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。     

带时依协变量的重复测量资料的混合线性模型分析及其MIXED过程实现

目的 探讨混合线性模型在带有时依协变量的重复测量资料分析中的应用.方法 以治疗轻、中度原发性高血压病临床试验资料为例,考虑到给药方案在各个时间点随病情而变化,利用SAS中的MIXED过程,选择合适的协方差结构来实现带有时依协变量的重复测量资料的统计分析.结果 时依协变量(给药方案)对治疗轻、中度原发性高血压病有统计学意义(P＜0.05);时间因素有统计学意义(P＜0.05);给药方案与时间因素之间有交互效应(P＜0.05)、给药方案与处理因素之间有交互效应(P＜0.05).结论 采用混合线性模型对带有时依协变量的临床试验重复测量资料进行统计分析,可以更客观地进行药物疗效评价.     

方差分析和混合线性模型在重复测量数据中的应用探讨

[目的]通过混合效应线性模型与重复测量的方差分析在重复测量资料中的应用比较,说明两种方法右处理重复测量资料时的特点.[方法]对四川大学华西医院精神科就诊的139名患者进行随访调查研究,对调查表中的抑郁量袭分数分别运用重复测量的方差分析模型和混合线性模型处理.[结果]混合效应模型和重复测量的方差分析都是处理重复测量资科的重要的统计方法,前者在选择协方差结构下可对重复测量资料的固定效应和随机效应参数及协方差矩阵进行参数估计和统计检验,后者只能对重复测量资料的固定效应做出统计推断.[结论]混合效应模型在处理临床中的重复测量的资料比重复测量的方差分析,对资料的要求更宽松,所得的结果更加客观.     

重复测量线性混合模型中方差-协方差结构的选择

线性混合效应模型在医学重复测量资料的数据分析与设计中广泛应用。本文围绕医学实例阐述了重复测量线性混合效应模型在对不同方差 -协方差结构建模时协方差结构的选择 ,并对结果进行分析 ,为重复测量线性混合效应模型在医学研究中的应用提供了方便     

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。     

析因设计重复测量资料的统计分析及SAS程序实例

目的探讨析因设计重复测量资料的统计分析方法。方法通过构造统计模型,并结合实例给出SAS程序来实现析因设计重复测量资料的统计分析。结果给出了一般线性模型和混合线性模型对处理因素和时间因素进行比较的具体做法。结论在数据之间相关性较为复杂时,混合线性模型更加适合于析因设计的重复测量资料的统计分析。     

脱落率加权调整在医学重复测量资料敏感性分析中的应用及其SAS程序实现

目的:探讨脱落率加权调整在医学重复测量资料敏感性分析中的应用和SAS实现过程。方法:运用SAS 9.4软件编写SAS程序,采用重复测量混合效应模型对多变量重复测量资料进行协方差分析;同时,分别引入试验总体脱落率和各组脱落率,构建基于脱落率加权调整的模式混合模型进行敏感性分析。结果:重复测量资料安慰剂组、低剂量组和高剂量...     

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。     

最小化法使用常规统计检验方法的探讨

目的探讨最小化分组的资料是否可以采用常规的统计分析方法进行统计分析。方法对最小化法使用常规协方差分析的结果与随机化检验的结果进行比较,同时运用MonteCarlo方法考察最小化法分组资料进行协方差分析得到的检验统计量F的经验分布类型和对应P值的经验分布。结果对于最小化分组资料来说,协方差分析的结果与随机化检验的结果非常接近,最小化法协方差分析的F值的经验分布服从F分布,P值服从均匀分布。结论最小化法分组资料可以采用常规的协方差分析来进行统计分析,但分析模型中最好包含分组时考虑的影响因素。     

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。     

Modelling covariance structure in the analysis of repeated measures data

The term 'repeated measures' refers to data with multiple observations on the same sampling unit. In most cases, the multiple observations are taken over time, but they could be over space. It is usually plausible to assume that observations on the same unit are correlated. Hence, statistical analysis of repeated measures data must address the issue of covariation between measures on the same unit. Until recently, analysis techniques available in computer software only offered the user limited and inadequate choices. One choice was to ignore covariance structure and make invalid assumptions. Another was to avoid the covariance structure issue by analysing transformed data or making adjustments to otherwise inadequate analyses. Ignoring covariance structure may result in erroneous inference, and avoiding it may result in inefficient inference. Recently available mixed model methodology permits the covariance structure to be incorporated into the statistical model. The MIXED procedure of the SAS((R)) System provides a rich selection of covariance structures through the RANDOM and REPEATED statements. Modelling the covariance structure is a major hurdle in the use of PROC MIXED. However, once the covariance structure is modelled, inference about fixed effects proceeds essentially as when using PROC GLM. An example from the pharmaceutical industry is used to illustrate how to choose a covariance structure. The example also illustrates the effects of choice of covariance structure on tests and estimates of fixed effects. In many situations, estimates of linear combinations are invariant with respect to covariance structure, yet standard errors of the estimates may still depend on the covariance structure.     

The problem of measurement error in modelling the effect of compliance in a randomized trial.

This paper explores the implications of measurement error in the analysis of compliance-response relationships in data from randomized trials. Given that compliance measures are rarely, if ever, error-free indicators of exposure it is argued that both the designs for the collection of compliance data and the statistical models for their resulting analysis should be changed to take the possibility of measurement error into account. An analysis which ignores measurement error in the compliance measurements will provide biased estimates of compliance-response relationships. Provided that one has two or more indicators of compliance for each subject, more appropriate models can be fitted using covariance structure modelling software. If one wishes to explore interactions from repeated measures data on both compliance and response then it is also important that one recognizes that the response measures are also error-prone and that they too are dealt with appropriately.     

Analysis of lognormally distributed exposure data with repeated measures and values below the limit of detection using SAS

Studies of determinants of occupational exposure frequently involve left-censored lognormally distributed data, often with repeated measures. Left censoring occurs when observations are below the analytical limit of detection (LOD); repeated measures data results from taking multiple measurements on the same worker. A common method of dealing with this type of data has been to substitute a value (such as LOD/2) for the censored data followed by statistical analysis using the 'usual' methods. Recently, maximum likelihood estimation (MLE) methods have been employed to reduce bias associated with the substitution method. We compared substitution and MLE methods using simulated lognormally distributed exposure data subjected to varying amounts of censoring using two procedures available in SAS: LIFEREG and NLMIXED. In these simulations, the MLE method resulted in less bias and performed well even for censoring up to 80%, whereas the substitution method resulted in considerable bias. We illustrate the NLMIXED procedure using a dataset of chlorpyrifos air measurements collected from termiticide applicators on consecutive days over a 5-day workweek. We provide sample SAS code for several situations including one and two groups, with and without repeated measures, random slopes, and nested random effects.     

多反应变量重复测量资料的协方差类型模型应用及SAS实现

目的 探讨协方差类型模型在多反应变量的重复测量资料分析中的应用方法 为了评价盐酸吡格列酮片治疗2型糖尿病的有效性,以安慰剂为对照,对240例2型糖尿病患者的空腹血糖和餐后2 h血糖重复观测数据进行多反应变量的协方差类型模型分析,对模型的固定效应参数矩阵作最小二乘估计并进行组间比较,同时给出误差效应的方差协方差矩阵,利用...     

Tutorial in biostatistics. An introduction to hierarchical linear modelling.

Hierarchical linear models are useful for understanding relationships in hierarchical data structures, such as patients within hospitals or physicians within hospitals. In this tutorial we provide an introduction to the technique in general terms, and then specify model notation and assumptions in detail. We describe estimation techniques and hypothesis testing procedures for the three types of parameters involved in hierarchical linear models: fixed effects, covariance components, and random effects. We illustrate the application using an example from the Type II Diabetes Patient Outcomes Research Team (PORT) study and use two popular PC-based statistical computing packages, HLM/2L and SAS Proc Mixed, to perform two-level hierarchical analysis. We compare output from the two packages applied to our example data as well as to simulated data. We elaborate on model interpretation and provide guidelines for model checking.     

The analysis of very small samples of repeated measurements I: An adjusted sandwich estimator

The statistical analysis of repeated measures or longitudinal data always requires the accommodation of the covariance structure of the repeated measurements at some stage in the analysis. The general linear mixed model is often used for such analyses, and allows for the specification of both a mean model and a covariance structure. Often the covariance structure itself is not of direct interest, but only a means to producing valid inferences about the response. Existing methods of analysis are often inadequate where the sample size is small. More precisely, statistical measures of goodness of fit are not necessarily the right measure of the appropriateness of a covariance structure and inferences based on conventional Wald‐type procedures do not approximate sufficiently well their nominal properties when data are unbalanced or incomplete. This is shown to be the case when adopting the Kenward–Roger adjustment where the sample size is very small. A generalization of an approach to Wald tests using a bias‐adjusted empirical sandwich estimator for the covariance matrix of the fixed effects parameters from generalized estimating equations is developed for Gaussian repeated measurements. This is shown to attain the correct test size but has very low power. Copyright © 2010 John Wiley & Sons, Ltd.     

Simultaneous small‐sample comparisons in longitudinal or multi‐endpoint trials using multiple marginal models

Simultaneous inference in longitudinal, repeated‐measures, and multi‐endpoint designs can be onerous, especially when trying to find a reasonable joint model from which the interesting effects and covariances are estimated. A novel statistical approach known as multiple marginal models greatly simplifies the modelling process: the core idea is to “marginalise” the problem and fit multiple small models to different portions of the data, and then estimate the overall covariance matrix in a subsequent, separate step. Using these estimates guarantees strong control of the family‐wise error rate, however only asymptotically. In this paper, we show how to make the approach also applicable to small‐sample data problems. Specifically, we discuss the computation of adjusted P values and simultaneous confidence bounds for comparisons of randomised treatment groups as well as for levels of a nonrandomised factor such as multiple endpoints, repeated measures, or a series of points in time or space. We illustrate the practical use of the method with a data example.