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...     

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.     

Covariance models for nested repeated measures data: analysis of ovarian steroid secretion data.

We consider several covariance models for analysing repeated measures data from a study of ovarian steroid secretion in reproductive-aged women. Urinary oestradiol and serum oestrogen were repeatedly observed over three or four menstrual periods, each period separated by one year. For each menstrual period, daily first morning urine specimens were collected 8 to 18 times, and serum specimens 2 to 5 times. Thus, measurements were repeatedly observed over menstrual cycle days within menstrual periods. Owing to missing observations, the number of observations differed from subject to subject. In this study, there were two repeat factors: menstrual cycle day and menstrual period. The first repeat factor, cycle day, is nested within the second repeat factor, menstrual period. In analysing these nested repeated measures data, the correlation structure should be modelled that will account for both repeat factors. We present several covariance models for defining appropriate covariance structures for these data.     

纵向资料带时变协变量的随机系数模型和协方差模式模型的统计分析

目的 探讨随机系数模型和协方差模式模型在带有时变协变量的纵向资料分析中的应用.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,以用药量为时变协变量,利用随机系数模型和协方差模式模型进行分析,并通过SAS中的MIXED过程得以实现.结果 两种模型拟合结果近似,组间差异无统计学意义(P＞0.05);用药量差异有统计学意义(P＜0.05);时间因素差异有统计学意义(P＜0.05);年龄差异有统计学意义(P＜0.05);治疗前舒张压差异有统计学意义(P＜0.05).结论 随机系数模型和协方差模式模型考虑了数据相关性,考虑了时变协变量的影响,并可以处理有缺失值的资料,可以更客观的进行药物疗效评价.     

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.     

Effects of automated alerts on unnecessarily repeated serology tests in a cardiovascular surgery department: a time series analysis

Background  

Laboratory testing is frequently unnecessary, particularly repetitive testing. Among the interventions proposed to reduce unnecessary testing, Computerized Decision Support Systems (CDSS) have been shown to be effective, but their impact depends on their technical characteristics. The objective of the study was to evaluate the impact of a Serology-CDSS providing point of care reminders of previous existing serology results, embedded in a Computerized Physician Order Entry at a university teaching hospital in Paris, France.     

The SAEM algorithm for group comparison tests in longitudinal data analysis based on non-linear mixed-effects model

Non-linear mixed-effects models (NLMEMs) are used to improve information gathering from longitudinal studies and are applied to treatment evaluation in disease-evolution studies, such as human immunodeficiency virus (HIV) infection. The estimation of parameters and the statistical tests are critical issues in NLMEMs since the likelihood and the Fisher information matrix have no closed form. An alternative method to numerical integrations, in which convergence is slow, and to methods based on linearization, in which asymptotic convergence has not been proved, is the Stochastic Approximation Expectation-Maximization (SAEM) algorithm. For the Wald test and the likelihood ratio test, we propose estimating the Fisher information matrix by stochastic approximation and the likelihood by importance sampling. We evaluate these SAEM-based tests in a simulation study in the context of HIV viral load decrease after initiation of an antiretroviral treatment. The results from this simulation illustrate the theoretical convergence properties of SAEM. We also propose a method based on the SAEM algorithm to compute the minimum sample size required to perform a Wald test of a given power for a covariate effect in NLMEMs. Lastly, we illustrate these tests on the evaluation of the effect of ritonavir on the indinavir pharmacokinetics in HIV patients and compare the results with those obtained using the adaptative Gaussian quadrature method implemented in the SAS procedure NLMIXED.     

Specification of covariance structure in longitudinal data analysis for randomized clinical trials

Misspecification of the covariance structure for repeated measurements in longitudinal analysis may lead to biased estimates of the regression parameters and under or overestimation of the corresponding standard errors in the presence of missing data. The so‐called sandwich estimator can ‘correct’ the variance, but it does not reduce the bias in point estimates. Removing all assumptions from the covariance structure (i.e. using an unstructured (UN) covariance) will remove such biases. However, an excessive amount of missing data may cause convergence problems for iterative algorithms, such as the default Newton–Raphson algorithm in the popular SAS PROC MIXED. This article examines, both through theory and simulations, the existence and the magnitude of these biases. We recommend the use of UN covariance as the default strategy for analyzing longitudinal data from randomized clinical trials with moderate to large number of subjects and small to moderate number of time points. We also present an algorithm to assist in the convergence when the UN covariance is used. Copyright © 2009 John Wiley & Sons, Ltd.     

Principal interactions analysis for repeated measures data: application to gene-gene and gene-environment interactions

Many existing cohorts with longitudinal data on environmental exposures, occupational history, lifestyle/ behavioral characteristics, and health outcomes have collected genetic data in recent years. In this paper, we consider the problem of modeling gene-gene and gene-environment interactions with repeated measures data on a quantitative trait. We review possibilities of using classical models proposed by Tukey (1949) and Mandel (1961) using the cell means of a two-way classification array for such data. Although these models are effective for detecting interactions in the presence of main effects, they fail miserably if the interaction structure is misspecified. We explore a more robust class of interaction models that are based on a singular value decomposition of the cell-means residual matrix after fitting the additive main effect terms. This class of additive main effects and multiplicative interaction models (Gollob, 1968) provide useful summaries for subject-specific and time-varying effects as represented in terms of their contribution to the leading eigenvalues of the interaction matrix. It also makes the interaction structure more amenable to geometric representation. We call this analysis 'principal interactions analysis'. While the paper primarily focuses on a cell-mean-based analysis of repeated measures outcome, we also introduce resampling-based methods that appropriately recognize the unbalanced and longitudinal nature of the data instead of reducing the response to cell means. We illustrate the proposed methods by using data from the Normative Aging Study, a longitudinal cohort study of Boston area veterans since 1963. We carry out simulation studies under an array of classical interaction models and common epistasis models to illustrate the properties of the principal interactions analysis procedure in comparison with the classical alternatives. Copyright ? 2012 John Wiley & Sons, Ltd.     

A model selection approach to analysis of variance and covariance

An alternative to analysis of variance is a model selection approach where every partition of the treatment means into clusters with equal value is treated as a separate model. The null hypothesis that all treatments are equal corresponds to the partition with all means in a single cluster. The alternative hypothesis correspond to the set of all other partitions of treatment means. A model selection approach can also be used for a treatment by covariate interaction, where the null hypothesis and each alternative correspond to a partition of treatments into clusters with equal covariate effects. We extend the partition‐as‐model approach to simultaneous inference for both treatment main effect and treatment interaction with a continuous covariate with separate partitions for the intercepts and treatment‐specific slopes. The model space is the Cartesian product of the intercept partition and the slope partition, and we develop five joint priors for this model space. In four of these priors the intercept and slope partition are dependent. We advise on setting priors over models, and we use the model to analyze an orthodontic data set that compares the frictional resistance created by orthodontic fixtures. Copyright © 2009 John Wiley & Sons, Ltd.     

Luteinizing hormone, its beta-subunit variant, and epithelial ovarian cancer: the gonadotropin hypothesis revisited.

The gonadotropin hypothesis postulates that excessive gonadotropin stimulation results in increased proliferation and subsequent malignant transformation of ovarian epithelium. The authors evaluated this hypothesis by analyzing the association between serum levels of wild-type luteinizing hormone (LH) and ovarian cancer risk. They also examined the relation between a variant of LH containing two missense point mutations (Trp(8)Arg and Ile(15)Thr) in its beta-subunit and ovarian cancer risk. Fifty-eight cases of epithelial ovarian cancer and 116 controls matched on age, menopausal status, and date of blood donation were included in a case-control study nested within the New York University Women's Health Study, a prospective cohort enrolled between 1985 and 1991 in New York City. Wild-type serum levels and variant LH status were determined by immunofluorometric assays in which monoclonal antibodies specific for wild-type and variant LH were used. Compared with women in the lowest tertile of wild-type LH, women in the highest tertile had a lower risk of ovarian cancer, after adjustment for potential confounders (odds ratio = 0.42, 95% confidence interval: 0.09, 2.09). Women heterozygous for variant LH were not at increased risk (adjusted odds ratio = 0.95, 95% confidence interval: 0.27, 3.34). The results suggest that neither wild-type LH levels nor variant LH status is associated with increased risk of epithelial ovarian cancer.     

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...     

Efficiency comparisons of rank and permutation tests based on summary statistics computed from repeated measures data

A popular method of using repeated measures data to compare treatment groups in a clinical trial is to summarize each individual's outcomes with a scalar summary statistic, and then to perform a two-group comparison of the resulting statistics using a rank or permutation test. Many different types of summary statistics are used in practice, including discrete and continuous functions of the underlying repeated measures data. When the repeated measures processes of the comparison groups differ by a location shift at each time point, the asymptotic relative efficiency of (continuous) summary statistics that are linear functions of the repeated measures has been determined and used to compare tests in this class. However, little is known about the non-null behaviour of discrete summary statistics, about continuous summary statistics when the groups differ in more complex ways than location shifts or where the summary statistics are not linear functions of the repeated measures. Indeed, even simple distributional structures on the repeated measures variables can lead to complex differences between the distribution of common summary statistics of the comparison groups. The presence of left censoring of the repeated measures, which can arise when these are laboratory markers with lower limits of detection, further complicates the distribution of, and hence the ability to compare, summary statistics. This paper uses recent theoretical results for the non-null behaviour of rank and permutation tests to examine the asymptotic relative efficiencies of several popular summary statistics, both discrete and continuous, under a variety of common settings. We assume a flexible linear growth curve model to describe the repeated measures responses and focus on the types of settings that commonly arise in HIV/AIDS and other diseases.     

Bayesian hierarchical model for multiple repeated measures and survival data: an application to Parkinson's disease

Multilevel item response theory models have been increasingly used to analyze the multivariate longitudinal data of mixed types (e.g., continuous and categorical) in clinical studies. To address the possible correlation between multivariate longitudinal measures and time to terminal events (e.g., death and dropout), joint models that consist of a multilevel item response theory submodel and a survival submodel have been previously developed. However, in multisite studies, multiple patients are recruited and treated by the same clinical site. There can be a significant site correlation because of common environmental and socioeconomic status, and similar quality of care within site. In this article, we develop and study several hierarchical joint models with the hazard of terminal events dependent on shared random effects from various levels. We conduct extensive simulation study to evaluate the performance of various models under different scenarios. The proposed hierarchical joint models are applied to the motivating deprenyl and tocopherol antioxidative therapy of Parkinsonism study to investigate the effect of tocopherol in slowing Parkinson's disease progression. Copyright © 2014 John Wiley & Sons, Ltd.     

Multivariate tests of means in independent groups designs. Effects of covariance heterogeneity and nonnormality

Health evaluation research often employs multivariate designs in which data on several outcome variables are obtained for independent groups of subjects. This article examines statistical procedures for testing hypotheses of multivariate mean equality in two-group designs. The conventional test for multivariate means, Hotelling's T2, rests on certain assumptions about the distribution of the data and the population variances and covariances. When these assumptions are violated, which is often the case in applied health research, T2 will result in invalid conclusions about the null hypothesis. This article describes parametric procedures that are robust, or insensitive, to assumption violations. A numeric example illustrates the statistical concepts that are presented and a computer program to implement these robust solutions is introduced.     

Thai SF-36 health survey: tests of data quality,scaling assumptions,reliability and validity in healthy men and women

Background  

Since its translation to Thai in 2000, the SF-36 Health Survey has been used extensively in many different clinical settings in Thailand. Its popularity has increased despite the absence of published evidence that the translated instrument satisfies scoring assumptions, the psychometric properties required for valid interpretation of the SF-36 summated ratings scales. The purpose of this paper was to examine these properties and to report on the reliability and validity of the Thai SF-36 in a non-clinical general population.     

A Bayesian hierarchical model for multi-level repeated ordinal data: analysis of oral practice examinations in a large anaesthesiology training programme.

Oral practice examinations (OPEs) are used in many anaesthesiology programmes to familiarize anaesthesiology residents with the format of the oral examination administered by the American Board of Anesthesiology. The OPE outcome (final grade) consists of 'Definite Not Pass', 'Probable Not Pass', 'Probable Pass' and 'Definite Pass'. In our study to assess the validity of the OPE, residents took an average of two (ranging from one to six) OPEs, each of which was evaluated by two board certified anaesthesiologists randomly selected from a pool of 12. A key question of interest was to identify factors, for example, the length of training, didactic experience and other characteristics, that most influence OPE outcome. In addition, we were interested in assessing the reliability of the final grade, that is, the covariance parameters are of interest as well. However, estimating variance components in multi-level data with an unequal number of repeated ordinal outcomes presents several statistical challenges, such as how to estimate high dimensional random effects parameters, especially for ordinal outcomes. We propose a Bayesian hierarchical proportional odds model for data with such complexity. The flexibility of such a model allows us to make inference on the association of OPE outcomes with other factors and to estimate the variance components as well.     

Tests of non-null hypothesis on proportions for stratified data

It is more reasonable to interpret the efficacy of therapies under non-null hypothesis, hence tests of non-null hypothesis have been carried out. Most clinical trials adopt multi-center campaign and yield stratified data. However, the existing non-null hypothesis tests are not suitable for stratified data. This paper proposes the tests of non-null hypothesis on proportions for stratified data. Averaging the treatment-control difference in each stratum yields the mean treatment-control difference. Comparing its expectation with the minimal detectable difference leads to set up a non-null hypothesis. Its variance is used to construct the equation of the basic relationship for stratified designs under the non-null hypothesis. Then follow the derivations for the one- and two-sample tests. Their performance is demonstrated by the Monte Carlo method. As far as the two-sample tests are concerned, they reduce to the Cochran test and the Mantel-Haenszel test, on setting the minimal detectable difference equal to zero, and to the Dunnett-Gent test when there is only one stratum. As for the one-sample test, it also reduces to its classical counterparts in these situations. The observed power coincides with the prescribed power and the relevant operating characteristic curves. The tests can be applied to the active control clinical trials with multi-center or stratified designs for establishing the clinical superiority or non-inferiority of a tested drug versus control. Worked examples illustrate the methodology.     

Semi-parametric and non-parametric methods for the analysis of repeated measurements with applications to clinical trials.

Techniques applicable for the analysis of longitudinal data when the response variable is non-normal are not nearly as comprehensive as for normally-distributed outcomes. However, there have been several recent developments. Semi-parametric and non-parametric methodology for the analysis of repeated measurements is reviewed. The commonly encountered design in which, for each subject, one assesses a univariate response variable at multiple fixed time points, is considered. The types of outcomes considered include binary, ordered categorical, and continuous (but extremely non-normal) response variables. All of the methods considered allow for incomplete data due to the occurrence of missing observations. In addition, discrete and/or continuous covariates, which may be time-dependent, are accommodated by some of the approaches. The methods are demonstrated using data from three clinical trials.     

Likelihood-based concordance tests for analysis of ascertained twin pair multinomial data

The classic twin model design has a wide application in human genetics. Under the assumption that nongenetic effects are shared to the same degree by monozygotic (MZ) and dizygotic (DZ) twin pairs, a test of the equality of casewise concordances between MZ and DZ twins provides a clue to the influence of genetic and environmental factors on a disease. The casewise concordance is the conditional probability that given that one member of a twin pair is affected, the other is also affected. When disease prevalence is low or cost-effectiveness is considered, collection of twin pairs by ascertainment for performing casewise concordance analysis is required. In this article, by defining an overall casewise concordance parameter, several likelihood-based tests, such as likelihood ratio test LR, score test Score, the usual Wald test Wald and an alternative Wald test WaldA are investigated for a test of the equality of concordances between ascertained MZ and DZ twin pairs under multinomial models. Simulation studies were conducted for data with small sample sizes. The results show that the type I error rates and power of LR and Score are stable only when the overall casewise concordances are not extremely small or large. The Wald has higher power performance in most cases but would slightly inflate type I error rates; the WaldA is the most robust and recommended approach.