混合模型在临床试验重复测量资料中的应用

目的探讨临床试验重复测量资料的统计分析方法。方法通过实例说明并比较各种固定效应模型和混合模型的优缺点。结果临床试验研究资料常为重复测量资料,比较各处理组的测量值差别是否有显著性,可以采用传统的统计方法如t检验、方差分析和协方差分析等;也可以采用混合模型对整个研究过程中所有时点的测量值进行分析。结论由于在重复测量资料中,同一受试者的不同观测值之间具有相关性特点,故对其指定协方差结构尤其重要。Mixed过程提供了丰富的协方差结构,可以充分利用重复测量资料的信息,又能处理缺失值,是重复测量资料最优的统计分析方法。     

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。     

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.     

混合线性模型在军事训练重复测量资料中的应用

目的探讨混合线性模型在有关军事训练重复测量资料分析中的价值。方法采用SAS软件中的MIXED过程对部队士兵进行100m跑前后各时间点采集的心率、血氧饱和度进行分析。结果混合线性模型对数据的完整性、反应变量的独立性和方差齐性不作要求，从而扩大了线性模型的适用范围，而且能得到个体化的分析结果，大大提高了现有资料的利用效率。结论混合线性模型能对军事训练中获取的重复测量资料准确、全面地进行分析，为部队改进训练方法、增强战斗力服务，因此，具有很高的应用价值。     

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。     

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     

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。     

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.     

混合线性模型的应用

目的介绍混合线性模型的结构，固定效应项和随机效应的含义。对具有内部相关性的资料．宣选用混合线性模型进行配合。方法用一个具有聚集性结构的例子和一个重复测量的例子说明配合混合线性模型的方法和步骤。结果分析了资料的层次结构，识别不同层次上的协变量，讨论了模型中固定效应矩阵和随机效应矩阵的结构，使模型参数估计值更易于理解和解释。由于混合线性模型克服了一般线性模型对反应变量必须具有独立和等方差的要求，从而扩大了线性模型的应用范围。对于具有聚集性质的资料及重复测量资料具有很好的拟合效果。结论这一模型计算较复杂，应用SAS／STAT软件包中的PROMIXED过程能很好地解决计算问题。     

基于随机系数模型的重复测量资料分析方法

目的探讨随机系数模型在重复测量资料分析中的应用。方法以实例说明随机系数模型，包括线性随机系数模型和多项式随机系数模型在重复测量资料中的应用，并与重复测量方差分析进行比较。结果重复测量方差分析结果显示，处理因素无统计学意义，时间因素有统计学意义；随机系数模型拟合结果还提示因变量与时间之间可能存在非线性关系。结论随机系数模型拟合结果基本与重复测量方差分析结论一致，但随机系数模型可以考虑资料的相关性、非线性问题，因此更为准确可信。     

Statistical analysis of proliferative index data in clinical trials

Measurements of proliferative activity in colonic epithelial cells are being used as surrogate endpoints in clinical trials for colon cancer prevention. Proliferative index data exemplify an important type of clinical trial endpoint. The outcome variable is a proportion in which the denominator is an ancillary statistic and in which measurement error and technician judgement are important sources of variability. The paper proposes a statistical model for a repeated measures clinical trial with this type of endpoint, in the context of proliferative activity data. The model is a two-stage random effects linear model in the log scale. In addition to fixed effects covariates, it explicitly incorporates two major sources of variability: the number of epithelial cells counted and the reader effect. Although the resulting likelihood is complicated, one can fit an approximate likelihood with minimal loss of efficiency using standard packages. We apply the model to a pilot randomized clinical trial.     

The analysis of repeated 'direct' measures of change illustrated with an application in longitudinal imaging

The use of repeated measures of an outcome variable to improve statistical power and precision in randomized clinical trials and cohort studies is well documented. Linear mixed models have great utility in the analysis of such studies in many medical applications including imaging. However, in imaging studies and other applications the basic outcome can be a 'direct' measure of change in a variable, as opposed to a difference calculated by subtraction of one measured value from another. The correlation structure of such repeated measures of 'direct' change, in particular the non-independence of within-person consecutive measures, adds complexity to the analysis. In this paper, we present a family of hierarchical mixed models for the analysis of such data and explain how to implement them using standard statistical software. We illustrate the use of our models with data from a cohort of patients with Alzheimer's disease.     

Bayesian model of disease progression in GNE myopathy

One Sentence Summary: A Bayesian repeated measures model based on quantitative muscle strength data from a prospective Natural History Study was developed to determine disease progression and design clinical trials for GNE myopathy, a rare and slowly progressive muscle disease. GNE myopathy is a rare muscle disease characterized by slowly progressive weakness and atrophy of skeletal muscles. To address the significant challenges of defining the natural history and designing clinical trials for GNE myopathy, we developed a Bayesian latent variable repeated measures model to determine disease progression. The model is based on longitudinal quantitative muscle strength data collected as part of a prospective Natural History Study. The GNE Myopathy Progression Model provides an understanding of disease progression that would have otherwise required a natural history of unfeasible duration. “Disease age,” the model-generated measure of disease progression, highly correlates with a variety of clinical, functional and patient-reported outcomes. With the incorporation of a treatment effect parameter to the GNE Disease Progression Model, we describe a novel GNE Myopathy Disease Modification Analysis that significantly increases power and reduces the number of subjects required to test the effectiveness of novel therapies when compared to more traditional analysis methods. The GNE Myopathy Disease Progression Model and Disease Modification Analysis can be applied to muscle diseases with prospectively collected muscle strength data, and a variety of rare and slowly progressive diseases.     

Internal pilot design for balanced repeated measures

Repeated measures are common in clinical trials and epidemiological studies. Designing studies with repeated measures requires reasonably accurate specifications of the variances and correlations to select an appropriate sample size. Underspecifying the variances leads to a sample size that is inadequate to detect a meaningful scientific difference, while overspecifying the variances results in an unnecessarily large sample size. Both lead to wasting resources and placing study participants in unwarranted risk. An internal pilot design allows sample size recalculation based on estimates of the nuisance parameters in the covariance matrix. We provide the theoretical results that account for the stochastic nature of the final sample size in a common class of linear mixed models. The results are useful for designing studies with repeated measures and balanced design. Simulations examine the impact of misspecification of the covariance matrix and demonstrate the accuracy of the approximations in controlling the type I error rate and achieving the target power. The proposed methods are applied to a longitudinal study assessing early antiretroviral therapy for youth living with HIV.     

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.     

Translational methods in biostatistics: linear mixed effect regression models of alcohol consumption and HIV disease progression over time

Longitudinal studies are helpful in understanding how subtle associations between factors of interest change over time. Our goal is to apply statistical methods which are appropriate for analyzing longitudinal data to a repeated measures epidemiological study as a tutorial in the appropriate use and interpretation of random effects models. To motivate their use, we study the association of alcohol consumption on markers of HIV disease progression in an observational cohort. To make valid inferences, the association among measurements correlated within a subject must be taken into account. We describe a linear mixed effects regression framework that accounts for the clustering of longitudinal data and that can be fit using standard statistical software. We apply the linear mixed effects model to a previously published dataset of HIV infected individuals with a history of alcohol problems who are receiving HAART (n = 197). The researchers were interested in determining the effect of alcohol use on HIV disease progression over time. Fitting a linear mixed effects multiple regression model with a random intercept and random slope for each subject accounts for the association of observations within subjects and yields parameters interpretable as in ordinary multiple regression. A significant interaction between alcohol use and adherence to HAART is found: subjects who use alcohol and are not fully adherent to their HIV medications had higher log RNA (ribonucleic acid) viral load levels than fully adherent non-drinkers, fully adherent alcohol users, and non-drinkers who were not fully adherent. Longitudinal studies are increasingly common in epidemiological research. Software routines that account for correlation between repeated measures using linear mixed effects methods are now generally available and straightforward to utilize. These models allow the relaxation of assumptions needed for approaches such as repeated measures ANOVA, and should be routinely incorporated into the analysis of cohort studies.