纵向观测计数数据的对数线性模型

纵向观测数据是按时间顺序对个体的某一变量进行多次人观测获得的资料。本文利用广义线性模型对同计数数据进行了分析,充分考虑重复观测间的相关性。方法采用Ｚｅｇｅｒ和Ｌｉａｎｇ提出的广义估计方程在拟对数广义线性模型的同时,引入偏离参数,讨论三种协方差矩阵的结构。结果同时获得的回归参数,相关参数,偏离参数的估计,完成了较为实用的运行程序,并进行了实例讨论。结论医学研究和临床试验中经接触到纵向观测数据,对这类     

广义估计方程与准最小二乘在社区纵向数据分析中的应用

目的 应用广义估计方程和准最小二乘方法分析社区卫生服务中心纵向数据,探讨纵向数据分析的问题,为社区的随访的纵向数据的分析提供科学的方法. 方法 对收集的社区卫生服务中心的糖尿病病人血糖的纵向数据,分别使用广义估计方程和准最小二乘方法以及传统的线性回归模型进行分析并比较结果.同时比较三种方法的标准化残差图. 结果 广义估计方程不收敛时与传统线性模型的结果相同,显示糖尿病人血糖与教育水平相关,而广义估计方程收敛时与准最小二乘的结果相同,显示教育无统计学意义.从标准化残差图看广义估计方程和准最小二乘法对数据的拟合比传统回归好. 结论 广义估计方程和准最小二乘法都能有效的处理纵向数据.与广义估计方程相比,准最小二乘法有一些优势.     

广义估计方程在临床试验重复测量资料中的应用

目的：探讨广义估计方程在临床试验重复测量资料分析中的应用。方法：利用广义估计方程分析结果指标为分类变量的重复测量资料，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，广义估计方程能有效的考虑组内相关性，处理有缺失值的资料，可以获得中心效应的参数及其标准误的估计值，以及在考虑了中心效应之后，可以有效估计处理因素有无作用及其作用大小。结论：采用广义估计方程对临床试验重复测量资料进行统计分析，可以使药物疗效评价更为客观。     

具有相关关系的二分类资料处理方法比较

目的探讨分析具有相关关系的二分类资料的有效处理方法。方法采用蒙特卡罗模拟比较广义估计方程和广义随机效应模型与一般logistic回归在处理具有相关关系的二分类资料的区别。结果一般logisitc回归处理相关关系的二分类资料时假阳性率增加。广义估计方程与广义随机效应模型是处理该类型资料时,I类错误能稳定控制在0.05左右,且检验效能基本一致。结论广义估计方程和广义随机效应模型是处理具有相关关系的二分类资料的合适方法,不能采用一般logistic回归代替。     

广义估计方程在纵向资料中的应用

目的：探讨如何利用纵向资料拟合广义估计方程，为纵向资料分析提供方法学参考。方法：应用实例阐述纵向资料分析的特点和传统分析方法的不足，采用广义估计方程，解决实际存在的问题。结果：用药时间与临床疗效旱正相关（P〈0．0001）。试验组与对照组临床疗效差异有统计学意义（P=0．0413），试验组优于对照组。结论：在纵向资料分析中广义估计方程有一定的优势。     

非独立多分类数据的统计分析方法及SAS程序

目的采用广义估计方程、广义线性混合模型、非线性混合模型分析非独立分类数据。方法以眼科临床试验资料为实例,采用SAS9.2软件中GENMOD、GLIMMIX、NLMIXED过程拟合广义估计方程、线性混合效应模型、非线性混合效应模型。结果广义估计方程将非独立观测间的协方差结构处理为多余参数,模型中不能容纳随机效应;广义线性混合模型可以拟合多个随机效应,但不能对其提供统计学检验;非线性混合效应模型中因变量的分布形式可以自己指定,可以提供真实的似然函数及随机效应的统计学检验结果。3种分析方法的统计分析结论一致。结论 3种分析方法都是分析非独立分类数据的有力工具,研究者根据数据的特征及研究目的选择合适的方法对资料进行分析。     

医疗器械临床试验定量指标纵向数据中不同模型的比较研究

目的 通过比较一般线性模型、广义估计方程及混合效应模型在医疗器械试验定量指标纵向数据中的估计效果,探讨合适分析方法并提供参考.方法 以非劣效支架试验为例并结合应用蒙特卡洛随机模拟的方法,模拟不同样本量、不同数据相关程度及不同相关数据比例下的纵向数据,比较不同模型应用的准确性.结果 在不同数据相关程度及相关数据比例下,不...     

用广义估计方程分析有序多分类重复测量资料

目的 探讨利用重复测量资料拟合广义估计方程,为重复测量资料分析提供方法学参考.方法采用SAS软件包中的GENMOD过程,结合中医针刺手法组与非手法组治疗周围性面瘫的多中心临床试验实例,比较有协变量和无协变量的广义估计方程分析结果.结果周围性面瘫的疗效指标为House Brackmann（HB）分级.以4次随访的HB分级为反应变量,以中心、组别、首次HB分级为自变量,建立有协变量的广义估计方程,结果显示：中心之间疗效差异无统计学意义,不存在中心效应;手法组和非手法组之间疗效差异有统计学意义,手法组疗效优于非手法组;不同首次HB分级之间疗效差异有统计学意义,基础病情对疗效有影响.以首次HB分级和4次随访的HB分级为反应变量,以中心、组别为自变量,建立无协变量的广义估计方程,结果显示：中心之间疗效差异有统计学意义,存在中心效应;手法组和非手法组之间疗效差异无统计学意义,尚不能认为两组疗效不同.结论广义估计方程可以有效控制层次相关性,在分析有序多分类重复测量资料时具有优势.     

重复观测数据的半参数回归分析

目的 研究重复预测数据的回归分析技术。方法 利用半参数回归分析的原理与方法，结合重复观测数据的特点，建立重复观测数据的半参数回归模型，并进一步讨论模型参数的估计方法及假设检验公式。结果 讨论了重复观测数据的半参数回归模型的模型误差，分析了重复因素的效应及参数的影响，给出了其模型的方差分析表。结论 通过实例分析，表明对重复观测数据的处理，半参数回归分析的效果优于普通的最小二乘法和广义最小二乘法。     

随机系数发展模型与协方差模式模型在纵向数据分析中的应用及R实现

目的 应用随机系数发展模型与协方差模式模型分析社区卫生服务中心纵向数据,探讨纵向数据分析的问题,为社区随访数据处理提供科学方法.方法 使用R软件对社区卫生服务中心糖尿病重复测量数据分别拟合随机系数发展模型,协方差模式模型以及传统线性回归模型,并比较3种模型的分析结果.结果 随机系数发展模型和协方差模式模型的分析结果与传统线性回归模型不同,2模型较传统线性回归更多的考虑了数据的变异来源.随机系数发展模型与协方差模式模型变量的估计系数结果相近,2者在固定效应的估计上区别往往不是很大,2模型相比,信息标准统计相差也不大.随机系数发展模型倾向于解释组间随机效应,协方差模式模型更关注组内观测之间的联系.R软件nlme package相比于SAS proc mixed,其相应的结果比较与可视化的函数使用更为灵活方便,同时GLS函数提供更多的组内方差协方差模式以供选择.结论 随机系数发展模型与协方差模式模型都能较好的处理重复观测数据组内相关性的问题.2者处理组内相关性的出发点不同,如果强调组内观测之间的联系性,则选择协方差模式模型.相反,如果更关注组间的异质性,强调组间的随机效应,则选择随机系数发展模型.R软件nlme是比较完善的处理混合结构数据的分析包.     

Structured correlation in models for clustered data

Correlation is always a concern in the analysis of clustered data. One area of interest is to develop a general correlation modelling approach for high dimensional data with unbalanced hierarchical and heterogeneous data structures, e.g. multilevel data. Commonly used correlation structures might have limitation for such situations. In this paper, we propose two extensions, multiblock and multilayer correlations. These methods are very flexible in modelling correlation and can be incorporated in many multivariate approaches, while the major discussion focuses on the applications under the generalized estimating equations (GEE) methods. The approaches are especially useful in GEE when each cluster is large and complex but the number of clusters is small. If an incorrect correlation is applied to such data, the results are less efficient. Multiblock and multilayer correlations extend GEE methods to model complicated multilevel data with arbitrary number of levels and cluster size. The extended estimating equation for correlation parameters has an orthogonal property, and the computation is very efficient. A simulation study compares the conventional methods versus the proposed methods, and it shows the gain in relative efficiency and the flexibility in modelling various structures.     

临床试验中多个终点变量同时评价的多元logistic模型

目的研究临床试验中多个终点变量的同时分析。方法采用多元logistic回归模型,通过对原始资料的格式作适当变换,构造一个虚拟水平,视结果变量为1水平上的观察单位,以患者作为2水平单位,建立2水平logistic模型,对试验组和对照组的疗效,以及患者的年龄,性别,观察指标的基线值,中心效应等协变量进行分析。结果多终点的多元logistic回归模型既可以对单个结果变量进行分析,还可以对多个结果变量进行同时分析,并在扣除组间差异、协变量的影响后,估计两个结果变量之间的相关性。当受试者的多个结果有部分缺失时,该估计方法仍然是有效的。结论多元logistic回归模型可以对多个终点变量进行同时分析。     

Applying sample survey methods to clinical trials data

This paper outlines the utility of statistical methods for sample surveys in analysing clinical trials data. Sample survey statisticians face a variety of complex data analysis issues deriving from the use of multi-stage probability sampling from finite populations. One such issue is that of clustering of observations at the various stages of sampling. Survey data analysis approaches developed to accommodate clustering in the sample design have more general application to clinical studies in which repeated measures structures are encountered. Situations where these methods are of interest include multi-visit studies where responses are observed at two or more time points for each patient, multi-period cross-over studies, and epidemiological studies for repeated occurrences of adverse events or illnesses. We describe statistical procedures for fitting multiple regression models to sample survey data that are more effective for repeated measures studies with complicated data structures than the more traditional approaches of multivariate repeated measures analysis. In this setting, one can specify a primary sampling unit within which repeated measures have intraclass correlation. This intraclass correlation is taken into account by sample survey regression methods through robust estimates of the standard errors of the regression coefficients. Regression estimates are obtained from model fitting estimation equations which ignore the correlation structure of the data (that is, computing procedures which assume that all observational units are independent or are from simple random samples). The analytic approach is straightforward to apply with logistic models for dichotomous data, proportional odds models for ordinal data, and linear models for continuously scaled data, and results are interpretable in terms of population average parameters. Through the features summarized here, the sample survey regression methods have many similarities to the broader family of methods based on generalized estimating equations (GEE). Sample survey methods for the analysis of time-to-event data have more recently been developed and implemented in the context of finite probability sampling. Given the importance of survival endpoints in late phase studies for drug development, these methods have clear utility in the area of clinical trials data analysis. A brief overview of methods for sample survey data analysis is first provided, followed by motivation for applying these methods to clinical trials data. Examples drawn from three clinical studies are provided to illustrate survey methods for logistic regression, proportional odds regression and proportional hazards regression. Potential problems with the proposed methods and ways of addressing them are discussed.     

Concordance correlation coefficients estimated by generalized estimating equations and variance components for longitudinal repeated measurements

The concordance correlation coefficient (CCC) is a commonly accepted measure of agreement between two observers for continuous responses. This paper proposes a generalized estimating equations (GEE) approach allowing dependency between repeated measurements over time to assess intra‐agreement for each observer and inter‐ and total agreement among multiple observers simultaneously. Furthermore, the indices of intra‐, inter‐, and total agreement through variance components (VC) from an extended three‐way linear mixed model (LMM) are also developed with consideration of the correlation structure of longitudinal repeated measurements. Simulation studies are conducted to compare the performance of the GEE and VC approaches for repeated measurements from longitudinal data. An application of optometric conformity study is used for illustration. In conclusion, the GEE approach allowing flexibility in model assumptions and correlation structures of repeated measurements gives satisfactory results with small mean square errors and nominal 95% coverage rates for large data sets, and when the assumption of the relationship between variances and covariances for the extended three‐way LMM holds, the VC approach performs outstandingly well for all sample sizes. Copyright © 2017 John Wiley & Sons, Ltd.     

Correlation structure and variable selection in generalized estimating equations via composite likelihood information criteria

The method of generalized estimating equations (GEE) is popular in the biostatistics literature for analyzing longitudinal binary and count data. It assumes a generalized linear model for the outcome variable, and a working correlation among repeated measurements. In this paper, we introduce a viable competitor: the weighted scores method for generalized linear model margins. We weight the univariate score equations using a working discretized multivariate normal model that is a proper multivariate model. Because the weighted scores method is a parametric method based on likelihood, we propose composite likelihood information criteria as an intermediate step for model selection. The same criteria can be used for both correlation structure and variable selection. Simulations studies and the application example show that our method outperforms other existing model selection methods in GEE. From the example, it can be seen that our methods not only improve on GEE in terms of interpretability and efficiency but also can change the inferential conclusions with respect to GEE. Copyright © 2016 John Wiley & Sons, Ltd.     

GEE estimation of a misspecified time-varying covariate: an example with the effect of alcoholism treatment on medical utilization

The generalized estimation equation (GEE) method is widely used in longitudinal data analysis, particularly when the outcome variable is non-Gaussian distributed. Under mild regulatory conditions, the parameter estimates are consistent and their asymptotic variances are efficient. In an observational study focusing on alcoholism patients, we applied the GEE method to longitudinal count data from medical utilization records from a large national managed care organization. The health services research question was whether there was a change in medical utilization for patients after engaging in alcoholism treatment as compared to before treatment. Thus, the main effect of interest was a time-varying covariate indicating whether the patient had undergone treatment yet or not. GEE under five different working correlations was employed and mixed results regarding the significance of the treatment effect were found. Because of the large sample size, i.e. 8485 patients with an average of 46 repeated measurements per patient, differences across the estimates produced by the different working correlation structures was suspicious. It is shown that these differences are maybe caused by the fact that the time-varying covariate in the marginal mean model is misspecified. A simulation study is performed to demonstrate that misspecification of the time-varying covariate in the marginal mean structure can cause differences in GEE results across various choices of working correlation structure.     

Public health application comparing multilevel analysis with logistic regression: immunization coverage among long-term care facility residents

PURPOSE: Public health studies often sample populations using nested sampling plans. When the variance of the residual errors is correlated between individual observations as a result of these nested structures, traditional logistic regression is inappropriate. We used nested nursing home patient data to show that one-level logistic regression and hierarchical multilevel regression can yield different results. METHODS: We performed logistic and multilevel regression to determine nursing home resident characteristics associated with receiving pneumococcal immunizations. Nursing home characteristics such as type of ownership, immunization program type, and certification were collected from a sample of 249 nursing homes in 14 selected states. Nursing home resident data including demographics, receipt of immunizations, cognitive patterns, and physical functioning were collected on 100 randomly selected residents from each facility. RESULTS: Factors associated with receipt of pneumococcal vaccination using logistic regression were similar to those found using multilevel regression model with some exceptions. Predictors using logistic regression that were not significant using multilevel regression included race, speech problems, infections, renal failure, legal responsibility for oneself, and affiliation with a chain. Unstable health conditions were significant only in the multilevel model. CONCLUSIONS: When correlation of resident outcomes within nursing home facilities was not considered, statistically significant associations were likely due to residual correlation effects. To control the probability of type I error, epidemiologists evaluating public health data on nested populations should use methods that account for correlation among observations.     

Sample size for a two-group comparison of repeated binary measurements using GEE

Controlled clinical trials often randomize subjects to two treatment groups and repeatedly evaluate them at baseline and intervals across a treatment period of fixed duration. A popular primary objective in these trials is to compare the change rates in the repeated measurements between treatment groups. Repeated measurements usually involve missing data and a serial correlation within each subject. The generalized estimating equation (GEE) method has been widely used to fit the time trend in repeated measurements because of its robustness to random missing and mispecification of the true correlation structure. In this paper, we propose a closed form sample size formula for comparing the change rates of binary repeated measurements using GEE for a two-group comparison. The sample size formula is derived incorporating missing patterns, such as independent missing and monotone missing, and correlation structures, such as AR(1) model. We also propose an algorithm to generate correlated binary data with arbitrary marginal means and a Markov dependency and use it in simulation studies.