的率估计和分析十分重要。最近10来年,贝叶斯(Bayes)统计已被用于此方面的研究,本文就此作一概述。Bayes统计基本概念与方法基于总体信息、样本信息和先验信息进行的统计推断被称为Bayes统计〔1〕。它区别于经典统计之处主要为:1)利用先验信息;2)未知参数被看作随机变量而不是…     

贝叶斯时空模型在包虫病研究中的应用与前景

随着计算机技术的发展和时空数据的丰富,贝叶斯时空模型得到了迅速发展,越来越多的学者开始将其运用到传染病空间流行病学研究中。包虫病作为严重危害人类健康的一种全球性自然疫源性疾病,其流行过程复杂,受到多种因素影响。贝叶斯时空模型为包虫病的研究提供了一种新方法,通过建模不仅可以分析其影响因素,还可以进行流行趋势预测和疾病分布...     

Bayesian hierarchical model for analyzing multiresponse longitudinal pharmacokinetic data

Traditional Chinese medicine (TCM) is a very complex mixture containing many different ingredients. Thus, statistical analysis of traditional Chinese medicine data becomes challenging, as one needs to handle the association among the observed data across different time points and across different ingredients of the multivariate response. This paper builds a 3‐stage Bayesian hierarchical model for analyzing multivariate response pharmacokinetic data. Usually, the dimensionality of the parameter space is very huge, which leads to the parameter‐estimation difficulty. So we take the hybrid Markov chain Monte Carlo algorithms to obtain the posterior Bayesian estimation of corresponding parameters in our model. Both simulation study and real‐data analysis show that our theoretical model and Markov chain Monte Carlo algorithms perform well, and especially the correlation among different ingredients can be calculated very accurately.     

Bayesian空间泊松模型对小区域非传染病患病率的估计

目的为地理小区域非传染病患病率的估计及疾病地理分布情况的探讨提供方法学上的理论依据。方法以四川省2000年8～10岁儿童甲状腺肿大率为例，为克服甲状腺肿大的空间自相关性和异质性，构建Bayesian空间泊松模型，用Gibbs抽样的MCMC模型技术估计各县（区）的甲状腺肿大率。结果用Bayesian空间泊松模型得到的估计率与粗率相比，前者得到的非病区、中等病区及重病区数目比后者要少，轻病区数目要多。结论利用Bayesian空间泊松模型有利于消除抽样引起的极端值，使得其估计值比由原样本得到的粗率稳健。     

A comparison of Bayesian hierarchical modeling with group‐based exposure assessment in occupational epidemiology

We build a Bayesian hierarchical model for relating disease to a potentially harmful exposure, by using data from studies in occupational epidemiology, and compare our method with the traditional group‐based exposure assessment method through simulation studies, a real data application, and theoretical calculation. We focus on cohort studies where a logistic disease model is appropriate and where group means can be treated as fixed effects. The results show a variety of advantages of the fully Bayesian approach and provide recommendations on situations where the traditional group‐based exposure assessment method may not be suitable to use. Copyright © 2013 John Wiley & Sons, Ltd.     

Bayesian hierarchical EMAX model for dose-response in early phase efficacy clinical trials

A primary goal of a phase II dose-ranging trial is to identify a correct dose before moving forward to a phase III confirmatory trial. A correct dose is one that is actually better than control. A popular model in phase II is an independent model that puts no structure on the dose-response relationship. Unfortunately, the independent model does not efficiently use information from related doses. One very successful alternate model improves power using a pre-specified dose-response structure. Past research indicates that EMAX models are broadly successful and therefore attractive for designing dose-response trials. However, there may be instances of slight risk of nonmonotone trends that need to be addressed when planning a clinical trial design. We propose to add hierarchical parameters to the EMAX model. The added layer allows information about the treatment effect in one dose to be “borrowed” when estimating the treatment effect in another dose. This is referred to as the hierarchical EMAX model. Our paper compares three different models (independent, EMAX, and hierarchical EMAX) and two different design strategies. The first design considered is Bayesian with a fixed trial design, and it has a fixed schedule for randomization. The second design is Bayesian but adaptive, and it uses response adaptive randomization. In this article, a randomized trial of patients with severe traumatic brain injury is provided as a motivating example.     

A hierarchical model for spatially clustered disease rates

Maps of regional disease rates are potentially useful tools in examining spatial patterns of disease and for identifying clusters. Bayes and empirical Bayes approaches to this problem have proven useful in smoothing crude maps of disease rates. In recent years, models including both spatially correlated random effects and spatially unstructured random effects have been very popular. The spatially correlated random effects have been proposed in an attempt to capture a general clustering in the data. As an alternative, we propose replacing the spatially structured random effect with fixed clustering effects associated with particular areas. A reversible jump Markov chain Monte Carlo (RJMCMC) algorithm for posterior inference is described. We illustrate the model using the well-known New York leukaemia data.     

Bayesian hierarchical modeling of drug stability data

Stability data are commonly analyzed using linear fixed or random effect model. The linear fixed effect model does not take into account the batch-to-batch variation, whereas the random effect model may suffer from the unreliable shelf-life estimates due to small sample size. Moreover, both methods do not utilize any prior information that might have been available. In this article, we propose a Bayesian hierarchical approach to modeling drug stability data. Under this hierarchical structure, we first use Bayes factor to test the poolability of batches. Given the decision on poolability of batches, we then estimate the shelf-life that applies to all batches. The approach is illustrated with two example data sets and its performance is compared in simulation studies with that of the commonly used frequentist methods.     

Bayesian hierarchical joint modeling of repeatedly measured continuous and ordinal markers of disease severity: Application to Ugandan diabetes data

Modeling of correlated biomarkers jointly has been shown to improve the efficiency of parameter estimates, leading to better clinical decisions. In this paper, we employ a joint modeling approach to a unique diabetes dataset, where blood glucose (continuous) and urine glucose (ordinal) measures of disease severity for diabetes are known to be correlated. The postulated joint model assumes that the outcomes are from distributions that are in the exponential family and hence modeled as multivariate generalized linear mixed effects model associated through correlated and/or shared random effects. The Markov chain Monte Carlo Bayesian approach is used to approximate posterior distribution and draw inference on the parameters. This proposed methodology provides a flexible framework to account for the hierarchical structure of the highly unbalanced data as well as the association between the 2 outcomes. The results indicate improved efficiency of parameter estimates when blood glucose and urine glucose are modeled jointly. Moreover, the simulation studies show that estimates obtained from the joint model are consistently less biased and more efficient than those in the separate models.     

A Bayesian method for estimating prevalence in the presence of a hidden sub-population

When estimating the prevalence of a binary trait in a population, the presence of a hidden sub‐population that cannot be sampled will lead to nonidentifiability and potentially biased estimation. We propose a Bayesian model of trait prevalence for a weighted sample from the non‐hidden portion of the population, by modeling the relationship between prevalence and sampling probability. We studied the behavior of the posterior distribution on population prevalence, with the large‐sample limits of posterior distributions obtained in simple analytical forms that give intuitively expected properties. We performed MCMC simulations on finite samples to evaluate the effectiveness of statistical learning. We applied the model and the results to two illustrative datasets arising from weighted sampling. Our work confirms that sensible results can be obtained using Bayesian analysis, despite the nonidentifiability in this situation. Copyright © 2012 John Wiley & Sons, Ltd.     

A Bayesian hierarchical model with novel prior specifications for estimating HIV testing rates

Human immunodeficiency virus (HIV) infection is a severe infectious disease actively spreading globally, and acquired immunodeficiency syndrome (AIDS) is an advanced stage of HIV infection. The HIV testing rate, that is, the probability that an AIDS‐free HIV infected person seeks a test for HIV during a particular time interval, given no previous positive test has been obtained prior to the start of the time, is an important parameter for public health. In this paper, we propose a Bayesian hierarchical model with two levels of hierarchy to estimate the HIV testing rate using annual AIDS and AIDS‐free HIV diagnoses data. At level one, we model the latent number of HIV infections for each year using a Poisson distribution with the intensity parameter representing the HIV incidence rate. At level two, the annual numbers of AIDS and AIDS‐free HIV diagnosed cases and all undiagnosed cases stratified by the HIV infections at different years are modeled using a multinomial distribution with parameters including the HIV testing rate. We propose a new class of priors for the HIV incidence rate and HIV testing rate taking into account the temporal dependence of these parameters to improve the estimation accuracy. We develop an efficient posterior computation algorithm based on the adaptive rejection metropolis sampling technique. We demonstrate our model using simulation studies and the analysis of the national HIV surveillance data in the USA. Copyright © 2015 John Wiley & Sons, Ltd.     

Epigenetic change detection and pattern recognition via Bayesian hierarchical hidden Markov models

Epigenetics is the study of changes to the genome that can switch genes on or off and determine which proteins are transcribed without altering the DNA sequence. Recently, epigenetic changes have been linked to the development and progression of disease such as psychiatric disorders. High‐throughput epigenetic experiments have enabled researchers to measure genome‐wide epigenetic profiles and yield data consisting of intensity ratios of immunoprecipitation versus reference samples. The intensity ratios can provide a view of genomic regions where protein binding occur under one experimental condition and further allow us to detect epigenetic alterations through comparison between two different conditions. However, such experiments can be expensive, with only a few replicates available. Moreover, epigenetic data are often spatially correlated with high noise levels. In this paper, we develop a Bayesian hierarchical model, combined with hidden Markov processes with four states for modeling spatial dependence, to detect genomic sites with epigenetic changes from two‐sample experiments with paired internal control. One attractive feature of the proposed method is that the four states of the hidden Markov process have well‐defined biological meanings and allow us to directly call the change patterns based on the corresponding posterior probabilities. In contrast, none of existing methods can offer this advantage. In addition, the proposed method offers great power in statistical inference by spatial smoothing (via hidden Markov modeling) and information pooling (via hierarchical modeling). Both simulation studies and real data analysis in a cocaine addiction study illustrate the reliability and success of this method. Copyright © 2012 John Wiley & Sons, Ltd.