重复测量数据的混合模型及其MIXED过程实现—混合线性模型及其SAS软件实现（二）

目的：重复测量数据存在自相关及随机误差分布于不同层次,不宜使用常规分析方法,本文研讨使用混合线性模型及SAS软件实现的分析方法;方法：利用MIXED对多个处理组的重复测量数据进行混合模型分析。结果：通过固定效应与随机效应及对协方差矩阵的估计,使重复测量数据得以合理的分析。结论：MIXED可以有效地,全面地分析重复测量数据。     

医学诊断试验评价的ROC分析—重复测量诊断数据的ROC曲线

目的 探讨诊断试验中重复有序分类测量数据的ROC分析方法。方法 在有序模型基础上构造相应的ROC模型,然后选用累积logistic模型作为联系函数,采用GEE方法进行参数估计。结果 通过累积logistic模型的参数估计,能够得到ROC曲线方程、ROC曲线下面积及标准误。结论 上术方法影像诊断试验中常见的重复测量数据进行有效地分析与处理。     

混合线性模型在临床试验中重复测量资料的应用

目的：探讨混合线性模型在临床试验重复测量资料分析中的应用。方法：利用混合线性模型分析结果指标为定量资料的重复测量资料，通过参数和标准误的估计得出统计学结论。结果：对于临床试验重复测量资料，混合线性模型能有效的考虑数据相关性，处理有缺失值的资料，可以获得组别、时间及有无交互作用的结论。结论：采用混合线性模型对临床试验重复测量资料进行统计分析，可以更客观的进行药物疗效评价。     

医学随访医院中重复有序分类资料的分析方法

介绍医学随访研究中重复有序分类资料的分析方法－累积比数模型和相邻比数模型，方法：采用加权最小二乘法对模型中的参数进行估计，并根据剩余Ｘ＾２的大小选择模型。选择有效互作用的模型对资料的边缘合计进行拟合，剩余Ｘ＾２为５．６２。结论：累积比数模型用于复有序分类反应资料的分析更有效。     

多分类反应变量的多水平多项式模型及其应用

目的 具有多层次结构特征的分类离散数据不宜用常规方法分析,本文探讨了多水平多项式模型原理应用。方法 分别从无序分类两种情形,研究多水平多项式模型的构造及估计的实现。结果 实例验证多水平模型能给予准确而详尽的结果。结论对多次结构的多分类离散度数据应用使用多交错面式模型分析,在实际应用时尖注意模型的构造及估计方法的选择。     

分类重复测量数据的非线性混合效应模型

[目的]探讨分类重复测量数据的非线性混合效应模型及SAS8.0软件NLMIXED过程实现。[方法]直接拟合分类反应变量的非线性概率模型,结合重复测量资料的特点,采用附加高斯积分来获得最大似然的参数估计。[结果]非线性混合效应模型能很好地拟合分类反应变量的重复测量资料,它允许固定效应和随机效应进入模型的非线性部分,可方便地分析随机缺失等非均衡数据。[结论]分类反应变量重复测量资料的非线性混合效应模型分析结果合理、容易解释,为分类重复测量资料提供一种新的分析思路。     

医学随访研究中重复有序分类资料的分析方法

介绍医学随访研究中重复有序分类资料的分析方法—累积比数模型和相邻比数模型。方法 :采用加权最小二乘法对模型中的参数进行估计 ,并根据剩余 χ2 的大小选择模型。结果 :选择有交互作用的模型对资料的边缘合计进行拟合 ,剩余 χ2 为 5 62。结论 :累积比数模型用于重复有序分类反应资料的分析更有效。     

广义估计方程与多水平logistic回归模型在临床纵向数据分析中的应用及比较

目的探讨广义估计方程和多水平模型的应用与临床纵向研究以解决个体重复观测数据内部的相关性问题。方法根据临床纵向实例数据的特点,拟合因变量为二分类的广义估计方程和多水平模型,并与一般logistic模型比较。结果广义估计方程和多水平模型的分析结果与一般logistic模型不同。由于未能考虑个体内重复观测数据的相关性,一般logistic模型错误显示临床分期与近期疗效相关,而广义估计方程和多水平模型分析结果则显示相关无统计学意义。经分层分析也未发现临床分期与近期疗效的关联。结论广义估计方程和多水平模型都能有效地考虑重复观测数据内部相关性并能处理有缺失值的资料。与多水平模型相比,广义估计方程的参数估计较为稳定,可有效的估计各解释变量的效应。     

混合响应类型的多水平模型在重复测量资料中的应用和实现

目的将混合响应类型的多水平模型应用到具有两个不同类型结局变量的重复测量资料的分析中。方法对原始资料的格式作适当变换,构造一个水平1虚拟变量,将2个结局变量作为水平1上的观察单位,各时间点的重复测量为水平2单位,受试者为水平3单位,用MLwiN2.25软件拟合混合响应类型的三水平模型,对试验组和对照组的疗效,以及受试者的年龄、性别、观察指标的基线值,时间、组别和时间的交互效应进行分析。结果该模型在考虑了两个不同类型的结局变量在各个水平上的相关性后,可以对两个结局变量同时进行影响因素分析,获得解释变量对两个结局变量影响的估计,且只要数据缺失随机则估计是有效且无偏的。结论由于混合响应类型的多水平模型允许结局变量具有不同类型,并且把数据间的相关性分解为重复测量相关性和结局变量间相关性两部分,可有效地进行重复测量资料的动态变化趋势分析,分析结果更为细致。     

重复有序观测数据分析探讨

累积比数模型不适于分析在不同时间重复测量的有序数据。为此，本文在累积比数模型基础上，提出一种回归－自回归混合模型，用以解决重复测量数据的不独立性问题。该模型可根据不同的实验设计灵活变化，并且能够给出类似于方差分析的剩余差分析结果。文中给出了应用实例。     

Multilevel time series models with applications to repeated measures data

The analysis of repeated measures data can be conducted efficiently using a two-level random coefficients model. A standard assumption is that the within-individual (level 1) residuals are uncorrelated. In some cases, especially where measurements are made close together in time, this may not be reasonable and this additional correlation structure should also be modelled. A time series model for such data is proposed which consists of a standard multilevel model for repeated measures data augmented by an autocorrelation model for the level 1 residuals. First- and second-order autoregressive models are considered in detail, together with a seasonal component. Both discrete and continuous time are considered and it is shown how the autocorrelation parameters can themselves be structured in terms of further explanatory variables. The models are fitted to a data set consisting of repeated height measurements on children.     

Multilevel modeling versus cross‐sectional analysis for assessing the longitudinal tracking of cardiovascular risk factors over time

Correlated data are obtained in longitudinal epidemiological studies, where repeated measurements are taken on individuals or groups over time. Such longitudinal data are ideally analyzed using multilevel modeling approaches, which appropriately account for the correlations in repeated responses in the same individual. Commonly used regression models are inappropriate as they assume that measurements are independent. In this tutorial, we use multilevel modeling to demonstrate its use for analysis of correlated data obtained from serial examinations on individuals. We focus on cardiovascular epidemiological research where investigators are often interested in quantifying the relations between clinical risk factors and outcome measures (X and Y, respectively), where X and Y are measured repeatedly over time, for example, using serial observations on participants attending multiple examinations in a longitudinal cohort study. For instance, it may be of interest to evaluate the relations between serial measures of left ventricular mass (outcome) and of its potential determinants (i.e., body mass index and blood pressure), both of which are measured over time. In this tutorial, we describe the application of multilevel modeling to cardiovascular risk factors and outcome data (using serial echocardiographic data as an example of an outcome). We suggest an analytical approach that can be implemented to evaluate relations between any potential outcome of interest and risk factors, including assessment of random effects and nonlinear relations. We illustrate these steps using echocardiographic data from the Framingham Heart Study with SAS PROC MIXED. Copyright © 2013 John Wiley & Sons, Ltd.     

Analysing repeated measurements data: a practical comparison of methods.

A variety of methods are available for analysing repeated measurements data where the outcome is continuous. However, there is little information on how established methods, such as summary statistics and repeated measures analysis of variance (RMAOV), compare in practice with methods that have become available to applied statisticians more recently, such as marginal models (based on generalized estimating equation methodology) and multilevel models (that is, hierarchical random effects models). The aim of this paper is to exemplify the use of these methods, and directly compare their results by application to a clinical trial data set. The focus is on practical aspects rather than technical issues. The data considered were taken from a clinical trial of treatments for asthma in 240 children, in which a baseline and four post-randomization measurements of outcomes were taken. The simplicity of the method of summary statistics using the post-randomization mean of observations provided a useful initial analysis. However, fixed time effects or treatment-time interactions cannot be included in such an analysis, and choice of appropriate weighting when there is substantial missing data is problematic. RMAOV, marginal models and multilevel models generally provided similar estimates and standard errors for the treatment effects, although in one example with a relatively complex variance structure the marginal model produced less efficient estimates. Two advantages of multilevel models are that they provide direct estimates of variance components which are often of interest in their own right, and that they can be naturally extended to handle multivariate outcomes.     

多水平CFA模型在构念效度评价中的应用

目的 探讨如何利用多水平CFA模型对系统结构数据进行构念（结构）效度的评价。方法 结合职业紧张研究数据。利用LISREL软件实现参数估计，以RMSEA、GFI、SRMR作为拟合优度检验的评价指标。结果 对具有系统结构特征的问卷调查数据在评价构念效度时，采用单水平模型拟合，参数估计有偏低倾向，经多水平CFA模型拟合优度检验结果有所改进。进一步对模型进行修正后，模型拟合较好。结论 估计具有系统结构特征的问卷调查数据的效度，采用多水平CFA模型更趋合理。     

An approach to joint analysis of longitudinal measurements and competing risks failure time data

Joint analysis of longitudinal measurements and survival data has received much attention in recent years. However, previous work has primarily focused on a single failure type for the event time. In this paper we consider joint modelling of repeated measurements and competing risks failure time data to allow for more than one distinct failure type in the survival endpoint which occurs frequently in clinical trials. Our model uses latent random variables and common covariates to link together the sub-models for the longitudinal measurements and competing risks failure time data, respectively. An EM-based algorithm is derived to obtain the parameter estimates, and a profile likelihood method is proposed to estimate their standard errors. Our method enables one to make joint inference on multiple outcomes which is often necessary in analyses of clinical trials. Furthermore, joint analysis has several advantages compared with separate analysis of either the longitudinal data or competing risks survival data. By modelling the event time, the analysis of longitudinal measurements is adjusted to allow for non-ignorable missing data due to informative dropout, which cannot be appropriately handled by the standard linear mixed effects models alone. In addition, the joint model utilizes information from both outcomes, and could be substantially more efficient than the separate analysis of the competing risk survival data as shown in our simulation study. The performance of our method is evaluated and compared with separate analyses using both simulated data and a clinical trial for the scleroderma lung disease.     

多水平零膨胀计数模型在骨关节疼痛影响因素中的应用研究

目的针对两地区村民骨关节调查资料组群结构且零过多问题,阐明多水平零膨胀计数回归模型。方法介绍多水平Poisson和多水平ZIP模型原理,进一步完成山西省农村地区居民风湿性骨关节疼痛部位数影响因素分析的多水平模型SAS软件实现。结果多水平ZIP回归部分的随机项表明,两调查地区不同村庄居民关节是否疼痛以及疼痛部位数差别有统计学意义。logistic回归估计参数表明年龄、婚姻状况和高血压是影响关节疼痛与否的主要因素。而Pois-son部分估计结果表明年龄、地区、性别和地区交互作用是居民骨关节疼痛部位数的主要因素。Vuong检验进一步证实多水平ZIP模型比多水平Poisson模型更优。结论多水平ZIP回归模型是解决调查研究中组群结构及零发生次数过多问题模型拟合的最佳选择。     

Meta分析中多变量多水平模型方法的探讨

为了探讨多变量多水平模型在Ｍｅｔａ 分析中的应用价值，根据Ｍｅｔａ 分析中具有两个“效应尺度”的数据，拟合双变量两水平模型，估计有关参数以及预测值。结果表明，在模型中可同时获得两个平均“效应尺度”及其相关系数的估计，以及其影响因素的估计。Ｍｅｔａ 分析中如果具有不止一个“效应尺度”，则多变量多水平模型可获得多个平均“效应尺度”的估计值及其可信区间，也可分析多个平均“效应尺度”估计值之间的相关关系，探讨有关因素对这一关系的影响