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Is The Age-Period-Cohort Model Well Suited to an Epidemic Context? The Case of the French BSE Epidemic 年龄-时期-队列模型适合于流行病背景吗?法国疯牛病流行案例
Pub Date : 2012-10-24 DOI: 10.1515/1948-4690.1047
C. Sala, B. Durand, D. Costagliola, C. Ducrot, D. Calavas
Abstract Although Age-Period-Cohort (APC) models are routinely used in time-trend analyses of chronic diseases, few examples of their application to epidemic diseases are available. APC analyses of the French bovine spongiform encephalopathy (BSE) epidemic revealed an unexpected period effect, which was attributed to the design of the study, in connection with low BSE prevalence and a short surveillance period. The aim of our study was to evaluate the relevance of this hypothesis, the behaviour of the APC model in an epidemic context (e.g. the BSE epidemic) and the impact of including the period effect in an APC model on the estimate of birth cohort effects. We simulated datasets mimicking the French BSE epidemic and its variable pattern, as well as duration and the surveillance time period, and analysed them with a categorical APC model. Results showed a period effect in 44% of analysed datasets, although no period effect had been introduced in the data simulation process. This type of artefactual period effect was detected when a sudden change in cohort prevalence occurred over a short period of time. Additionally, in the context of BSE, including a period effect in the model may dramatically affect the estimation of cohort prevalence, depending on epidemic pattern and, as expected, duration and the surveillance time period according to the year in which highly infected birth cohorts are detected as BSE cases.
虽然年龄-时期-队列(Age-Period-Cohort, APC)模型通常用于慢性疾病的时间趋势分析,但很少有将其应用于流行病的例子。对法国牛海绵状脑病(BSE)流行的APC分析揭示了一种意想不到的时期效应,这归因于该研究的设计,与低疯牛病流行率和短监测期有关。我们研究的目的是评估这一假设的相关性,流行病背景下APC模型的行为(例如疯牛病),以及APC模型中包括时期效应对出生队列效应估计的影响。我们模拟了法国疯牛病流行及其变化模式、持续时间和监测时间段的数据集,并使用分类APC模型对其进行了分析。结果显示44%的分析数据集存在周期效应,尽管在数据模拟过程中没有引入周期效应。当队列患病率在短时间内发生突然变化时,检测到这种类型的人工周期效应。此外,在疯牛病的背景下,在模型中包括时期效应可能会极大地影响队列患病率的估计,这取决于流行模式,以及(如预期的)持续时间和根据检测到高度感染的出生队列为疯牛病病例的年份的监测时间段。
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引用次数: 0
HIV Sexual Networks: The Montreal Experience 艾滋病毒性网络:蒙特利尔经验
Pub Date : 2012-01-24 DOI: 10.1515/1948-4690.1039
B. Brenner, E. Moodie
While highly active antiretroviral therapy (HAART) has transformed HIV/AIDS to a chronic, treatable disease in Canada, HIV incidence continues to rise among male-sex-male (MSM) populations. Montreal, Canada, is a unique environment for a comprehensive surveillance study on HIV transmission dynamics. Phylogenetic strategies show that half of all new MSM infections in Montreal may arise through onward transmission by individuals who are in primary HIV infection (PHI) (< 6 months post-infection) and often unaware of their HIV status. Large cluster networks, wherein one infection leads to 5-31 onward transmissions, constitute the fastest-growing sub-epidemic, representing 25% and 39% of genotyped incident infections in 2005 and 2009, respectively. This has disturbing implications in light of the introduction of non-B subtype and drug-resistant sub-epidemics. Biological and behavioural correlates of cluster membership are being investigated to establish risk determinants implicated in the onward transmission of the MSM epidemic. Our findings underscore the opportunities and challenges in implementing new testing and tailored prevention paradigms for different MSM populations.
虽然高效抗逆转录病毒疗法(HAART)已将艾滋病毒/艾滋病转变为加拿大的一种可治疗的慢性疾病,但男性-男性(MSM)人群中的艾滋病毒发病率继续上升。加拿大蒙特利尔是开展艾滋病毒传播动态综合监测研究的独特环境。系统发育策略显示,蒙特利尔所有新的MSM感染中有一半可能是由原发HIV感染(感染后< 6个月)的个体(通常不知道自己的HIV状态)通过继续传播而引起的。一个感染导致5-31人继续传播的大型聚集性网络构成了增长最快的亚流行病,分别占2005年和2009年基因型事件感染的25%和39%。鉴于非b亚型和耐药亚流行的出现,这具有令人不安的影响。正在调查群集成员的生物学和行为相关性,以确定与男男性行为者流行病进一步传播有关的风险决定因素。我们的研究结果强调了针对不同男男性行为人群实施新的检测和量身定制的预防范例的机遇和挑战。
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引用次数: 9
Maximum a Posteriori Estimation in Dynamical Models of Primary HIV Infection 原发HIV感染动态模型中的最大后验估计
Pub Date : 2012-01-08 DOI: 10.1515/1948-4690.1040
J. Drylewicz, D. Commenges, R. Thiébaut
Dynamical models based on ordinary differential equations (ODE) are increasingly used to model viral infections such as HIV. This kind of model is based on biological knowledge and takes into account complex non-linear interactions between markers. The estimation of such models is made difficult by the lack of analytical solutions and several methods based on Bayesian or frequentist approaches have been proposed. However, because of identifiability issues, in a frequentist approach some parameters have to be fixed to values taken from the literature. In this paper we propose a Maximum A Posteriori (MAP) approach to estimate all the parameters of ODE models, allowing prior knowledge on biological parameters to be taken into account. The MAP approach has two main advantages: the computation time can be fast (relative to the full Bayesian approach) and it is straightforward to incorporate complex prior information. We applied this method to an original model of primary HIV infection taking into account several biological hypotheses for the HIV-immune system interaction. Parameters were estimated using HIV RNA load and CD4 count measurements of 710 patients from the Concerted Action on SeroConversion to AIDS and Death in Europe (CASCADE) Collaboration.
基于常微分方程(ODE)的动力学模型越来越多地用于模拟病毒感染,如HIV。这种模型以生物学知识为基础,并考虑到标记之间复杂的非线性相互作用。由于缺乏解析解,这类模型的估计变得困难,人们提出了几种基于贝叶斯或频率方法的方法。然而,由于可识别性问题,在频率论方法中,一些参数必须固定为取自文献的值。在本文中,我们提出了一种最大后验(MAP)方法来估计ODE模型的所有参数,允许考虑生物参数的先验知识。MAP方法有两个主要优点:计算时间可以很快(相对于全贝叶斯方法),并且可以直接合并复杂的先验信息。我们将这种方法应用于原发HIV感染的原始模型,同时考虑到HIV-免疫系统相互作用的几种生物学假设。使用来自欧洲血清转化为艾滋病和死亡协调行动(CASCADE)合作的710名患者的HIV RNA载量和CD4计数测量来估计参数。
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引用次数: 13
Statistical Considerations in Determining HIV Incidence from Changes in HIV Prevalence 从艾滋病毒流行率的变化确定艾滋病毒发病率的统计考虑
Pub Date : 2011-11-06 DOI: 10.2202/1948-4690.1044
R. Brookmeyer, J. Konikoff
The development of methods for estimating HIV incidence is critical for tracking the epidemic and for designing, targeting and evaluating HIV prevention efforts. One method for estimating incidence is based on changes in HIV prevalence. That method is attracting increased attention because national population-based HIV prevalence surveys, such as Demographic and Health Surveys, are being conducted throughout the world. Here, we consider some statistical issues associated with estimating HIV incidence from two population-based HIV prevalence surveys conducted at two different points in time. We show that the incidence estimator depends on the relative survival rate. We evaluate the sensitivity of estimates to incorrect assumptions about the relative survival rate, and show that small errors in the relative survival can, in some situations, create large biases in HIV incidence. We determine sample sizes of prevalence surveys to estimate incidence with precision and show how the sample sizes depend on baseline prevalence, the relative survival rate, and the population HIV incidence rate. We find that even if the relative survival rate were known exactly, there are situations where prohibitively large prevalence surveys would be required to produce reliable incidence estimates. These situations can occur either when the baseline prevalence is large, the relative survival rate is near 1, or the population incidence is small. Because information on the relative survival rate may be limited or not specific to the population under study, we suggest an approach to empirically estimate this critical parameter by augmenting population-based prevalence surveys with a mortality follow-up sub-study. We determine sample sizes of the prevalence surveys and mortality sub-studies for this augmented design and provide the necessary R code (version 2.13.0) for sample size determinations. We conclude that caution should be exercised when solely relying on changes in prevalence as the method for determining HIV incidence because of the method's sensitivity to mortality assumptions and the very large sample size requirements in some settings.
制定估计艾滋病毒发病率的方法对于跟踪这一流行病以及设计、确定和评估艾滋病毒预防工作至关重要。估计发病率的一种方法是基于艾滋病毒流行率的变化。这种方法正在引起越来越多的注意,因为世界各地正在进行以人口为基础的艾滋病毒流行情况调查,例如人口和健康调查。在这里,我们考虑了在两个不同时间点进行的两次基于人群的艾滋病毒流行率调查中与估计艾滋病毒发病率相关的一些统计问题。我们表明,发病率估计取决于相对存活率。我们评估了估计对不正确的相对存活率假设的敏感性,并表明在某些情况下,相对存活率的小误差可能会造成艾滋病毒发病率的大偏差。我们确定患病率调查的样本量,以精确估计发病率,并显示样本量如何取决于基线患病率、相对存活率和人口艾滋病毒发病率。我们发现,即使确切地知道相对存活率,在某些情况下,要产生可靠的发病率估计,就需要进行大规模的患病率调查。这些情况可能发生在基线患病率较高、相对存活率接近1或人群发病率较低的情况下。由于相对存活率的信息可能有限或并非特定于所研究的人群,我们建议通过增加基于人群的患病率调查和死亡率随访子研究来经验估计这一关键参数。我们确定了这个增强设计的患病率调查和死亡率子研究的样本量,并提供了必要的R代码(版本2.13.0)来确定样本量。我们的结论是,当仅仅依靠流行率的变化作为确定艾滋病毒发病率的方法时,应该谨慎行事,因为该方法对死亡率假设很敏感,而且在某些情况下需要非常大的样本量。
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引用次数: 11
Using HIV Diagnostic Data to Estimate HIV Incidence: Method and Simulation 使用HIV诊断数据估计HIV发病率:方法和模拟
Pub Date : 2011-10-11 DOI: 10.2202/1948-4690.1011
P. Yan, Fan Zhang, H. Wand
We propose a new approach to estimate the number of new infections with the human immunodeficiency virus (HIV), by integrating the back-calculation method based on HIV diagnostic data with proportions of recent infections among newly diagnosed individuals. This is done by establishing an explicit link between the distribution of time-since-infection given being tested and the distribution of time-to-testing given being infected. The trend in the proportions of recent infections identifies the time-to-testing distribution, which would have not been identifiable based on HIV surveillance data alone, and makes back-calculation possible. The integration of the proportions of recent infections among newly diagnosed HIV into the model allows a probabilistic interpretation of the estimated proportions of recent infections based on the results of laboratory tests, in terms of the estimated distribution of the time-since-infection given being tested.
我们提出了一种估计人类免疫缺陷病毒(HIV)新感染人数的新方法,该方法将基于HIV诊断数据的反向计算方法与新诊断个体中最近感染的比例相结合。这是通过在被检测的感染时间分布与被感染的检测时间分布之间建立明确的联系来实现的。最近感染比例的趋势确定了检测时间分布,这是单独根据艾滋病毒监测数据无法确定的,并使反向计算成为可能。将新诊断的艾滋病毒中最近感染的比例纳入模型,可以根据实验室检测结果,根据被检测的自感染时间的估计分布,对最近感染的估计比例作出概率解释。
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引用次数: 22
A Sequential Phase 2b Trial Design for Evaluating Vaccine Efficacy and Immune Correlates for Multiple HIV Vaccine Regimens. 一项评估多种HIV疫苗方案的疫苗效力和免疫相关因素的序贯2b期试验设计
Pub Date : 2011-10-01 DOI: 10.2202/1948-4690.1037
Peter B Gilbert, Douglas Grove, Erin Gabriel, Ying Huang, Glenda Gray, Scott M Hammer, Susan P Buchbinder, James Kublin, Lawrence Corey, Steven G Self

Five preventative HIV vaccine efficacy trials have been conducted over the last 12 years, all of which evaluated vaccine efficacy (VE) to prevent HIV infection for a single vaccine regimen versus placebo. Now that one of these trials has supported partial VE of a prime-boost vaccine regimen, there is interest in conducting efficacy trials that simultaneously evaluate multiple prime-boost vaccine regimens against a shared placebo group in the same geographic region, for accelerating the pace of vaccine development. This article proposes such a design, which has main objectives (1) to evaluate VE of each regimen versus placebo against HIV exposures occurring near the time of the immunizations; (2) to evaluate durability of VE for each vaccine regimen showing reliable evidence for positive VE; (3) to expeditiously evaluate the immune correlates of protection if any vaccine regimen shows reliable evidence for positive VE; and (4) to compare VE among the vaccine regimens. The design uses sequential monitoring for the events of vaccine harm, non-efficacy, and high efficacy, selected to weed out poor vaccines as rapidly as possible while guarding against prematurely weeding out a vaccine that does not confer efficacy until most of the immunizations are received. The evaluation of the design shows that testing multiple vaccine regimens is important for providing a well-powered assessment of the correlation of vaccine-induced immune responses with HIV infection, and is critically important for providing a reasonably powered assessment of the value of identified correlates as surrogate endpoints for HIV infection.

在过去12年中进行了五项预防性艾滋病毒疫苗效力试验,所有试验都评估了单一疫苗方案与安慰剂相比预防艾滋病毒感染的疫苗效力(VE)。现在,其中一项试验已经支持了一种主要-加强疫苗方案的部分有效性,因此有兴趣进行功效试验,同时评估同一地理区域内的多种主要-加强疫苗方案与同一安慰剂组的疗效,以加快疫苗开发的步伐。本文提出了这样一种设计,其主要目标是(1)评估每种方案与安慰剂相比,在免疫接种前后HIV暴露的VE;(2)评估有可靠证据表明VE阳性的各疫苗方案的VE持久性;(3)如果任何疫苗方案显示可靠的VE阳性证据,则迅速评估保护的免疫相关因素;(4)比较不同疫苗方案的VE。该设计采用对疫苗危害、无效和高效事件的连续监测,选择以尽可能快地淘汰不良疫苗,同时防止过早淘汰在接受大多数免疫接种之前不具有效力的疫苗。对设计的评估表明,测试多种疫苗方案对于提供疫苗诱导的免疫反应与HIV感染相关性的有力评估非常重要,并且对于提供确定的相关物作为HIV感染替代终点的价值的合理有力评估至关重要。
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引用次数: 39
Sample Size for a Binomial Proportion with Autocorrelation. 自相关二项比例的样本量。
Pub Date : 2011-10-01 Epub Date: 2011-10-24 DOI: 10.2202/1948-4690.1036
Amalia S Magaret, Jeffrey Stanaway

A flexible sample size computation is desired for a binomial outcome consisting of repeated binary measures with autocorrelation over time. This type of outcome is common in viral shedding studies, in which each individual's outcome is a proportion: the number of samples on which virus is detected out of number of samples assessed. Autocorrelation between proximal samples occurs in some conditions such as herpes infection, in which reactivation is episodic. We determine a sample size computation that accounts for: (1) participant-level differences in outcome frequency, (2) autocorrelation in time between samples, and (3) varying number of samples per participant. In addition, we develop a computation appropriate for crossover designs that accounts for the dependence of the investigational treatment effect on the pretreatment detection frequency. The computations are validated through comparison with real and simulated data, and sensitivity to misspecification of parameter values is examined graphically.

一个灵活的样本量计算是需要的二项结果组成的重复二进制测量自相关随时间。这种类型的结果在病毒脱落研究中很常见,其中每个个体的结果是一个比例:在评估的样本数量中检测到病毒的样本数量。近端样本之间的自相关性发生在某些情况下,如疱疹感染,其中再激活是偶发性的。我们确定了一个样本大小计算,该计算考虑:(1)结果频率的参与者水平差异,(2)样本之间时间的自相关性,以及(3)每个参与者的样本数量的变化。此外,我们开发了一种适用于交叉设计的计算,该计算考虑了研究处理效果对预处理检测频率的依赖性。通过与真实数据和模拟数据的比较,验证了计算结果的正确性,并通过图形检验了对参数值错配的敏感性。
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引用次数: 1
Joint Modeling of HCV and HIV Co-Infection among Injecting Drug Users in Italy and Spain Using Individual Cross-Sectional Data 意大利和西班牙注射吸毒者中HCV和HIV合并感染的个体横断面数据联合建模
Pub Date : 2011-07-05 DOI: 10.2202/1948-4690.1010
E. Del Fava, Z. Shkedy, Niel Hens, M. Aerts, B. Suligoi, L. Camoni, F. Vallejo, L. Wiessing, M. Kretzschmar
The aim of the analysis presented in this paper is to study co-infection with hepatitis C virus (HCV) and human immunodeficiency virus (HIV) in injecting drug users (IDUs) using a joint modeling approach that makes use of multivariate statistical methods for current status data. Using marginal models, we estimate association measures between HCV and HIV infections at individual level, i.e., odds ratios and correlation coefficients, and we regress them against some risk factors, e.g., the length of the injecting career, the age at first injection, the ever sharing of syringes, and the frequency of current injecting. In addition, we fit random-effects models that take into account the individual heterogeneity in the acquisition of the infections. For our analysis, we use cross-sectional data from two independent serological surveys, one carried out in Italy (IT) in 2005 on 856 subjects, and the other in three Spanish (ES) cities, between 2001 and 2003, on 589 subjects. We found that the infections are positively associated within individuals, e.g., ORIT=2.56 with 95% confidence interval (CI) (1.43, 6.68) and ORES= 2.42, with 95% CI (1.41, 4.30). We found that the odds ratio and the correlation between HCV and HIV infections increase positively with the length of the injecting career. Moreover, they are found to be significantly positive in case IDUs have never shared syringes or report low injecting frequencies. The variance of the individual random effects is positive, e.g., σb2=0.34 (0.14, 0.62), indicating that there is significant individual heterogeneity in the acquisition of the infections. Our results show that a significant association between HCV and HIV infections within IDUs is related to significant individual heterogeneity in the acquisition of the infections. Indeed, the association between these infections in IDUs who report ever sharing syringes is not significant, which can be explained by a higher homogeneity in their behaviors and, therefore, in their acquisition of the infections.
本文分析的目的是使用联合建模方法研究注射吸毒者(IDUs)中丙型肝炎病毒(HCV)和人类免疫缺陷病毒(HIV)的联合感染,该方法利用当前状态数据的多变量统计方法。使用边际模型,我们在个体水平上估计了HCV和HIV感染之间的关联度量,即比值比和相关系数,并将其与一些危险因素(如注射生涯的长度、首次注射的年龄、是否共用注射器以及当前注射的频率)进行回归。此外,我们拟合随机效应模型,考虑到个体感染的异质性。在我们的分析中,我们使用了来自两个独立血清学调查的横断面数据,一个是2005年在意大利(IT)进行的856名受试者,另一个是2001年至2003年在三个西班牙(ES)城市进行的589名受试者。我们发现个体感染呈正相关,例如,ORIT=2.56, 95%可信区间(CI) (1.43, 6.68), ORES= 2.42, 95%可信区间(CI)(1.41, 4.30)。我们发现HCV和HIV感染的比值比和相关性随着注射生涯的延长而增加。此外,如果注射吸毒者从未共用注射器或报告注射频率低,则发现它们显着呈阳性。个体随机效应的方差为正,σb2=0.34(0.14, 0.62),表明感染的个体异质性显著。我们的研究结果表明,注射吸毒者中HCV和HIV感染之间的显著关联与感染获得的显著个体异质性有关。事实上,在报告曾经共用注射器的注射吸毒者中,这些感染之间的关联并不显著,这可以解释为他们的行为具有较高的同质性,因此,在他们获得感染的过程中。
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引用次数: 18
Using Approximate Bayesian Computation to Estimate Transmission Rates of Nosocomial Pathogens 用近似贝叶斯计算估计医院病原体的传播率
Pub Date : 2011-06-22 DOI: 10.2202/1948-4690.1025
C. Drovandi, A. Pettitt
In this paper, we apply a simulation based approach for estimating transmission rates of nosocomial pathogens. In particular, the objective is to infer the transmission rate between colonised health-care practitioners and uncolonised patients (and vice versa) solely from routinely collected incidence data. The method, using approximate Bayesian computation, is substantially less computer intensive and easier to implement than likelihood-based approaches we refer to here. We find through replacing the likelihood with a comparison of an efficient summary statistic between observed and simulated data that little is lost in the precision of estimated transmission rates. Furthermore, we investigate the impact of incorporating uncertainty in previously fixed parameters on the precision of the estimated transmission rates.
在本文中,我们应用基于模拟的方法来估计医院病原体的传播率。具体而言,其目标是仅从常规收集的发病率数据推断移民保健从业人员与非移民患者之间的传播率(反之亦然)。该方法使用近似贝叶斯计算,与我们在这里提到的基于似然的方法相比,它的计算机密集程度大大降低,并且更容易实现。我们发现,通过用观测数据和模拟数据之间的有效汇总统计量的比较来代替似然,估计传输速率的精度几乎没有损失。此外,我们还研究了在先前固定参数中加入不确定性对估计传输速率精度的影响。
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引用次数: 18
Joint Modeling of HCV and HIV Infections among Injecting Drug Users in Italy Using Repeated Cross-Sectional Prevalence Data 意大利注射吸毒者中HCV和HIV感染的联合建模使用重复横断面流行数据
Pub Date : 2011-05-24 DOI: 10.2202/1948-4690.1009
E. Del Fava, Adetayo S Kasim, Muhammad Usman, Z. Shkedy, Niel Hens, M. Aerts, K. Bollaerts, Gianpaolo Scalia Tomba, P. Vickerman, A. J. Sutton, L. Wiessing, M. Kretzschmar
During their injecting career, injecting drug users (IDUs) are exposed to some infections, like hepatitis C virus (HCV) infection and human immunodeficiency virus (HIV) infection, due to their injecting behavioral risk factors, such as sharing syringes or other paraphernalia containing infected blood, or sexual behavior risk factors. If we consider that these IDUs might belong to a social network of people where these behavioral risk factors are spread, then HCV and HIV infections might be associated at both the individual and the population level. In this paper, we study the association between HCV and HIV infection at the population level using aggregate data. Our aim is to define a hierarchy of structured models with which the association between HCV and HIV infection at population level and the time trend of prevalence can be investigated. The data analyzed in the paper are “diagnostic testing data,” which consist of repeated cross-sectional prevalence measurements from 1998 to 2006 for HCV and HIV infection, obtained from a sample of 515 drug treatment centers spread among the 20 regions in Italy, where subjects went for a serum diagnostic test. Since we do not have any individual data, it is not possible to relate these prevalence data to socio-demographic or behavioral risk data. Each region defines a cluster with repeated prevalence data for HCV and HIV infection over time. Several modeling approaches, such as generalized linear mixed models (GLMMs) and hierarchical Bayesian models are applied to the data. First, we test different covariance structures for the region-specific random effects in the GLMM context; second, a hierarchical Bayesian model is used to refit the best GLMM in order to obtain the posterior distribution for the parameters of primary interest. We found that the correlation at population level between HCV and HIV is approximately 0.68 and the prevalence of the two infections generally decreased over the years, compared to the situation in 1998.
注射吸毒者(IDUs)在其注射生涯中,由于其注射行为风险因素,如共用注射器或其他含有受感染血液的器具,或性行为风险因素,会暴露于某些感染,如丙型肝炎病毒(HCV)感染和人类免疫缺陷病毒(HIV)感染。如果我们考虑到这些注射吸毒者可能属于这些行为风险因素传播的人群的社会网络,那么HCV和HIV感染可能在个人和群体水平上都有关联。在本文中,我们使用汇总数据在人群水平上研究了HCV和HIV感染之间的关系。我们的目标是定义一个层次结构模型,通过该模型可以调查人群水平上HCV和HIV感染之间的关系以及患病率的时间趋势。论文中分析的数据是“诊断测试数据”,包括1998年至2006年丙型肝炎病毒和艾滋病毒感染的重复横断面流行测量,从意大利20个地区的515个药物治疗中心的样本中获得,受试者在那里进行血清诊断测试。由于我们没有任何个人数据,因此不可能将这些流行率数据与社会人口统计学或行为风险数据联系起来。每个地区都定义了一个集群,其中包含一段时间内丙型肝炎病毒和艾滋病毒感染的重复流行数据。采用了广义线性混合模型(glmm)和层次贝叶斯模型等建模方法。首先,我们测试了不同协方差结构在GLMM背景下的区域特异性随机效应;其次,利用层次贝叶斯模型对最佳GLMM进行重构,得到主感兴趣参数的后验分布;我们发现HCV和HIV在人群水平上的相关性约为0.68,与1998年的情况相比,这两种感染的患病率逐年下降。
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引用次数: 8
期刊
Statistical communications in infectious diseases
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