非正态及非线性重复测量资料分析模型及其医学应用
|
摘要
重复测量资料是指对同一受试对象的某个或某些指标进行多次观察或测量获得的数据,在医学研究领域极为多见,观测指标的类型也多种多样,表现为定量变量,分类变量及等级变量;例如,在Ⅱ期高血压病的疗效评价中,为患者定期检测血压(包括舒张压/收缩压等)值为定量变量资料;在乳腺增生患者的治疗中,定期记录患者治疗期间的变化,检测指标为是否有改善的二分类变量;在介入治疗冠心病患者出院随访研究中,分别检查并记录出院时、出院后3月、6月和9月的疗效,不同时段结局可以是痊愈、好转、有改善、变化较小或无改变等,表现为等级分类变量;在一些情况下,记录的反应变量为计数数据,如单位时间(年或月)内癫痫发作次数。
据反应变量与自变量参数之间的关系,又可分为线性重复测量资料模型和非线性重复测量资料模型;如定期监测高血压病患者的血压值,探讨患者血压与时间变量及其它解释变量间关系,可以用线性模型来拟合,称其为线性重复测量资料模型:在药动学研究中,个体口服一定剂量药物后连续采集检测血样中药物浓度,描述药物在体内吸收、分布、排泄的药动学过程,大多情况下表现为非线性特征,如Ⅱ室模型;在HⅣ病毒动力学研究中,血液里病毒粒浓度的定量分析是检测HⅣ感染者“病毒”路径,描述感染特征的一种常规手段,采用系列微分方程描述免疫细胞的繁殖、感染和凋亡以及病毒颗粒的繁殖和清除等特征的变化等,均可收集到非线性重复测量资料,要描述解释变量与反应变量参数间的非线性关系,可构建非线性重复测量资料模型。复发事件数据指同一个体在一段时间里多次经历同一事件,例如一名冠心病患者在一段时间内经历多次冠心病的发作,一名癌症患者在化、放疗后再一次次经历复发等,该资料具有重复测量和生存分析数据的特性。上面提及的资料均不满足经典线性模型分析要求的正态性和线性条件。
重复测量资料线性模型理论已经成熟,应用也较普及,线性混合效应模型被视为最理想的方法。它可假定方差-协方差具有某特定结构形式,用来说明异方差性和相关性,既不像单变量分析方法那样严格,也不如多变量方差分析那样对协方差完全无约束;分析观察时点可相等或不等,能充分利用含有完全随机缺失观察值的资料,建模灵活。但对于非正态及非线性重复测量资料模型分析理论及应用目前尚处于初级阶段,有待于进一步完善相关理论,在医学研究领域推广、普及和应用。线性混合效应模型允许反应变量来自指数家族任一分布,包括离散分布(如二项分布,泊松分布等)和连续分布(正态分布,beta分布和卡方分布等),用连接函数将反应变量的均数与个体的线性预测值联系起来,构建广义线性混合效应模型(当随机效应不存在时退化为广义线性模型)和非线性混合效应模型,用来处理非正态、非独立二分类,等级多分类及计数重复测量资料。脆弱模型是用以描述子组中个体“生存”情况与时间之间关联性的一种模型,将随机效应、变量间的联系及未观测到的异质性引入到生存分析模型中,为复发事件数据高效方便的分析提供了新思路。
重复测量资料类型广泛,医学应用非常多见。本文深入全面地从反应变量的类型(定性、定量、等级变量)来探讨相应的统计分析模型,并进行比较分析;从反应变量与解释变量参数之间的关系,系统探索线性模型和非线性模型。其主要内容分七部分:
第一部分介绍重复测量资料的特性及其方差协方差结构。
第二部分介绍线性混合效应模型重复测量资料统计分析基础理论。
第三部分介绍广义估计方程(GEE)理论及其在二分类、有序多分类变量和计数重复测量资料分析中的应用。广义估计方程是边际模型估计方法的一种,是在广义线性模型和纵向数据准似然估计的基础上发展起来的一种拟似然估计方法,可用于非独立重复测量数据分析:它是在未完全指明个体观测的联合分布,仅根据(单变量)边际分布似然和个体重复测量向量的“作业”相关矩阵进行参数估计的,是一种半参数方法。即便在时间依赖协方差矩阵误指时,GEE方法也可得出一致和渐近的正确估计,当反应变量表现为非连续型变量(如二分类、等级或计数资料)时,GEE方法是常用得最适方法之一。
第四部分阐述广义线性混合效应模型(GLMMs)理论及其在二分类、多分类等级变量及其计数重复测量资料分析中的应用。广义线性混合效应模型是线性混合效应模型的自然延伸,该类模型可用于解决连续型和分类变量的纵向研究问题,GLMMs是唯一具有随机效应指数分布族的回归方法,采用一个连接函数将反应变量的均数与个体的线性预测值联系起来;它可以用随机效应拟合各类型相关数据结构模型:当随机效应不存在时,广义线性混合效应模型就退化为广义线性模型。
第五部分介绍非线性混合效应模型(NLMEs)理论及其在药物代谢动力学、二分类、等级变量及其计数重复测量资料中的应用。非线性混合效应模型不仅能识别与估计个体间和个体内的变异,而且也考虑了解释变量与反应变量参数的非线性关系,允许固定效应和随机效应进入模型的非线性部分:反应变量可以服从正态分布、二项分布或泊松分布;常用于处理药代动力学、非线性生长曲线研究,也可以直接拟合二分类、等级及计数重复测量资料的非线性模型;近年在工农业、环境和医学界备受关注。
第六部分介绍条件脆弱模型理论及其在医学复发事件数据分析中的应用。脆弱模型是Cox比例风险模型的延伸,目的是解释由不能被观测的协变量引起的异质性,脆弱对基线风险函数有乘积效应,即以乘法算子对子组内每一个体的危险率产生影响。脆弱值大的子组比脆弱值值小的子组要在更短的时间内经历事件的发生。一般可认为同一子组内个体有相同的脆弱,因此也称为共享脆弱模型,生存时间被认为是在共享脆弱的条件下独立:脆弱被认为是服从某种分布的随机效应,常认为服从gamma分布。条件脆弱模型将解释观测异质性的随机效应和反映事件相依性的基本事件分层(变化的基线风险)联系起来,把复发事件数据过程的关键特征都包含在模型中,是复发事件数据拟合的理想模型。
第七部分通过对非正态、非独立和非线性资料分析方法的介绍,进一步阐述了广义估计方程、广义线性混合效应模型和非线性混合效应模型在医学研究二分类、有序多分类、计数变量以及非线性重复测量资料,脆弱模型对复发事件数据等方面的分析,探讨了SAS软件和R软件分析方法与软件实现,提出了实际应用中有关模型构建、参数估计、软件实现等方面的建议与评价,为非正态、非独立和非线性资料分析应用提供了新思路。
文中主要采用SAS9.1.3分析软件GENMOD、GLIMMIX和NLMIXED过程对医学分类及非线性重复测量资料进行了对比分析,采用免费软件R2.4.0实现了临床研究中复发事件数据的分析:运用模型理论与实例分析相结合、方法研究与软件实现相结合的思路,系统介绍了非正态、非线性重复测量资料在模型分析与软件中的应用,结合实例,摸索与总结出具体应用的技能与经验,系统阐述了非正态、非线性资料分析模型及原理,为医学资料的分析提供了方法学基础,也为理论模型与软件应用的结合提供了条件,尤其在淡化抽象的统计理论,以基于理论而又高于理论的思路,突出各种方法的实际应用方面打开了新局面,为正确运用广义估计方程、广义线性混合效应模型、非线性混合效应模型和脆弱模型提供可靠性高、准确性好、信息量大的、解决实际问题可行性强的多元统计方法提出了新观点。
Repeated measurements datas(RM) refers to datas in which the response of each experimental unit or subject is observed on multiple occasions or under multiple conditions . The data is very common in medical field, and the responses may be all variety of variables, including quantitative variables, qualitative variables and ranked variables; for example ,in clinical medical study about II phrase hypertension patients,the blood pressure(systolic pressure and diastolic pressure) are measured regularly,the response is quantitative variable; in clinical curative study of galactophore hyperpasia patients,recording the curative preformance of the patients during treatment , the outcome variable is dichotomous response (improvement ,no improvement); in the trace study for interposition theraty of coronary heart disease , recording the effects at the time of leaving the hospital and three month,six month and nine month after leaving the hospital,the outcomes are recovery,mend,amend,little change and no change, the response is ordinal categorical variable; in other cases ,the response may be recorded as counts data,such as the number of falling sickness at unit time(year or month).
According to the relationship of coefficeents of responde and covariates, RM data can be divided into linear and nonlinear ;for example ,regularly examine the blood pressure of hypertension patients ,the relationship of the outcome variable and time variable or other covariates can be fitted by linear model, then this is a linear RM data .But ,in pharmacokinetics analysis, serial blood samples are collected from each of several subjects following doses of a drug and assayed for drug concentration, in order to gaining insight into within-subject parmacokinetic processes of absorption, distribution and elimination. In most cases, the pharmacokinetic processes are nonlinear model. In HIV dynamics study, with the advent of assays capable of quantifying the concetration of viral particles in the blood, monitoring of such "viral load" measurements is now a routine feature of HIV-infected individuals, using a system of differential equations whose parameters characterize rates of production, infection and death of immune system cells and viral production and clearance. The above two example belong to nonlinear RM data ,the relationship of parameters between response and covariate is nonlinear. Recurrent event data means the subject experiences the same type of event more than once, such as heart attacks of coronary heart disease patients, recur of cancer patient, these data have the character of RM data and survival data. Above cases all don't satisfy normality and linear condition of traditional linear models. We must find another statistical model to analysis.
Methods of linear modeling of RM data are well developed, their applications are very popular. Linear mixed effect model among those mehods is the most ideal method. It assume the variance-covariance to have some kind of structure, which be used to recognize heterogeneous variance and within-subject collrelation. It isn't not only more strict than univariate variance analysis, but also less strict to covariance structure than multivariante variance, can analysis balance and unbalance data ,can exploit miss data ,can model flexibly the linear model. However the theories and applications of unnormality and nonlinear model for repeated measurement data are still at the initial stage, need to be completed and popularized. An natural extention of linear mixed effect mode allow response come from an exponential family of distributions , including dispersed distribution (binomial, poisson, et all) and continuous distribution (normal ,beta and chi-square).The mean response and linear predictor are connected by link function, these is generalized linear mixed model.
The types of repeated measurement datas are widespread, they are common in medical applications. Hence it is necessary to study deeply and completely all kinds of models of RM datas. The paper describe and be compared with all kinds of statistical models (linear and nonlinear models)of RM datas from two aspects ,one is different types of response (quantitative , qualitative and ordered variable),the other is the relationship of the parameters between response and covariates. The content include seven parts:
First part introduce the character and variance-covariance pattern of RM data;
Second part introduce the theory of linear mixed effect model;
Third part introduce the theory of generalized estimate equation and applications in binary,ordered and count data:The generalized estimating equations(GEE) methodology for the analysis of RM is a marginal model approach, The GEE approach is an extension of the generalized linear model and of quasilikelihood to longitudinal data analysis, it ia a regression model for correlated repeated measurement data. The method is semiparametric in that the estimating equation are derived without full specification of the joint distribution of a subject's observations . instead, we specify only the likelihood for the (univariate) marginal distributions and a "working" covariance matrix for the vector of repeated measurements from each subject .The GEE method yields consistent and asymptotically normal solutions, even with misspecification of the time dependence, when the response is categorical variable (binary , ordered or count data), GEE is one of the most appropriate models.
Forth part introduce the theory of generalized linear mixed effect model and applications in binary,ordered and count data:Generalized linear mixed effect modes are natural extention of linear mixed effect modes which can be used for both continuous and discrete longitudinal data. GLMMs are a unified approach to exponetial family regression methods with random effects. The mean response and linear predictor are connected by link function,when there isn't random effect, the model be changed a generalized linear model. All types of correlation structure in the repeated measurement data is induced by introducing a random effect.
Fifth part introduce the theory of nonlinear mixed effect model and applications in nonlinear RM data ,binary,ordered and count data:Nonlinear mixed effect model not only recognize and estimate variability both between and within individuals,but also allow both fixed and random effects enter the model nonlinearly. The depentent variable is normal, binomial,poisson distribution,the applications of the most common are Pharmacokinetic, nonlinear growth curve and fit directely nolinear model for categorical response repeated measurement datas; These year ,the model enjoyed widespread attention within biological,agriculture and medical reseach community.
Sixth part introduce the theory of frailty model and applications in recurrent event datas: Frailty modes are extensions of Cox proportional hazards model,which aims to account for heterogeneity caused by unmeasured covariates. The frailty has a multiplicative effect on the baseline hazard function ,namely the individual harzard rates are influenced by frailty in the multiplication way. The subgroup which frailty value is bigger than other will be susceptible to experience the event in a earlier time. Individuals in a cluster are assumed to share the same frailty which is why this model is called shared frailty model .The survival times are assumed to be conditional independent with reaponse to the shared frailty. The frailty is a random efect which is assumed to obey some kinds of distribution. The frailty distribution most often applied are the gamma distribution. The conditional frialty model combines a random effect to incorporate unobserved heterogeneity with event-based stratification(varying baseline hazards) to invorporate event dependence .They will be the ideal model for the repeated event data.
Seven parts By introducing the analysis methods for nonnormal,nonindependent and nonlinear datas, deeply expound the application of generalized estimate equation, generalized linear mixed effect model and nonlinear mixed effect model in categorical data (dichotomous,ordinal,count )and of frailty model for recurrent event data, discuss the analysis methods and realization for SAS software and R software, put forward some suggestion and appraise for model construction, parameter estimate ,soft realization et all in medical applications, provide new ideal of analysis for nonnormal, nonindependent and nonlinear datas.
The paper analysis and contrast GENMODE,GLIMMIX and NLMIXED procedures of SAS9.1.3 at the application in medical categorical and nonlinear repeated measurement data , conduct recurrent event data using free software R2.4.0;Using the idea of combining the model theories with example analysis , linking method researches and software realization , systematicly introduce the application of model analysis and software realization for nonnornal ,nonlinear repeated measurement datas , summarize skills and experiences about practical application by analyzing examples, systmeticly explain models of analysis and theories for nonnormal,nonindependent and nonlinear datas, proving the methodology basis for analyzing the medical datas , providing the conditions for theory models and software applications, especially light abstract statistical theory , using the idea of being base on theory but be higher than theory ,open some new situation for the practice applications of all kinds of methods ;proving some new , reliable , exact ,informative,feasible viewpoint for multivariable statistical methods to resolve practical problem by using correctly generalized estimate equation,generalized linear mixed effect model,nonlinear mixed effect model and frailty model.
据反应变量与自变量参数之间的关系,又可分为线性重复测量资料模型和非线性重复测量资料模型;如定期监测高血压病患者的血压值,探讨患者血压与时间变量及其它解释变量间关系,可以用线性模型来拟合,称其为线性重复测量资料模型:在药动学研究中,个体口服一定剂量药物后连续采集检测血样中药物浓度,描述药物在体内吸收、分布、排泄的药动学过程,大多情况下表现为非线性特征,如Ⅱ室模型;在HⅣ病毒动力学研究中,血液里病毒粒浓度的定量分析是检测HⅣ感染者“病毒”路径,描述感染特征的一种常规手段,采用系列微分方程描述免疫细胞的繁殖、感染和凋亡以及病毒颗粒的繁殖和清除等特征的变化等,均可收集到非线性重复测量资料,要描述解释变量与反应变量参数间的非线性关系,可构建非线性重复测量资料模型。复发事件数据指同一个体在一段时间里多次经历同一事件,例如一名冠心病患者在一段时间内经历多次冠心病的发作,一名癌症患者在化、放疗后再一次次经历复发等,该资料具有重复测量和生存分析数据的特性。上面提及的资料均不满足经典线性模型分析要求的正态性和线性条件。
重复测量资料线性模型理论已经成熟,应用也较普及,线性混合效应模型被视为最理想的方法。它可假定方差-协方差具有某特定结构形式,用来说明异方差性和相关性,既不像单变量分析方法那样严格,也不如多变量方差分析那样对协方差完全无约束;分析观察时点可相等或不等,能充分利用含有完全随机缺失观察值的资料,建模灵活。但对于非正态及非线性重复测量资料模型分析理论及应用目前尚处于初级阶段,有待于进一步完善相关理论,在医学研究领域推广、普及和应用。线性混合效应模型允许反应变量来自指数家族任一分布,包括离散分布(如二项分布,泊松分布等)和连续分布(正态分布,beta分布和卡方分布等),用连接函数将反应变量的均数与个体的线性预测值联系起来,构建广义线性混合效应模型(当随机效应不存在时退化为广义线性模型)和非线性混合效应模型,用来处理非正态、非独立二分类,等级多分类及计数重复测量资料。脆弱模型是用以描述子组中个体“生存”情况与时间之间关联性的一种模型,将随机效应、变量间的联系及未观测到的异质性引入到生存分析模型中,为复发事件数据高效方便的分析提供了新思路。
重复测量资料类型广泛,医学应用非常多见。本文深入全面地从反应变量的类型(定性、定量、等级变量)来探讨相应的统计分析模型,并进行比较分析;从反应变量与解释变量参数之间的关系,系统探索线性模型和非线性模型。其主要内容分七部分:
第一部分介绍重复测量资料的特性及其方差协方差结构。
第二部分介绍线性混合效应模型重复测量资料统计分析基础理论。
第三部分介绍广义估计方程(GEE)理论及其在二分类、有序多分类变量和计数重复测量资料分析中的应用。广义估计方程是边际模型估计方法的一种,是在广义线性模型和纵向数据准似然估计的基础上发展起来的一种拟似然估计方法,可用于非独立重复测量数据分析:它是在未完全指明个体观测的联合分布,仅根据(单变量)边际分布似然和个体重复测量向量的“作业”相关矩阵进行参数估计的,是一种半参数方法。即便在时间依赖协方差矩阵误指时,GEE方法也可得出一致和渐近的正确估计,当反应变量表现为非连续型变量(如二分类、等级或计数资料)时,GEE方法是常用得最适方法之一。
第四部分阐述广义线性混合效应模型(GLMMs)理论及其在二分类、多分类等级变量及其计数重复测量资料分析中的应用。广义线性混合效应模型是线性混合效应模型的自然延伸,该类模型可用于解决连续型和分类变量的纵向研究问题,GLMMs是唯一具有随机效应指数分布族的回归方法,采用一个连接函数将反应变量的均数与个体的线性预测值联系起来;它可以用随机效应拟合各类型相关数据结构模型:当随机效应不存在时,广义线性混合效应模型就退化为广义线性模型。
第五部分介绍非线性混合效应模型(NLMEs)理论及其在药物代谢动力学、二分类、等级变量及其计数重复测量资料中的应用。非线性混合效应模型不仅能识别与估计个体间和个体内的变异,而且也考虑了解释变量与反应变量参数的非线性关系,允许固定效应和随机效应进入模型的非线性部分:反应变量可以服从正态分布、二项分布或泊松分布;常用于处理药代动力学、非线性生长曲线研究,也可以直接拟合二分类、等级及计数重复测量资料的非线性模型;近年在工农业、环境和医学界备受关注。
第六部分介绍条件脆弱模型理论及其在医学复发事件数据分析中的应用。脆弱模型是Cox比例风险模型的延伸,目的是解释由不能被观测的协变量引起的异质性,脆弱对基线风险函数有乘积效应,即以乘法算子对子组内每一个体的危险率产生影响。脆弱值大的子组比脆弱值值小的子组要在更短的时间内经历事件的发生。一般可认为同一子组内个体有相同的脆弱,因此也称为共享脆弱模型,生存时间被认为是在共享脆弱的条件下独立:脆弱被认为是服从某种分布的随机效应,常认为服从gamma分布。条件脆弱模型将解释观测异质性的随机效应和反映事件相依性的基本事件分层(变化的基线风险)联系起来,把复发事件数据过程的关键特征都包含在模型中,是复发事件数据拟合的理想模型。
第七部分通过对非正态、非独立和非线性资料分析方法的介绍,进一步阐述了广义估计方程、广义线性混合效应模型和非线性混合效应模型在医学研究二分类、有序多分类、计数变量以及非线性重复测量资料,脆弱模型对复发事件数据等方面的分析,探讨了SAS软件和R软件分析方法与软件实现,提出了实际应用中有关模型构建、参数估计、软件实现等方面的建议与评价,为非正态、非独立和非线性资料分析应用提供了新思路。
文中主要采用SAS9.1.3分析软件GENMOD、GLIMMIX和NLMIXED过程对医学分类及非线性重复测量资料进行了对比分析,采用免费软件R2.4.0实现了临床研究中复发事件数据的分析:运用模型理论与实例分析相结合、方法研究与软件实现相结合的思路,系统介绍了非正态、非线性重复测量资料在模型分析与软件中的应用,结合实例,摸索与总结出具体应用的技能与经验,系统阐述了非正态、非线性资料分析模型及原理,为医学资料的分析提供了方法学基础,也为理论模型与软件应用的结合提供了条件,尤其在淡化抽象的统计理论,以基于理论而又高于理论的思路,突出各种方法的实际应用方面打开了新局面,为正确运用广义估计方程、广义线性混合效应模型、非线性混合效应模型和脆弱模型提供可靠性高、准确性好、信息量大的、解决实际问题可行性强的多元统计方法提出了新观点。
Repeated measurements datas(RM) refers to datas in which the response of each experimental unit or subject is observed on multiple occasions or under multiple conditions . The data is very common in medical field, and the responses may be all variety of variables, including quantitative variables, qualitative variables and ranked variables; for example ,in clinical medical study about II phrase hypertension patients,the blood pressure(systolic pressure and diastolic pressure) are measured regularly,the response is quantitative variable; in clinical curative study of galactophore hyperpasia patients,recording the curative preformance of the patients during treatment , the outcome variable is dichotomous response (improvement ,no improvement); in the trace study for interposition theraty of coronary heart disease , recording the effects at the time of leaving the hospital and three month,six month and nine month after leaving the hospital,the outcomes are recovery,mend,amend,little change and no change, the response is ordinal categorical variable; in other cases ,the response may be recorded as counts data,such as the number of falling sickness at unit time(year or month).
According to the relationship of coefficeents of responde and covariates, RM data can be divided into linear and nonlinear ;for example ,regularly examine the blood pressure of hypertension patients ,the relationship of the outcome variable and time variable or other covariates can be fitted by linear model, then this is a linear RM data .But ,in pharmacokinetics analysis, serial blood samples are collected from each of several subjects following doses of a drug and assayed for drug concentration, in order to gaining insight into within-subject parmacokinetic processes of absorption, distribution and elimination. In most cases, the pharmacokinetic processes are nonlinear model. In HIV dynamics study, with the advent of assays capable of quantifying the concetration of viral particles in the blood, monitoring of such "viral load" measurements is now a routine feature of HIV-infected individuals, using a system of differential equations whose parameters characterize rates of production, infection and death of immune system cells and viral production and clearance. The above two example belong to nonlinear RM data ,the relationship of parameters between response and covariate is nonlinear. Recurrent event data means the subject experiences the same type of event more than once, such as heart attacks of coronary heart disease patients, recur of cancer patient, these data have the character of RM data and survival data. Above cases all don't satisfy normality and linear condition of traditional linear models. We must find another statistical model to analysis.
Methods of linear modeling of RM data are well developed, their applications are very popular. Linear mixed effect model among those mehods is the most ideal method. It assume the variance-covariance to have some kind of structure, which be used to recognize heterogeneous variance and within-subject collrelation. It isn't not only more strict than univariate variance analysis, but also less strict to covariance structure than multivariante variance, can analysis balance and unbalance data ,can exploit miss data ,can model flexibly the linear model. However the theories and applications of unnormality and nonlinear model for repeated measurement data are still at the initial stage, need to be completed and popularized. An natural extention of linear mixed effect mode allow response come from an exponential family of distributions , including dispersed distribution (binomial, poisson, et all) and continuous distribution (normal ,beta and chi-square).The mean response and linear predictor are connected by link function, these is generalized linear mixed model.
The types of repeated measurement datas are widespread, they are common in medical applications. Hence it is necessary to study deeply and completely all kinds of models of RM datas. The paper describe and be compared with all kinds of statistical models (linear and nonlinear models)of RM datas from two aspects ,one is different types of response (quantitative , qualitative and ordered variable),the other is the relationship of the parameters between response and covariates. The content include seven parts:
First part introduce the character and variance-covariance pattern of RM data;
Second part introduce the theory of linear mixed effect model;
Third part introduce the theory of generalized estimate equation and applications in binary,ordered and count data:The generalized estimating equations(GEE) methodology for the analysis of RM is a marginal model approach, The GEE approach is an extension of the generalized linear model and of quasilikelihood to longitudinal data analysis, it ia a regression model for correlated repeated measurement data. The method is semiparametric in that the estimating equation are derived without full specification of the joint distribution of a subject's observations . instead, we specify only the likelihood for the (univariate) marginal distributions and a "working" covariance matrix for the vector of repeated measurements from each subject .The GEE method yields consistent and asymptotically normal solutions, even with misspecification of the time dependence, when the response is categorical variable (binary , ordered or count data), GEE is one of the most appropriate models.
Forth part introduce the theory of generalized linear mixed effect model and applications in binary,ordered and count data:Generalized linear mixed effect modes are natural extention of linear mixed effect modes which can be used for both continuous and discrete longitudinal data. GLMMs are a unified approach to exponetial family regression methods with random effects. The mean response and linear predictor are connected by link function,when there isn't random effect, the model be changed a generalized linear model. All types of correlation structure in the repeated measurement data is induced by introducing a random effect.
Fifth part introduce the theory of nonlinear mixed effect model and applications in nonlinear RM data ,binary,ordered and count data:Nonlinear mixed effect model not only recognize and estimate variability both between and within individuals,but also allow both fixed and random effects enter the model nonlinearly. The depentent variable is normal, binomial,poisson distribution,the applications of the most common are Pharmacokinetic, nonlinear growth curve and fit directely nolinear model for categorical response repeated measurement datas; These year ,the model enjoyed widespread attention within biological,agriculture and medical reseach community.
Sixth part introduce the theory of frailty model and applications in recurrent event datas: Frailty modes are extensions of Cox proportional hazards model,which aims to account for heterogeneity caused by unmeasured covariates. The frailty has a multiplicative effect on the baseline hazard function ,namely the individual harzard rates are influenced by frailty in the multiplication way. The subgroup which frailty value is bigger than other will be susceptible to experience the event in a earlier time. Individuals in a cluster are assumed to share the same frailty which is why this model is called shared frailty model .The survival times are assumed to be conditional independent with reaponse to the shared frailty. The frailty is a random efect which is assumed to obey some kinds of distribution. The frailty distribution most often applied are the gamma distribution. The conditional frialty model combines a random effect to incorporate unobserved heterogeneity with event-based stratification(varying baseline hazards) to invorporate event dependence .They will be the ideal model for the repeated event data.
Seven parts By introducing the analysis methods for nonnormal,nonindependent and nonlinear datas, deeply expound the application of generalized estimate equation, generalized linear mixed effect model and nonlinear mixed effect model in categorical data (dichotomous,ordinal,count )and of frailty model for recurrent event data, discuss the analysis methods and realization for SAS software and R software, put forward some suggestion and appraise for model construction, parameter estimate ,soft realization et all in medical applications, provide new ideal of analysis for nonnormal, nonindependent and nonlinear datas.
The paper analysis and contrast GENMODE,GLIMMIX and NLMIXED procedures of SAS9.1.3 at the application in medical categorical and nonlinear repeated measurement data , conduct recurrent event data using free software R2.4.0;Using the idea of combining the model theories with example analysis , linking method researches and software realization , systematicly introduce the application of model analysis and software realization for nonnornal ,nonlinear repeated measurement datas , summarize skills and experiences about practical application by analyzing examples, systmeticly explain models of analysis and theories for nonnormal,nonindependent and nonlinear datas, proving the methodology basis for analyzing the medical datas , providing the conditions for theory models and software applications, especially light abstract statistical theory , using the idea of being base on theory but be higher than theory ,open some new situation for the practice applications of all kinds of methods ;proving some new , reliable , exact ,informative,feasible viewpoint for multivariable statistical methods to resolve practical problem by using correctly generalized estimate equation,generalized linear mixed effect model,nonlinear mixed effect model and frailty model.
引文
[1] Greenhouse SW,Geisser S.On methods in the analysis of profile data.Psychometrika, 1959,24:95-112
[2] Huynh H,Feldt LS.Conditions under which mean square ratios in repeated measur ements design have exact F-distributions.J Amer Stat Ass,1970,65:1582-1589
[3] Danford MB, Hughes HM,McNee RC.On the analysis of repeated-measurements experiments.Biometrics, 1960,16:547-565
[4] Cole JW,Grizzle JE.Application of multivariate analysis of variance to repeated measures experiments.Biometrics, 1966,22:810-828
[5] Thomas DR. Univariate repeated measures techniques applied to multivariate data.Psychometrika, 1983,48:451 -464
[6] Boik RJ.The mixed model for multivariate repeated measures: validity conditions and an approximate test.Psychometrika, 1988,53:469-486
[7] Laird NM,Ware H.Random-effects models for longitudinal data.Biometrics,1982,38(4):963-974
[8] Grizzle JE, Starmer CF,Koch GGAnalysis of categorical data by linear models.Biometrics, 1969,25:489-504
[9] Koch GG,Reinfurt DW.The analysis of categorical data from mixed models.Biometrics, 1971,27:157-173
[10] Koch GG, Landis JR, Freeman JL, et al.A General Methodology for the Analysis of Experiments with Repeated Measurement of Categorical Data.Biometrics, 1977,33:133-158
[11] Landis JR, Miller ME, Davis CS, et al.Some general methods for the analysis of categorical data in longitudinal studies.Stat Med, 1988,7(1-2): 109-137
[12] Crowder MJ,Hand DJ. Analysis of Repeated Measures. London: Chapman and Hall, 1990
[13] Liang KY,Zeger SL.Longitudinal data analysis using generalized linear models.Biometrics, 1986,73:13-22
[14] Zeger SL,Liang KY.Longitudinal data analysis for discrete and continuous outcomes.Biometrics, 1986,42(1): 121 -130
[15] Stiratelli R, Laird N,Ware JH.Random-effects models for serial observations with binary response.Biometrics, 1984,40(4):961 -971
[16] Anderson DA,Aitkin M.Variance component models with binary response: Inteviewer variability.J. Roy.Statist. Soc. Ser. B,1985,47:203-210
[17] Gilmour AR, Anderson RD,Rae AL. The analysis of binomial data by a generalized linear mixed model.Biometrika, 1985,72:593-599
[18] Schall R.Estimation in generalized linear models with random effects.Biometrika, 1991,78:719-727
[19] Breslow NE,CIayton DG.Approximate inference in generalized linear mixed models.Journal of the American Statistical Association,1993,88(421):9-25
[20] Wolfinger R,O'Connell M.Generalized linear mixed models: A pseudo-likelihood approach.Journal of Statistical Computation and Simulation,1993,48:233-243
[21] McCulloch CE,Searle SR. Generalized, Linear, and Mixed Models. New York: JohnWiley & Sons, 2000
[22] Zeger SL,Liang KY.An overview of methods for the analysis of longitudinal data.Stat Med, 1992,11 (14-15): 1825-1839
[23] Sheiner LB, Rosenberg B,Marathe VV.Estimation of population characteristics of pharmacokinetic parameters from routine clinical data.J Pharmacokinet Biopharm,1977,5(5):445-479
[24] Beal SL.Population pharmacokinetic data and parameter estimation based on their first two statistical moments.Drug Metabolism Reviews, 1984,15:173-193
[25]Sheiner LB.The population approach to pharmacokinetic data analysis:rationale and standard data analysis methods.Drug Metabolism Reviews,1984,15:153-171
[26]Zeger SL,Liang KY,Albert PS.Models for longitudinal data:a generalized estimating equation approach.Biometrics,1988,44(4):1049-1060
[27]Lindstrom MJ,Bates DM.Nonlinear mixed effects models for repeated measures data.Biometrics,1990,46(3):673-687
[28]Vonesh EF,Carter RL.Mixed-effeets nonlinear regression for unbalanced repeated measures.Biometrics,1992,48:1-17
[29]Davidian M,Giltinan DM.Nonlinear Models for Measurement Data.London:Chapman & Hall,1995
[30]Pinheiro JC,Bates DM Model Building for Nonlinear Mixed-Effects Models.Technical Report 91In:Department of Biostatistics,University of Wisconsin - Madison,1995.
[31]Vonesh EF,Chinchilli VM.Linear and Nonlinear Models for the Analysis of Repeated Measurements.New York:Marcel Dekker,1997
[32]Ke C,Wang Y.Semiparametric nonlinear mixed models and their applications.Journal of the American statistical asociation,2001,96:1272-1298
[33]Prentice RL,Williams BJ,Peterson AV.On the regression analysis of multivariate failure time data.Biometrika,1981,68:373-379
[34]Andersen PK,Gill RD.Cox's regression model for counting processes:a large sample study.Annals of Statistics,1982,10:1100-1120
[35]Wei LJ,Lin DY,Weissfeld L.Regression analysis of multivariate incomplete failure time data by modeling marginal distributions.Journal of the American Statistical Association,1989,84:1065-1073
[36]Clayton DG,Cuzick J.Multivariate generalizations of the proportional hazards model.Journal of the Royal Statistical Society,Series B,,1985,148:82-117
[37]Oakes DA.Frailty Models for Multiple Event Times.Netherlands:Kluwer Academic Publishers,1992.
[38]Hougaard P.Analysis of Multivariate Survival Data.New York Springer-Verlag,2000
[39]Lawless JF,Nadeau C.Some Simple Robust Methods for the Analysis of Recurrent Events.Technometrics,1995,37:158-168
[40]Lin DY,Wei LJ,Yang I,et al.Semiparametric Regression for the Mean and Rate Functions of Recurrent Events.J.R.Statist.Soc.B,2000,62:711-730
[41]Nelson WB.Recurrent Events Data Analysis for Product Repairs,Disease Recurrences,and Other Applications:The ASA-SIAM Series on Statistics and Applied Probability,2003
[42]陈长生,徐勇勇,曹秀堂.医学研究中重复观测数据的统计分析方法.中国卫生统计,1996,13(6):55-58
[43]陈长生,徐勇勇,曹秀堂.不等距重复观测数据组间比较的正交回归模型.中国卫生统计,1996,13(3):1-5
[44]陈峰,任仕泉,陆守曾.非独立计量数据的内部相关性研究.现代预防医学,1998,25(3):269-271
[45]任仕泉,陈峰,等.非独立数据及其协方差结构表达.中国卫生统计,1998,15(4):4-8
[46]任仕泉.非独立数据统计分析方法及其医学应用:[博士学位论文].成都:华西医科大学,1999
[47]李贤.重复测量数值型变量统计分析与设计:[硕士学位论文].山西:山西医科大学,1999
[48]李贤,刘桂芬,何大卫,等.重复测量设计样本含量估计.中国卫生统计,2001,18(4):204-206
[49]李贤,刘桂芬,何大卫.多因素重复测量设计裂区方差分析.中国卫生统计,2001,18(1):22-23
[50]赵晋芳.重复测量线性混合效应模型在医学研究中的应用:[硕士学位论文].山西:山西医科大学,2002
[51]陈启光.纵向研究中重复测量资料的广义估计方程分析.中国卫生统计,1995,12(1):22-25
[52]熊林平,郭祖超.重复测量分类数据的分析.中国卫生统计,1997,14(1):1-3
[53]熊林平,曹秀堂,侩勇勇,等.纵向观测计数数据的对数线性模型.中国卫生统计,1999,16(2):68-71
[54]李康,赵景波.重复有序观测数据分析探讨.中国卫生统计,1994,11(2):9-12
[55]郑建中,张岩波.有序分类重复测量数据的多水平模型分析.现代预防医学,2003,30(1):6-8
[56]方积乾,陆盈.现代医学统计学.北京:人民卫生出版社,2002,295-302
[57]余松林,向惠云.重复测量资料分析方法与SAS程序.北京:科学出版社,2003
[58]Jennrich RI,Schluchter MD.Unbalanced repeated-measures models with structured covariance matrices.Biometrics,1986,42(4):805-820
[59]Jones RH.Serial correlation or random subject effects.Communications in Statistics,1990,19(10):1105-1123
[60]Vonesh EF,Chinchilli VM,Pu K.Goodness-of-fit in generalized nonlinear mixed-effects models.Biometrics,1996,52(2):572-587
[61]Daniels MJ,Zhao YD.Modelling the random effects covariance matrix in longitudinal data.Statistics in Medicine,2003,22:1631-1647
[62]Henderson CR.Selection index and expected genetic advance.in Statistical genetics and plant breeding,National Academy of Sciences National Research Council Publication NO.982,1963:141-163
[63]Harville DA.Extensions of the Gauss-Markov theorem to include the estimation of random effects.Annal of Statisticals,1976,4:384-395
[64]Davidian M,Giltinan DM.Some general estimation methods for nonlinear mixed-effects models.J Biopharm Stat,1993,3(1):23-55
[65]Akaike H.A new look at the statistical model identification.IEEE Trans.on Automatic Control,1974,19(6):716-723
[66]Schwarz G.Estimating the Dimension of a model.Annal of Statistics,1978,6(2):461-464
[67]Diggle PJ.An approach to the analysis of repeated measurements.Biometrics,1988,44(4):959-971
[68]Nelder JA,Wedderbum RWM.Generalized linear models.Journal of the Royal Statistical Society A,1972,135:370-384
[69]Sutradhar BC.An Overview on Regression Models for Discrete Longitudinal Responses.Statistical Science,2003,18(3):377-393
[70]Stiratelli R,Laird N,Ware JH.Random-effects models for serial observations with binary response.Biometrics,1984,40(4):961-971
[71]Bonney GE.Logistic regression for dependent binary observations.Biomerics,1987,43:951-973
[72]Ware JH,Lipsitz SR,Speized FE.lssues in the anlalysis of repeated categorical outcomes.Statistics in Medicine,1988,7:95-107
[73]Lu JC,Chen D,Zhou WX.Quasi-likelihood estimation for GLM with random scales.Journal of Statistical Planning and Inference,2006,136(2):401-429
[74]Lipsitz SR,Kim K,Zhao L.Analysis of repeated categorical data using generalized estimating equations Statistics in Medicine,1994,13(11):1149-1163
[75]Bishop J,Venables WN,Wang YG.Analysing commercial catch and effort data from a Penaeid trawl fishery:A comparison of linear models,mixed models,and generalised estimating equations approaches.Fisheries Research,2004,70(2-3):179-193
[76]Pendergast JF,Gange SJ,Newton MA,et al.A Survey of Methods for Analyzing Clustered Binary Response Data.International Statistical Review,1996,64(1):89-118
[77]Carr GJ,Chi EM.Analysis of variance for repeated measures Data:a generalized estimating equations approach.Statistics in Medicine, 1992,11(8): 1033-1140
[78] Balan RM,I.Schiopu-Kratina. Asymptotic results with generalized estimating equations for longitudinal data.Ann. Statist,2005,33(2):522-541
[79] Ballinger GA.Using Generalized Estimating Equations for Longitudinal Data Analysis.Organizational Research Methods,2004,7(2):127-150
[80] Dahmen G,Ziegler A.Generalized Estimating Equations in Controlled Clinical Trials: Hypotheses Testing.
[81] Jokinen J.Fast estimation algorithm for likelihood-based analysis of repeated categorical responses.Computational Statistics & Data Analysis.2006,51(3): 1509-1522
[82] McCullagh P,Nelder JA. Generalized Linear Models. London: Chapman and Hall, 1989
[83] Royall RM.model robust confidence intervals using maximum likelihoo estimators.International Statistical Review, 1986,54:221 -226
[84] Pan W,Wall MM.Small-sample adjustments in using the sandwich variance estimator in generalized estimating equations Statistics in Medicine,2002,21(10): 1429-1441
[85] Zou G,Donner A.Confidence interval estimation of the intraclass correlation coefficient for binary outcome data.Biometrics,2004,60(3):807-811
[86] Zhao LP,Prentice RL.Correlated binary regression using a generalized quadratic model.Biometrika, 1990,77:642-648
[87] Prentice RL,Zhao LP.Estimation equations for parameters in means and covariance of multivariate discrete and continous responses.Biomerics,1991,47:825-839
[88] Liang KY, Zeger SL,Quaqish B.Multivariate regression analysis for categorical data.Journal of the Royal Statistical Society,Series B,1992,54:3-40
[89] Carey VC, Zeger SL,Diggle P.Modelling multivariate binary data with alternating logistic regressions.Biomerika, 1993,80:517-526
[90] Gregori D.Some Notes on Evaluating the Prediction Error for the Generalized Estimating Equations.
[91] Park T.A comparison of the generalized estimating equation approach with the maximum likelihood approach for repeated measurements.Stat Med, 1993,12(18): 1723-1732
[92] Pan W.Akaike's information criterion in generalized estimating equations.Biometrics,2001,57(1):120-125
[93] Hardin JW,Hilbe JM. Generalized estimating equations. Boca Raton, FL: Chapman and Hall/CRC Press, 2003
[94] Lin DY, Wei LJ,Ying Z.Checking the Cox Model with Cumulative Sums of Martingale-Based Residuals.Biometrika, 1993,80:557-572
[95] Lin D, Wei L,Ying Z.Model-Checking Techniques Based on Cumulative Residuals.Biometrics,2002,58:1-12
[96] Contreras M,Ryan LM.Fitting nonlinear and constrained generalized estimating equations with optimization software.Biometrics,2000,56(4): 1268-1271
[97] Williamson JM, Lipsitz SR,Kim KM.GEECAT and GEEGOR: computer programs for the analysis of correlated categorical response data.Comput Methods Programs Biomed,1999,58(1):25-34
[98] Miller ME, Davis CS,Landis JR.The analysis of longitudinal polytomous data: generalized estimating equations and connections with weighted least squares.Biometrics, 1993,49(4): 1033-1044
[99] Lipsitz SR, Kim K,Zhao L.Aanalysis of repeated sategorical data using generalized estimating equations.Stat Med, 1994b, 13:1149-1163
[100] Brown H,Prescott R. Applied Mixed Models in Medicine. London: John Wiley and Sons, 1999
[101] Kleinman K, Lazarus R,PIatt R.A generalized linear mixed models approach for detecting incident clusters of disease in small areas, with an application to biological terrorism.Am J Epidemiol,2004,159(3):217-224
[102] Lin X,Breslow NE.Bias correction in generalized linear mixed models with multiple components of dispersion.Journai of Amrican Statistical Assosiation,1996,91:1007-1016
[103] Vonesh EF, Wang H, Nie L, et al.Conditional second-order generalized estimating equations for generalized linear and nonlinear mixed-effects models.Journal of the American Statistical Association,2002,96:282-291
[104] Zeger SL,Karim MR.Generalized linear models with random effects-a Gibbs sampling approach Journal of the American Statistical Association, 1991,86:79-86
[105] Steele BM.A modified EM algorithm for estimation in generalized mixed models.Biometrics, 1996,52(4): 1295-1310
[106] McCulloch CE.Maximum Likelihood Variance Components Estimation for Binary Data Journal of the American Statistical Association, 1994,89:330-335
[107] McCulloch CE.Maximum likelihood algorithms for generalized linear mixed models. J. Amer. Statist. Assoc., 1997,92:162-170
[108] Kuk AYC.Laplace importance sampling for generalized linear mixed models.Journal of Statistical Computation and Simulation, 1999,63:143-158
[109] Hobert JP.Hierarchical models: A current computational perspective.Journal of the American Statistical Association,2000,95:1312-1316
[110] Tanner M. Tools for statistical inference. New York: Springer, 1993
[111] Booth JG,Hobert JP.Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm. Journal of the Royal Statistical Society, Series B, 1999,61:265-285
[112] Zhu HT,Lee SY.Analysis of generalized linear mixed models via a stochastic approximation algorithm with Markov chain Monte-Carlo method Statistics and Computing,2002,12(2): 175-183
[113] Geman S,Geman D.Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images.IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984,6:721-741
[114] Metropolis N, Rosenbluth A, W., Rosenbluth MN, et al.Equations of state calculations by fast computing machines.Journal of Chemical Physics, 1953,21 (1087-1092)
[115] Hostings WK.Monte Carlo sampling methods using Markov chains and their applications.Biometrika, 1970,57(97-109)
[116] Gelman A,Meng XL.Simulating normalizing constant:from importance sampling to bridge sampling to path sampling.Statistical Science, 1998,13:163-185
[117] Meng XL,Wong WH.Simulating ratios of normalizing constants via a simple identity:a theoretical exploration.Statistica Sinica, 1996,6(821 -860)
[118] Song XY,Lee SY.Model comparison of generalized linear mixed models.Stat Med,2006,25(10): 1685-1698
[119] Cai B,Dunson DB.Bayesian covariance selection in generalized linear mixed models.Biometrics,2006,62(2):446-457
[120] Burton P, Gurrin L,Sly P.Extending the simple linear regression model to account for correlated responses: an introduction to generalized estimating equations and multi-level mixed modelling.Stat Med, 1998,17(11): 1261 -1291
[121] Agresti A, Booth JG, Hobert JP, et al.Random-Effects Modeling of Categorical Response Data.Sociological Methodology,2000,30(2000):27-80
[122] Barr SC,O'Neill TJ.The analysis of group truncated binary data with random effects: injury severity in motor vehicle accidents.Biometrics,2000,56(2):443-450
[123]Chen Z,Dunson DB.Random effects selection in linear mixed models.Biometrics.,2003,59(4):762-769
[124]Gerhard Tutz,Kauermann G.Generalized linear random effects models with varying coefficients.Computational Statistics & Data Analysis,2003,43(1):13-28
[125]Heagerty PJ.Marginally specified logistic-normal models for longitudinal binary data.Biometrics,1999,55(3):688-698
[126]Follmann DA,Hunsberger SA,Albert PS.Repeated probit regression when covariates are measured with error.Biometrics,1999,55(2):403-409
[127]McCullagh P.Regression models for ordinal data.Journal Royal Statistical Society B,1980,42:109-142
[128]J.Lammertyn,B.De Ketelaere,D.Marquenie,et al.Mixed models for muiticategoricai repeated response:modelling the time effect of physical treatments on strawberry sepal quality.Postharvest Biology and Teehnology,2003,30(2):195-207
[129]Jacqmin-Gadda H,Joly P,Commenges D,et al.Penalized likelihood approach to estimate a smooth mean curve on longitudinal data.Stat Med,2002,21(16):2391-2402
[130]Breslow NE,Lin X.Bias correction in generalised linear mixed models with a single component of dispersion.Biometrika,1995,82:81-91
[131]Kizilkaya K,Tempelman RJ.A general approach to mixed effects modeling of residual variances in generalized linear mixed models.Genet Sel Evol,2005,37(1):31-56
[132]梁文权.生物药剂学与药物动力学.北京:人民卫生出版社,2004,164-168
[133]孙瑞元,郑青山.数学药理学新论.北京:人卫社出版,2004
[134]Bates DM,Watts DG.Nonlinear regression analysis and its applications(韦博成,万方焕,朱宏图).北京:中国统计出版社,1997
[135]姚莉,张世强.提高非线性函数近似回归模型预测精度的探讨.中国卫生统计,1999,16(5):313-314
[136]赵修忠.常用非线性模型参数估计新方法及应用.数理医药学杂志,2000,13(3):215-216
[137]Davidian M,M.Giltinan D.Nonlinear Models for Repeated Measurement Data:An Overview and Update.Journal of Agricultural,Biological & Environmente Statistics,2003,8(4):387-419
[138]Jonsson EN,Karlsson.MO.Nonlinearity Detection:Advantages of Nonlinear Mixed-Effects Modeling.AAPS PharmSci,2000,2(3):1-10
[139]Oberg A,Davidian M.Estimating data transformations in nonlinear mixed effects models.Biometrics,2000,56(1):65-72
[140]Palmer MJ,Phillips BJ,Smith GT.Application of nonlinear models weth random coefficients to growth data Biometries,1991,47:623-635
[141]Lipsitz SR,Fitzmaurice GM.Estimating equations for measures of association between repeated binary responses.Biometrics,1996,52:903-912
[142]Manor O,Kark JD.A comparative study of four methods foe analyzing repeated measures data.Statistics in Medicine,1996,15(11):1143-1160
[143]Zeger SL,Liang KY.An overview of methods for the analysis of longitudinal data.Statistics in Medicine,1992,11:1825-1839
[144]Pinheiro JC,Bates DM.Approximations to the Log-Likelihood Function in the Nonlinear Mixed-Effects Model.Journal of Computational and Graphics Statistics,1995,4:12-35
[145]Vonesh EF.Non-linear models for the analysis of longitudinal data.Stat Med,1992,11(14-15):1929-1954
[146]Holliday T,Lawrance AJ,Davis TP.Engine-Mapping Experiments:A Two-Stage Regression Approach.Technometrics, 1998,40:120-126
[147] Stukel TA,Demidenko E.Two-stage method of estimation for general linear growth curve models.Biometrics, 1997,53(2):720-728
[148] Vonesh EF,Carter RL.Mixed-effects nonlinear regression for unbalanced repeated measures.Biometrics, 1992,48( 1): 1 -17
[149] Bryk A,Raudenbush S. Hierarchical Linear Models. Newbury Park.: Sage Publications, 1992
[150] Yeap BY,Davidian M.Robust two-stage estimation in hierarchical nonlinear models.Biometrics,2001,57(1):266-272
[151] Bates DM,Pinheiro JC.Computing REML or ML Estimates for Linear or Nonlinear Mixed-Effects Models. 1999
[152] Wolfinger R.Laplace's approximation for nonlinear mixed models.Biometrika,1993,80(791-795)
[153] Fattinger KE, Sheiner LB,Verotta DA.New method to explore the distribution of interindividual random effects in non-linear mixed effects models.Biometrics, 1995,51(4): 1236-1251
[154] Sheiner LB,Beal SL.Evaluation of method for estimating population pharmacokinetic parameters, I. Michaelis-Menten model: routine clinical pharmacokienetic data.Joumal of Pharmacokienetics and Biopharmaceutics, 1980,8:553-571
[155] Ko H,Davidian M.Correcting for measurement error in individual-level covariates in nonlinear mixed effects models.Biometrics,2000,56(2):368-375
[156] Yong DA, Zerbe G, Boyle DW, et al.On nonlinear random effects models for repeaed measurements.Communication in Statistics B, 1991,20:463-478
[157] Sheiner LB,Ludden TM.Population pharmacokinetics/pharmacodynamics.Annual review of pharmacolotical toxicology, 1992,32( 185-209)
[158] Dipak KD, Chen MH,Chang H.Bayesian Approach for Nonlinear Random Effects Models.Biometrics,1997,53:1239-1252
[159] 刘昌孝,孙瑞元. 药物评价实验设计与统计学基础. 北京: 军事医学科学出版社,2001
[160] Sadray S, Jonsson EN,Karlsson MO.Likelihood-based diagnostics for influential individuals in non-linear mixed effects model selection.Pharm Res, 1999,16(8): 1260-1265
[161] Lu JZ, Wen H,Xu YH.Determination of 5-Fu concentration in hepatic cancer patient serum by HPLC.Chin Hosp Pharm J,2004,24(2):83-84
[162] Luo TE,Liu GF.Application of Nonlinear Mixed Effects Model for Repeated Measurement Data and Implement.Chinese Journal of Health Statistics,2006,23(2): 104-107
[163] Johnston G,So YAnalysis of Data from Recurrent Events.Proceeding of the 27th Annual SAS USERS Group International Conference(SUGI 27)273-28
[164] Aalen OO.Heterogeneity in Survival Analysis.Statistics in Medicine, 1988,7:1121-1137
[165] Aalen OO.Modelling Heterogeneity in Survival Analysis by the Compound Poisson Distribution. Annals of Applied Probability, 1992,4(2):951-972
[166] Nelson WB.Recurrent Events Analysis for Product Repairs, Disease Recurrences, and Other Applications.The ASA-SIAM Series on Statistics and Applied Probability,2003
[167] Aalen OO,Tretli S.Analysing incidence of testis cancer by means of a frailty model.Cancer Causes and Control, 1999,10:285-292
[168] Cox DR.Regression Models and Life-Tables. Journal of the Royal Statistical Society B 1972,34:187-220
[169] Michiels S, Baujat B, Mane C, et al.Random effects survival models gave a better understanding of heterogeneity in individual patient data meta-analyses.J Clin Epidemiol,2005,58(3):238-245
[170] M.A.Wintrebert C, A.H.Zwinderman, Cam E, et al.Joint modelling of breeding and survival in the kittiwake using frailty models.EcoIogical Modelling,2005,181(2-3):203-213
[171] Gupta RC,Kirmani SNUA.Stochastic comparisons in frailty models.Journal of Statistical Planning and Inference,2006,136(10):3647-3658
[172] Greenwood M,Yule GU.An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents.Journal of the Royal Statistical Society, 1920,83:255-279
[173] Vaupel JW, Manton KG,Stallard E.The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality.Demography, 1979,16:439-454
[174] Clayton DG.A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence.Biometrika,1978,65:141-151
[175] Hien TVV.Estimation in semiparametric conditional shared frailty models with events before study entry.Computational Statistics & Data Analysis,2004,45(3):621-637
[176] Zhang Jj,Peng Yw.An alternative estimation method for the accelerated failure time frailty model.Computational Statistics & Data Analysis,2006
[177] Therneau T,Grambsch P. Modeling Survival Data: Extending the Cox Model. New York: Springer-Verlag, 2000
[178] Wienke A, Arbeev KG, Locatelli I, et al.A comparison of different bivariate correlated frailty models and estimation strategies.Mathematical Biosciences,2005,198(1):1-13
[179] Lim HJ, Liu J,Melzer-Lange M.Comparison of Methods for Analyzing Recurrent Events Data: Application to the Emergency Department Visits of Pediatric Firearm Victims.Accident Analysis & Prevention,2007,39(2):290-299
[180] Sastry N.A Nested Frailty Model for Survival Data, With an Application to the Study of Child Survival in Northeast Brazil.Journal of the American Statistical Association,1997,92(438):426-435
[181] Cortinas AJ,Burzykowski T.Aversion of theEMalgorithm for proportional hazards model with random effects.Biometrical J,2005,47:847-862
[182] Maples JJ, Murphy SA,Axinn WG.Two-level proportional hazards models.Biometrics,2002,58:754-763
[183] Klein JP.Semiparametric estimation of random effects using the Cox model based on the EM algorithm.Biometrica,1992,48:795-806
[184] Nielsen GG, Gill RD, Andersen P, et al.A counting process approach to maximum likelihood estimation of frailty models.Scandznatian J of Stotistrcs, 1992,19:25-43
[185] Hastie TJ,Tibshirani RJ.Varying-coefficient models (with discussion). JRSSB 1993,55:757-796
[186] Parner E.Asymptotic theory for the correlated Gamma-frailty model.Ann. Statist, 1998,26:183-214
[187] Rondeau V, Commenges D,Joly P.Maximum Penalized Likelihood Estimation in a Gamma-Frailty Model.Lifetime Data AnaIysis,2003,9(2): 139-153
[188] Yu B.Estimation of shared Gamma frailty models by a modified EM algorithm Computational Statistics & Data Analysis,2006,50(2):463-474
[189] Vu HTV,Knuiman MW.A hybrid ML-EM algorithm for calculation of maximum likelihood estimates in semiparametric shared frailty models.Computational Statistics & Data Analysis,2002,40(1):173-187
[190] Nielsen JD,Dean CB.Regression splines in the quasi-likelihood analysis of recurrent event data.Journal of Statistical Planning and Inference,2005,134(2):521-535
[191] Schoenfeld D.Partial residuals for the proportional hazards regression model.Biometrika,1982,69:239-241
[192] Fleming TR,Harrington DP. Counting Processes and Survival Analysis. New York: Wiley, 1991
[193] Lindstrom ML,Bates DM.Nonlinear mixed effects models for repeated measures data.Biometrics,1990,46(3):673-687
[194] Akaike H.a new look at th estatistical model identification.IEEE Transaction on Automatic Control,1974,AC-19:716-723
[195] Cox DR.Partial Likelihood.Biometrika,1975,66:188-190
[196] Cook,Weisberg. An Introduction to Regression Graphics. New York: Wiley, 1994
[1]Grizzle JE, Starmer CF,Koch GG.Analysis of categorical data by linear models.Biometrics,1969,25(3):489-504
[2]Koch GG,Reinfurt DW.The analysis of categorical data from mixed models.Biometrics, 1971,27:157-173
[3] Koch GG, Landis JR, Freeman JL, et al.A general methodology for the analysis of experiments with repeated measurment of categorical data.Biometrics, 1977,33:133-158
[4] Landis JR,Miller ME.Some general methods for the analysis of categorical data in longitudinal studies.Statistics in Medicine, 1988,7:109-137
[5] Crowder MJ,Hand DJ. Analysis of Repeated Measures. London: Chapman and Hall, 1990
[6]Liang KY,Zeger SL.Longitudinal data analysis using generalized linear models.Biometrics, 1986,73:13-22
[7]Zeger SL,Liang KY.Longitudinal data analysis for discrete and continuous outcomes.Biometrics, 1986,42(1): 121 -130
[8]Stiratelli R, Laird N,Ware JH.Random-effects models for serial observations with binary response.Biometrics, 1984,40(4):961 -971
[9] Anderson DA,Aitkin M.Variance component models with binary response: Inteviewer variability.J. Roy.Statist. Soc. Ser. B, 1985,47:203-210
[10] Gilmour AR, Anderson RD,Rae AL. The analysis of binomial data by a generalized linear mixed model.Biometrika, 1985,72:593-599
[11] Schall R.Estimation in generalized linear models with random effects.Biometrika, 1991,78:719-727
[12] Breslow NE,Clayton DG.Approximate inference in generalized linear mixed models.Journal of the American Statistical Association,1993,88(421):9-25
[13] Wolfinger R,O'Connell M.Generalized linear mixed models: A pseudo-likelihood approach.Journal of Statistical Computation and Simulation, 1993,48:233-243
[14] McCulloch CE,Searle SR. Generalized, Linear, and Mixed Models. New York: John Wiley & Sons, 2000
[15] Zeger SL, Liang KY,Albert PS.Models for longitudinal data: a generalized estimating equation approach.Biometrics, 1988,44(4): 1049-1060
[16] Davidian M,Giltinan DM. Nonlinear Models for Repeated Measurement Data. London: Chanpman and Hall, 1995
[17] Vonesh EF,Chinchilli VM. Linear and Nonlinear Models for the Analysis of Repeated Measurements. New York: Marcel Dekker, 1997
[18] McCullagh P.Regression models for ordinal data. Journal Royal Statistical Society B,1980,42:109-142
[19] Goodman LA.Simple models for the analysis of association in cross-classifications having ordered categories.Journal of the American Statistical Association, 1979,74:537-552
[20] Hedeker D,Gibbons RD.MIXOR: a computer program for mixed-effects ordinal regression analysis.Comput Methods Programs Biomed, 1996,49(2):157-176
[21] Williams OD,Grizzle JE.Analysis of tables having ordered response categoriesJournal of the American Statistical Association, 1972,67:53-64
[22] Simon G.Alternative analysis for singly ordered contingency tables.Journal of the American Statistical Association, 1974,69:971-976
[23] Gibbons RD,Bock RD.Trends in correlated proportions.Psychometrika, 1987(52)
[24] Peterson B,Harrell FE.Partial Proportional Odds Models for Ordinal Response Variables.Applied Statistics,1990,39(2):205-217
[25]Terza JV.Ordinal probit:a generalization.Communications in Statistical Theory and Methods, 1985,14(1-11)
[26] Hedeker D.A mixed-effects multinomial logistic regression model.Stat Med,2003,22:1433-1446
[27] Goldstein H. Multilevel Statistical Models.2nd edn. New York: Halstead Press, 1995
[28] Sheiner LB, Rosenberg B,Marathe W.Estimation of population characteristics of pharmacokinetic parameters from routine clinical data.J Pharmacokinet Biopharm,1977,5(5):445-479
[29] Beal SL.Population pharmacokinetic data and parameter estimation based on their first two statistical moments.Drug Metabolism Reviews,1984,15:173-193
[30] Sheiner LB.The population approach to pharmacokinetic data analysis: rationale and standard data analysis methods.Drug Metabolism Reviews, 1984,15:153-171
[31]Lindstrom MJ,Bates DM.Nonlinear mixed effects models for repeated measures data.Biometrics, 1990,46(3):673-687
[32]Vonesh EF,Carter RL.Mixed-effects nonlinear regression for unbalanced repeated measures.Biometrics, 1992,48:1 -17
[33] Davidian M,Giltinan DM. Nonlinear Models for Measurement Data. London: Chapman & Hall, 1995
[34] Pinheiro JC,Bates DM Model Building for Nonlinear Mixed-Effects Models. Technical Report 91 In: Department of Biostatistics, University of Wisconsin- Madison, 1995.
[35] Ke C,Wang Y.Semiparametric nonlinear mixed models and their applications.Journal of the American statistical asociation,2001,96:1272-1298
[36] Vonesh EF, Chinchilli VM,Pu KW.Goodness-Of-Fit in Generalized Nonlinear Mixed-Effects Models.Biometrics,1996,52:572-587
[37] Vonesh EG, Wang H, Nie L, et al.Conditional Second-Order Generalized Estimating Equations for Generalized Linear and Nonlinear Mixed-Effects Models.Journal of the American Statistical Association,2002,97:271 -283
[38]Vonesh EF,Schork MA.Sample Size in the multivariate analysis of repeated measurements.Biometrics, 1986,42:601-610
[39]Rochon J.Sample size calculation for two-group repeated-measures experiments Biometrics,1991,17:1383-1398
[40] Overall JE, Shobaki G,Anderson CB.Comparative Evaluation of Two Models for Estimating Sample Sizes for Tests on Trends across Repeated Measurements.Statistics in Medicine,1998,17:1643-1658
[41] Nelson WB. Recurrent Events Data Analysis for Product Repairs,Disease Recurrences, and Other Applications: The ASA-SIAM Series on Statistics and Applied Probability, 2003
[42] Prentice RL, Williams BJ,Peterson AV.On the regression analysis of multivariate failure time data.Biometrika,1981,68:373-379
[43] Andersen PK,Gill RD.Cox's regression model for counting processes: a large sample study.Annals of Statistics, 1982,10:1100-1120
[44] Wei LJ, Lin DY,Weissfeld L.Regression analysis of multivariate incomplete failure time data by modeling marginal distributions.Journal of the American Statistical Association, 1989,84:1065-1073
[45] Lee EW, Wei LJ,Amato DA.COX-type regression analysis for large number of small groups of correlated failure time observations Kulwer Academic Publishers,Dordrecht, 1992:237-247
[46] Greenwood M,Yule GU.An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents.Journal of the Royal Statistical Society, 1920,83:255-279
[47] Vaupel JW, Manton KG,Stallard E.The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality.Demography, 1979,16:439-454
[48] Clayton DGA model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence.Biometrika, 1978,65:141-151
[49] Hougaard P. Analysis of Multivariate Survival Data. New York Springer-Verlag, 2000
[50] Hougaard P.A class of multivariate failure time distributions.Biometrika,1986b,73:671-678
[51]Hougaard P.Survival models for heterogeneous populations derived from stable distributions.Biometrika, 1986a,73:671 -678
[52] Yashin AI, Vaupel JW,Iachine IA.Correlated individual frailty:an advantageous approach to survival analysis of bivariate data.Mathematical Population Studies, 1995,5:145-159
[53] Akaike H.a new look at th estatistical model identification.lEEE Transaction on Automatic Control, 1974,AC-19:716-723
[54] Schwarz G. Estimating the Dimension of a model.Annal of Statistics, 1978,6(2):461 - 464
[55] McCullagh P,Nelder JA. Generalized Linear Models. London: Chapman and Hall, 1989
[56] Cox DR.Partial Likelihood.Biometrika,1975,66:188-190
[57]Pan W.Akaike's information criterion in generalized estimating equations.Biometrics,2001,57(1): 120-125
[58] Pan W.Model selection in estimating equations.Biometrics,2001,57(2):529-534
[59] Lin X,Breslow NE.Bias correction in generalized linear mixed models with multiple components of dispersion.Journal of Amrican Statistical Assosiation, 1996,91:1007-1016
[60] Vonesh EF, Wang H, Nie L, et al.Conditional second-order generalized estimating equations for generalized linear and nonlinear mixed-effects models.Journai of the American Statistical Association,2002,96:282-291
[61] Zeger SL,Karim MR.Generalized linear models with random effects-a Gibbs sampling approach Journal of the American Statistical Association, 1991,86:79-86
[62]Steele BM.A modified EM algorithm for estimation in generalized mixed models.Biometrics, 1996,52(4): 1295-1310
[63] McCulloch CE.Maximum Likelihood Variance Components Estimation for Binary Data Journal of the American Statistical Association, 1994,89:330-335
[64] McCulloch CE.Maximum likelihood algorithms for generalized linear mixed models. J. Amer. Statist. Assoc.,1997,92:162-170
[65] Kuk AYC.Laplace importance sampling for generalized linear mixed models.Journai of Statistical Computation and Simulation, 1999,63:143-158
[66] Hobert JP.Hierarchical models: A current computational perspective.Journal of the American Statistical Association,2000,95:1312-1316
[67] Tanner M. Tools for statistical inference. New York: Springer, 1993
[68] Booth JG,Hobert JP.Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm.Journal of the Royal Statistical Society, Series B, 1999,61:265-285
[69] Zhu HT,Lee SY.Analysis of generalized linear mixed models via a stochastic approximation algorithm with Markov chain Monte-Carlo method Statistics and Computing,2002,12(2): 175-183
[70] Geman S,Geman D.Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images.IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984,6:721-741
[71] Metropolis N, Rosenbluth A, W., Rosenbluth MN, et al.Equations of state calculations by fast computing machines.Journal of Chemical Physics, 1953,21 (1087-1092)
[72]Hostings WK.Monte Carlo sampling methods using Markov chains and their applications.Biometrika, 1970,57(97-109)
[73] Gelman A,Meng XL.SimuIating normalizing constant:from importance sampling to bridge sampling to path sampling.Statistical Science, 1998,13:163-185
[74] Meng XL,Wong WH.Simulating ratios of normalizing constants via a simple identity:a theoretical exploration.Statistica Sinica,1996,6(821-860)
[75]Song XY,Lee SY.Model comparison of generalized linear mixed models.Stat Med,2006,25(10):1685-1698
[76]Cai B,Dunson DB.Bayesian covariance selection in generalized linear mixed models.Biometrics,2006,62(2):446-457
[77] Cook,Weisberg. An Introduction to Regression Graphics. New York: Wiley, 1994
[78] Lin DY, Wei LJ,Ying Z.Checking the Cox Model with Cumulative Sums of Martingale-Based Residuals.Biometrika, 1993,80:557-572
[79]Lin D, Wei L,Ying Z.Model-Checking Techniques Based on Cumulative Residuals.Biometrics,2002,58:1 -12
[80] Su JQ,Wei LJ.A lack-of-fit test for the mean function in a genralized linear model.Joumal of the American Statistical Association, 1991,86:420-426
[81]Pan Z,Lin DY.Goodness-of-fit methods for generalized linear mixed models.Biometrics,2005,61 (4): 1000-1009
[2] Huynh H,Feldt LS.Conditions under which mean square ratios in repeated measur ements design have exact F-distributions.J Amer Stat Ass,1970,65:1582-1589
[3] Danford MB, Hughes HM,McNee RC.On the analysis of repeated-measurements experiments.Biometrics, 1960,16:547-565
[4] Cole JW,Grizzle JE.Application of multivariate analysis of variance to repeated measures experiments.Biometrics, 1966,22:810-828
[5] Thomas DR. Univariate repeated measures techniques applied to multivariate data.Psychometrika, 1983,48:451 -464
[6] Boik RJ.The mixed model for multivariate repeated measures: validity conditions and an approximate test.Psychometrika, 1988,53:469-486
[7] Laird NM,Ware H.Random-effects models for longitudinal data.Biometrics,1982,38(4):963-974
[8] Grizzle JE, Starmer CF,Koch GGAnalysis of categorical data by linear models.Biometrics, 1969,25:489-504
[9] Koch GG,Reinfurt DW.The analysis of categorical data from mixed models.Biometrics, 1971,27:157-173
[10] Koch GG, Landis JR, Freeman JL, et al.A General Methodology for the Analysis of Experiments with Repeated Measurement of Categorical Data.Biometrics, 1977,33:133-158
[11] Landis JR, Miller ME, Davis CS, et al.Some general methods for the analysis of categorical data in longitudinal studies.Stat Med, 1988,7(1-2): 109-137
[12] Crowder MJ,Hand DJ. Analysis of Repeated Measures. London: Chapman and Hall, 1990
[13] Liang KY,Zeger SL.Longitudinal data analysis using generalized linear models.Biometrics, 1986,73:13-22
[14] Zeger SL,Liang KY.Longitudinal data analysis for discrete and continuous outcomes.Biometrics, 1986,42(1): 121 -130
[15] Stiratelli R, Laird N,Ware JH.Random-effects models for serial observations with binary response.Biometrics, 1984,40(4):961 -971
[16] Anderson DA,Aitkin M.Variance component models with binary response: Inteviewer variability.J. Roy.Statist. Soc. Ser. B,1985,47:203-210
[17] Gilmour AR, Anderson RD,Rae AL. The analysis of binomial data by a generalized linear mixed model.Biometrika, 1985,72:593-599
[18] Schall R.Estimation in generalized linear models with random effects.Biometrika, 1991,78:719-727
[19] Breslow NE,CIayton DG.Approximate inference in generalized linear mixed models.Journal of the American Statistical Association,1993,88(421):9-25
[20] Wolfinger R,O'Connell M.Generalized linear mixed models: A pseudo-likelihood approach.Journal of Statistical Computation and Simulation,1993,48:233-243
[21] McCulloch CE,Searle SR. Generalized, Linear, and Mixed Models. New York: JohnWiley & Sons, 2000
[22] Zeger SL,Liang KY.An overview of methods for the analysis of longitudinal data.Stat Med, 1992,11 (14-15): 1825-1839
[23] Sheiner LB, Rosenberg B,Marathe VV.Estimation of population characteristics of pharmacokinetic parameters from routine clinical data.J Pharmacokinet Biopharm,1977,5(5):445-479
[24] Beal SL.Population pharmacokinetic data and parameter estimation based on their first two statistical moments.Drug Metabolism Reviews, 1984,15:173-193
[25]Sheiner LB.The population approach to pharmacokinetic data analysis:rationale and standard data analysis methods.Drug Metabolism Reviews,1984,15:153-171
[26]Zeger SL,Liang KY,Albert PS.Models for longitudinal data:a generalized estimating equation approach.Biometrics,1988,44(4):1049-1060
[27]Lindstrom MJ,Bates DM.Nonlinear mixed effects models for repeated measures data.Biometrics,1990,46(3):673-687
[28]Vonesh EF,Carter RL.Mixed-effeets nonlinear regression for unbalanced repeated measures.Biometrics,1992,48:1-17
[29]Davidian M,Giltinan DM.Nonlinear Models for Measurement Data.London:Chapman & Hall,1995
[30]Pinheiro JC,Bates DM Model Building for Nonlinear Mixed-Effects Models.Technical Report 91In:Department of Biostatistics,University of Wisconsin - Madison,1995.
[31]Vonesh EF,Chinchilli VM.Linear and Nonlinear Models for the Analysis of Repeated Measurements.New York:Marcel Dekker,1997
[32]Ke C,Wang Y.Semiparametric nonlinear mixed models and their applications.Journal of the American statistical asociation,2001,96:1272-1298
[33]Prentice RL,Williams BJ,Peterson AV.On the regression analysis of multivariate failure time data.Biometrika,1981,68:373-379
[34]Andersen PK,Gill RD.Cox's regression model for counting processes:a large sample study.Annals of Statistics,1982,10:1100-1120
[35]Wei LJ,Lin DY,Weissfeld L.Regression analysis of multivariate incomplete failure time data by modeling marginal distributions.Journal of the American Statistical Association,1989,84:1065-1073
[36]Clayton DG,Cuzick J.Multivariate generalizations of the proportional hazards model.Journal of the Royal Statistical Society,Series B,,1985,148:82-117
[37]Oakes DA.Frailty Models for Multiple Event Times.Netherlands:Kluwer Academic Publishers,1992.
[38]Hougaard P.Analysis of Multivariate Survival Data.New York Springer-Verlag,2000
[39]Lawless JF,Nadeau C.Some Simple Robust Methods for the Analysis of Recurrent Events.Technometrics,1995,37:158-168
[40]Lin DY,Wei LJ,Yang I,et al.Semiparametric Regression for the Mean and Rate Functions of Recurrent Events.J.R.Statist.Soc.B,2000,62:711-730
[41]Nelson WB.Recurrent Events Data Analysis for Product Repairs,Disease Recurrences,and Other Applications:The ASA-SIAM Series on Statistics and Applied Probability,2003
[42]陈长生,徐勇勇,曹秀堂.医学研究中重复观测数据的统计分析方法.中国卫生统计,1996,13(6):55-58
[43]陈长生,徐勇勇,曹秀堂.不等距重复观测数据组间比较的正交回归模型.中国卫生统计,1996,13(3):1-5
[44]陈峰,任仕泉,陆守曾.非独立计量数据的内部相关性研究.现代预防医学,1998,25(3):269-271
[45]任仕泉,陈峰,等.非独立数据及其协方差结构表达.中国卫生统计,1998,15(4):4-8
[46]任仕泉.非独立数据统计分析方法及其医学应用:[博士学位论文].成都:华西医科大学,1999
[47]李贤.重复测量数值型变量统计分析与设计:[硕士学位论文].山西:山西医科大学,1999
[48]李贤,刘桂芬,何大卫,等.重复测量设计样本含量估计.中国卫生统计,2001,18(4):204-206
[49]李贤,刘桂芬,何大卫.多因素重复测量设计裂区方差分析.中国卫生统计,2001,18(1):22-23
[50]赵晋芳.重复测量线性混合效应模型在医学研究中的应用:[硕士学位论文].山西:山西医科大学,2002
[51]陈启光.纵向研究中重复测量资料的广义估计方程分析.中国卫生统计,1995,12(1):22-25
[52]熊林平,郭祖超.重复测量分类数据的分析.中国卫生统计,1997,14(1):1-3
[53]熊林平,曹秀堂,侩勇勇,等.纵向观测计数数据的对数线性模型.中国卫生统计,1999,16(2):68-71
[54]李康,赵景波.重复有序观测数据分析探讨.中国卫生统计,1994,11(2):9-12
[55]郑建中,张岩波.有序分类重复测量数据的多水平模型分析.现代预防医学,2003,30(1):6-8
[56]方积乾,陆盈.现代医学统计学.北京:人民卫生出版社,2002,295-302
[57]余松林,向惠云.重复测量资料分析方法与SAS程序.北京:科学出版社,2003
[58]Jennrich RI,Schluchter MD.Unbalanced repeated-measures models with structured covariance matrices.Biometrics,1986,42(4):805-820
[59]Jones RH.Serial correlation or random subject effects.Communications in Statistics,1990,19(10):1105-1123
[60]Vonesh EF,Chinchilli VM,Pu K.Goodness-of-fit in generalized nonlinear mixed-effects models.Biometrics,1996,52(2):572-587
[61]Daniels MJ,Zhao YD.Modelling the random effects covariance matrix in longitudinal data.Statistics in Medicine,2003,22:1631-1647
[62]Henderson CR.Selection index and expected genetic advance.in Statistical genetics and plant breeding,National Academy of Sciences National Research Council Publication NO.982,1963:141-163
[63]Harville DA.Extensions of the Gauss-Markov theorem to include the estimation of random effects.Annal of Statisticals,1976,4:384-395
[64]Davidian M,Giltinan DM.Some general estimation methods for nonlinear mixed-effects models.J Biopharm Stat,1993,3(1):23-55
[65]Akaike H.A new look at the statistical model identification.IEEE Trans.on Automatic Control,1974,19(6):716-723
[66]Schwarz G.Estimating the Dimension of a model.Annal of Statistics,1978,6(2):461-464
[67]Diggle PJ.An approach to the analysis of repeated measurements.Biometrics,1988,44(4):959-971
[68]Nelder JA,Wedderbum RWM.Generalized linear models.Journal of the Royal Statistical Society A,1972,135:370-384
[69]Sutradhar BC.An Overview on Regression Models for Discrete Longitudinal Responses.Statistical Science,2003,18(3):377-393
[70]Stiratelli R,Laird N,Ware JH.Random-effects models for serial observations with binary response.Biometrics,1984,40(4):961-971
[71]Bonney GE.Logistic regression for dependent binary observations.Biomerics,1987,43:951-973
[72]Ware JH,Lipsitz SR,Speized FE.lssues in the anlalysis of repeated categorical outcomes.Statistics in Medicine,1988,7:95-107
[73]Lu JC,Chen D,Zhou WX.Quasi-likelihood estimation for GLM with random scales.Journal of Statistical Planning and Inference,2006,136(2):401-429
[74]Lipsitz SR,Kim K,Zhao L.Analysis of repeated categorical data using generalized estimating equations Statistics in Medicine,1994,13(11):1149-1163
[75]Bishop J,Venables WN,Wang YG.Analysing commercial catch and effort data from a Penaeid trawl fishery:A comparison of linear models,mixed models,and generalised estimating equations approaches.Fisheries Research,2004,70(2-3):179-193
[76]Pendergast JF,Gange SJ,Newton MA,et al.A Survey of Methods for Analyzing Clustered Binary Response Data.International Statistical Review,1996,64(1):89-118
[77]Carr GJ,Chi EM.Analysis of variance for repeated measures Data:a generalized estimating equations approach.Statistics in Medicine, 1992,11(8): 1033-1140
[78] Balan RM,I.Schiopu-Kratina. Asymptotic results with generalized estimating equations for longitudinal data.Ann. Statist,2005,33(2):522-541
[79] Ballinger GA.Using Generalized Estimating Equations for Longitudinal Data Analysis.Organizational Research Methods,2004,7(2):127-150
[80] Dahmen G,Ziegler A.Generalized Estimating Equations in Controlled Clinical Trials: Hypotheses Testing.
[81] Jokinen J.Fast estimation algorithm for likelihood-based analysis of repeated categorical responses.Computational Statistics & Data Analysis.2006,51(3): 1509-1522
[82] McCullagh P,Nelder JA. Generalized Linear Models. London: Chapman and Hall, 1989
[83] Royall RM.model robust confidence intervals using maximum likelihoo estimators.International Statistical Review, 1986,54:221 -226
[84] Pan W,Wall MM.Small-sample adjustments in using the sandwich variance estimator in generalized estimating equations Statistics in Medicine,2002,21(10): 1429-1441
[85] Zou G,Donner A.Confidence interval estimation of the intraclass correlation coefficient for binary outcome data.Biometrics,2004,60(3):807-811
[86] Zhao LP,Prentice RL.Correlated binary regression using a generalized quadratic model.Biometrika, 1990,77:642-648
[87] Prentice RL,Zhao LP.Estimation equations for parameters in means and covariance of multivariate discrete and continous responses.Biomerics,1991,47:825-839
[88] Liang KY, Zeger SL,Quaqish B.Multivariate regression analysis for categorical data.Journal of the Royal Statistical Society,Series B,1992,54:3-40
[89] Carey VC, Zeger SL,Diggle P.Modelling multivariate binary data with alternating logistic regressions.Biomerika, 1993,80:517-526
[90] Gregori D.Some Notes on Evaluating the Prediction Error for the Generalized Estimating Equations.
[91] Park T.A comparison of the generalized estimating equation approach with the maximum likelihood approach for repeated measurements.Stat Med, 1993,12(18): 1723-1732
[92] Pan W.Akaike's information criterion in generalized estimating equations.Biometrics,2001,57(1):120-125
[93] Hardin JW,Hilbe JM. Generalized estimating equations. Boca Raton, FL: Chapman and Hall/CRC Press, 2003
[94] Lin DY, Wei LJ,Ying Z.Checking the Cox Model with Cumulative Sums of Martingale-Based Residuals.Biometrika, 1993,80:557-572
[95] Lin D, Wei L,Ying Z.Model-Checking Techniques Based on Cumulative Residuals.Biometrics,2002,58:1-12
[96] Contreras M,Ryan LM.Fitting nonlinear and constrained generalized estimating equations with optimization software.Biometrics,2000,56(4): 1268-1271
[97] Williamson JM, Lipsitz SR,Kim KM.GEECAT and GEEGOR: computer programs for the analysis of correlated categorical response data.Comput Methods Programs Biomed,1999,58(1):25-34
[98] Miller ME, Davis CS,Landis JR.The analysis of longitudinal polytomous data: generalized estimating equations and connections with weighted least squares.Biometrics, 1993,49(4): 1033-1044
[99] Lipsitz SR, Kim K,Zhao L.Aanalysis of repeated sategorical data using generalized estimating equations.Stat Med, 1994b, 13:1149-1163
[100] Brown H,Prescott R. Applied Mixed Models in Medicine. London: John Wiley and Sons, 1999
[101] Kleinman K, Lazarus R,PIatt R.A generalized linear mixed models approach for detecting incident clusters of disease in small areas, with an application to biological terrorism.Am J Epidemiol,2004,159(3):217-224
[102] Lin X,Breslow NE.Bias correction in generalized linear mixed models with multiple components of dispersion.Journai of Amrican Statistical Assosiation,1996,91:1007-1016
[103] Vonesh EF, Wang H, Nie L, et al.Conditional second-order generalized estimating equations for generalized linear and nonlinear mixed-effects models.Journal of the American Statistical Association,2002,96:282-291
[104] Zeger SL,Karim MR.Generalized linear models with random effects-a Gibbs sampling approach Journal of the American Statistical Association, 1991,86:79-86
[105] Steele BM.A modified EM algorithm for estimation in generalized mixed models.Biometrics, 1996,52(4): 1295-1310
[106] McCulloch CE.Maximum Likelihood Variance Components Estimation for Binary Data Journal of the American Statistical Association, 1994,89:330-335
[107] McCulloch CE.Maximum likelihood algorithms for generalized linear mixed models. J. Amer. Statist. Assoc., 1997,92:162-170
[108] Kuk AYC.Laplace importance sampling for generalized linear mixed models.Journal of Statistical Computation and Simulation, 1999,63:143-158
[109] Hobert JP.Hierarchical models: A current computational perspective.Journal of the American Statistical Association,2000,95:1312-1316
[110] Tanner M. Tools for statistical inference. New York: Springer, 1993
[111] Booth JG,Hobert JP.Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm. Journal of the Royal Statistical Society, Series B, 1999,61:265-285
[112] Zhu HT,Lee SY.Analysis of generalized linear mixed models via a stochastic approximation algorithm with Markov chain Monte-Carlo method Statistics and Computing,2002,12(2): 175-183
[113] Geman S,Geman D.Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images.IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984,6:721-741
[114] Metropolis N, Rosenbluth A, W., Rosenbluth MN, et al.Equations of state calculations by fast computing machines.Journal of Chemical Physics, 1953,21 (1087-1092)
[115] Hostings WK.Monte Carlo sampling methods using Markov chains and their applications.Biometrika, 1970,57(97-109)
[116] Gelman A,Meng XL.Simulating normalizing constant:from importance sampling to bridge sampling to path sampling.Statistical Science, 1998,13:163-185
[117] Meng XL,Wong WH.Simulating ratios of normalizing constants via a simple identity:a theoretical exploration.Statistica Sinica, 1996,6(821 -860)
[118] Song XY,Lee SY.Model comparison of generalized linear mixed models.Stat Med,2006,25(10): 1685-1698
[119] Cai B,Dunson DB.Bayesian covariance selection in generalized linear mixed models.Biometrics,2006,62(2):446-457
[120] Burton P, Gurrin L,Sly P.Extending the simple linear regression model to account for correlated responses: an introduction to generalized estimating equations and multi-level mixed modelling.Stat Med, 1998,17(11): 1261 -1291
[121] Agresti A, Booth JG, Hobert JP, et al.Random-Effects Modeling of Categorical Response Data.Sociological Methodology,2000,30(2000):27-80
[122] Barr SC,O'Neill TJ.The analysis of group truncated binary data with random effects: injury severity in motor vehicle accidents.Biometrics,2000,56(2):443-450
[123]Chen Z,Dunson DB.Random effects selection in linear mixed models.Biometrics.,2003,59(4):762-769
[124]Gerhard Tutz,Kauermann G.Generalized linear random effects models with varying coefficients.Computational Statistics & Data Analysis,2003,43(1):13-28
[125]Heagerty PJ.Marginally specified logistic-normal models for longitudinal binary data.Biometrics,1999,55(3):688-698
[126]Follmann DA,Hunsberger SA,Albert PS.Repeated probit regression when covariates are measured with error.Biometrics,1999,55(2):403-409
[127]McCullagh P.Regression models for ordinal data.Journal Royal Statistical Society B,1980,42:109-142
[128]J.Lammertyn,B.De Ketelaere,D.Marquenie,et al.Mixed models for muiticategoricai repeated response:modelling the time effect of physical treatments on strawberry sepal quality.Postharvest Biology and Teehnology,2003,30(2):195-207
[129]Jacqmin-Gadda H,Joly P,Commenges D,et al.Penalized likelihood approach to estimate a smooth mean curve on longitudinal data.Stat Med,2002,21(16):2391-2402
[130]Breslow NE,Lin X.Bias correction in generalised linear mixed models with a single component of dispersion.Biometrika,1995,82:81-91
[131]Kizilkaya K,Tempelman RJ.A general approach to mixed effects modeling of residual variances in generalized linear mixed models.Genet Sel Evol,2005,37(1):31-56
[132]梁文权.生物药剂学与药物动力学.北京:人民卫生出版社,2004,164-168
[133]孙瑞元,郑青山.数学药理学新论.北京:人卫社出版,2004
[134]Bates DM,Watts DG.Nonlinear regression analysis and its applications(韦博成,万方焕,朱宏图).北京:中国统计出版社,1997
[135]姚莉,张世强.提高非线性函数近似回归模型预测精度的探讨.中国卫生统计,1999,16(5):313-314
[136]赵修忠.常用非线性模型参数估计新方法及应用.数理医药学杂志,2000,13(3):215-216
[137]Davidian M,M.Giltinan D.Nonlinear Models for Repeated Measurement Data:An Overview and Update.Journal of Agricultural,Biological & Environmente Statistics,2003,8(4):387-419
[138]Jonsson EN,Karlsson.MO.Nonlinearity Detection:Advantages of Nonlinear Mixed-Effects Modeling.AAPS PharmSci,2000,2(3):1-10
[139]Oberg A,Davidian M.Estimating data transformations in nonlinear mixed effects models.Biometrics,2000,56(1):65-72
[140]Palmer MJ,Phillips BJ,Smith GT.Application of nonlinear models weth random coefficients to growth data Biometries,1991,47:623-635
[141]Lipsitz SR,Fitzmaurice GM.Estimating equations for measures of association between repeated binary responses.Biometrics,1996,52:903-912
[142]Manor O,Kark JD.A comparative study of four methods foe analyzing repeated measures data.Statistics in Medicine,1996,15(11):1143-1160
[143]Zeger SL,Liang KY.An overview of methods for the analysis of longitudinal data.Statistics in Medicine,1992,11:1825-1839
[144]Pinheiro JC,Bates DM.Approximations to the Log-Likelihood Function in the Nonlinear Mixed-Effects Model.Journal of Computational and Graphics Statistics,1995,4:12-35
[145]Vonesh EF.Non-linear models for the analysis of longitudinal data.Stat Med,1992,11(14-15):1929-1954
[146]Holliday T,Lawrance AJ,Davis TP.Engine-Mapping Experiments:A Two-Stage Regression Approach.Technometrics, 1998,40:120-126
[147] Stukel TA,Demidenko E.Two-stage method of estimation for general linear growth curve models.Biometrics, 1997,53(2):720-728
[148] Vonesh EF,Carter RL.Mixed-effects nonlinear regression for unbalanced repeated measures.Biometrics, 1992,48( 1): 1 -17
[149] Bryk A,Raudenbush S. Hierarchical Linear Models. Newbury Park.: Sage Publications, 1992
[150] Yeap BY,Davidian M.Robust two-stage estimation in hierarchical nonlinear models.Biometrics,2001,57(1):266-272
[151] Bates DM,Pinheiro JC.Computing REML or ML Estimates for Linear or Nonlinear Mixed-Effects Models. 1999
[152] Wolfinger R.Laplace's approximation for nonlinear mixed models.Biometrika,1993,80(791-795)
[153] Fattinger KE, Sheiner LB,Verotta DA.New method to explore the distribution of interindividual random effects in non-linear mixed effects models.Biometrics, 1995,51(4): 1236-1251
[154] Sheiner LB,Beal SL.Evaluation of method for estimating population pharmacokinetic parameters, I. Michaelis-Menten model: routine clinical pharmacokienetic data.Joumal of Pharmacokienetics and Biopharmaceutics, 1980,8:553-571
[155] Ko H,Davidian M.Correcting for measurement error in individual-level covariates in nonlinear mixed effects models.Biometrics,2000,56(2):368-375
[156] Yong DA, Zerbe G, Boyle DW, et al.On nonlinear random effects models for repeaed measurements.Communication in Statistics B, 1991,20:463-478
[157] Sheiner LB,Ludden TM.Population pharmacokinetics/pharmacodynamics.Annual review of pharmacolotical toxicology, 1992,32( 185-209)
[158] Dipak KD, Chen MH,Chang H.Bayesian Approach for Nonlinear Random Effects Models.Biometrics,1997,53:1239-1252
[159] 刘昌孝,孙瑞元. 药物评价实验设计与统计学基础. 北京: 军事医学科学出版社,2001
[160] Sadray S, Jonsson EN,Karlsson MO.Likelihood-based diagnostics for influential individuals in non-linear mixed effects model selection.Pharm Res, 1999,16(8): 1260-1265
[161] Lu JZ, Wen H,Xu YH.Determination of 5-Fu concentration in hepatic cancer patient serum by HPLC.Chin Hosp Pharm J,2004,24(2):83-84
[162] Luo TE,Liu GF.Application of Nonlinear Mixed Effects Model for Repeated Measurement Data and Implement.Chinese Journal of Health Statistics,2006,23(2): 104-107
[163] Johnston G,So YAnalysis of Data from Recurrent Events.Proceeding of the 27th Annual SAS USERS Group International Conference(SUGI 27)273-28
[164] Aalen OO.Heterogeneity in Survival Analysis.Statistics in Medicine, 1988,7:1121-1137
[165] Aalen OO.Modelling Heterogeneity in Survival Analysis by the Compound Poisson Distribution. Annals of Applied Probability, 1992,4(2):951-972
[166] Nelson WB.Recurrent Events Analysis for Product Repairs, Disease Recurrences, and Other Applications.The ASA-SIAM Series on Statistics and Applied Probability,2003
[167] Aalen OO,Tretli S.Analysing incidence of testis cancer by means of a frailty model.Cancer Causes and Control, 1999,10:285-292
[168] Cox DR.Regression Models and Life-Tables. Journal of the Royal Statistical Society B 1972,34:187-220
[169] Michiels S, Baujat B, Mane C, et al.Random effects survival models gave a better understanding of heterogeneity in individual patient data meta-analyses.J Clin Epidemiol,2005,58(3):238-245
[170] M.A.Wintrebert C, A.H.Zwinderman, Cam E, et al.Joint modelling of breeding and survival in the kittiwake using frailty models.EcoIogical Modelling,2005,181(2-3):203-213
[171] Gupta RC,Kirmani SNUA.Stochastic comparisons in frailty models.Journal of Statistical Planning and Inference,2006,136(10):3647-3658
[172] Greenwood M,Yule GU.An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents.Journal of the Royal Statistical Society, 1920,83:255-279
[173] Vaupel JW, Manton KG,Stallard E.The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality.Demography, 1979,16:439-454
[174] Clayton DG.A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence.Biometrika,1978,65:141-151
[175] Hien TVV.Estimation in semiparametric conditional shared frailty models with events before study entry.Computational Statistics & Data Analysis,2004,45(3):621-637
[176] Zhang Jj,Peng Yw.An alternative estimation method for the accelerated failure time frailty model.Computational Statistics & Data Analysis,2006
[177] Therneau T,Grambsch P. Modeling Survival Data: Extending the Cox Model. New York: Springer-Verlag, 2000
[178] Wienke A, Arbeev KG, Locatelli I, et al.A comparison of different bivariate correlated frailty models and estimation strategies.Mathematical Biosciences,2005,198(1):1-13
[179] Lim HJ, Liu J,Melzer-Lange M.Comparison of Methods for Analyzing Recurrent Events Data: Application to the Emergency Department Visits of Pediatric Firearm Victims.Accident Analysis & Prevention,2007,39(2):290-299
[180] Sastry N.A Nested Frailty Model for Survival Data, With an Application to the Study of Child Survival in Northeast Brazil.Journal of the American Statistical Association,1997,92(438):426-435
[181] Cortinas AJ,Burzykowski T.Aversion of theEMalgorithm for proportional hazards model with random effects.Biometrical J,2005,47:847-862
[182] Maples JJ, Murphy SA,Axinn WG.Two-level proportional hazards models.Biometrics,2002,58:754-763
[183] Klein JP.Semiparametric estimation of random effects using the Cox model based on the EM algorithm.Biometrica,1992,48:795-806
[184] Nielsen GG, Gill RD, Andersen P, et al.A counting process approach to maximum likelihood estimation of frailty models.Scandznatian J of Stotistrcs, 1992,19:25-43
[185] Hastie TJ,Tibshirani RJ.Varying-coefficient models (with discussion). JRSSB 1993,55:757-796
[186] Parner E.Asymptotic theory for the correlated Gamma-frailty model.Ann. Statist, 1998,26:183-214
[187] Rondeau V, Commenges D,Joly P.Maximum Penalized Likelihood Estimation in a Gamma-Frailty Model.Lifetime Data AnaIysis,2003,9(2): 139-153
[188] Yu B.Estimation of shared Gamma frailty models by a modified EM algorithm Computational Statistics & Data Analysis,2006,50(2):463-474
[189] Vu HTV,Knuiman MW.A hybrid ML-EM algorithm for calculation of maximum likelihood estimates in semiparametric shared frailty models.Computational Statistics & Data Analysis,2002,40(1):173-187
[190] Nielsen JD,Dean CB.Regression splines in the quasi-likelihood analysis of recurrent event data.Journal of Statistical Planning and Inference,2005,134(2):521-535
[191] Schoenfeld D.Partial residuals for the proportional hazards regression model.Biometrika,1982,69:239-241
[192] Fleming TR,Harrington DP. Counting Processes and Survival Analysis. New York: Wiley, 1991
[193] Lindstrom ML,Bates DM.Nonlinear mixed effects models for repeated measures data.Biometrics,1990,46(3):673-687
[194] Akaike H.a new look at th estatistical model identification.IEEE Transaction on Automatic Control,1974,AC-19:716-723
[195] Cox DR.Partial Likelihood.Biometrika,1975,66:188-190
[196] Cook,Weisberg. An Introduction to Regression Graphics. New York: Wiley, 1994
[1]Grizzle JE, Starmer CF,Koch GG.Analysis of categorical data by linear models.Biometrics,1969,25(3):489-504
[2]Koch GG,Reinfurt DW.The analysis of categorical data from mixed models.Biometrics, 1971,27:157-173
[3] Koch GG, Landis JR, Freeman JL, et al.A general methodology for the analysis of experiments with repeated measurment of categorical data.Biometrics, 1977,33:133-158
[4] Landis JR,Miller ME.Some general methods for the analysis of categorical data in longitudinal studies.Statistics in Medicine, 1988,7:109-137
[5] Crowder MJ,Hand DJ. Analysis of Repeated Measures. London: Chapman and Hall, 1990
[6]Liang KY,Zeger SL.Longitudinal data analysis using generalized linear models.Biometrics, 1986,73:13-22
[7]Zeger SL,Liang KY.Longitudinal data analysis for discrete and continuous outcomes.Biometrics, 1986,42(1): 121 -130
[8]Stiratelli R, Laird N,Ware JH.Random-effects models for serial observations with binary response.Biometrics, 1984,40(4):961 -971
[9] Anderson DA,Aitkin M.Variance component models with binary response: Inteviewer variability.J. Roy.Statist. Soc. Ser. B, 1985,47:203-210
[10] Gilmour AR, Anderson RD,Rae AL. The analysis of binomial data by a generalized linear mixed model.Biometrika, 1985,72:593-599
[11] Schall R.Estimation in generalized linear models with random effects.Biometrika, 1991,78:719-727
[12] Breslow NE,Clayton DG.Approximate inference in generalized linear mixed models.Journal of the American Statistical Association,1993,88(421):9-25
[13] Wolfinger R,O'Connell M.Generalized linear mixed models: A pseudo-likelihood approach.Journal of Statistical Computation and Simulation, 1993,48:233-243
[14] McCulloch CE,Searle SR. Generalized, Linear, and Mixed Models. New York: John Wiley & Sons, 2000
[15] Zeger SL, Liang KY,Albert PS.Models for longitudinal data: a generalized estimating equation approach.Biometrics, 1988,44(4): 1049-1060
[16] Davidian M,Giltinan DM. Nonlinear Models for Repeated Measurement Data. London: Chanpman and Hall, 1995
[17] Vonesh EF,Chinchilli VM. Linear and Nonlinear Models for the Analysis of Repeated Measurements. New York: Marcel Dekker, 1997
[18] McCullagh P.Regression models for ordinal data. Journal Royal Statistical Society B,1980,42:109-142
[19] Goodman LA.Simple models for the analysis of association in cross-classifications having ordered categories.Journal of the American Statistical Association, 1979,74:537-552
[20] Hedeker D,Gibbons RD.MIXOR: a computer program for mixed-effects ordinal regression analysis.Comput Methods Programs Biomed, 1996,49(2):157-176
[21] Williams OD,Grizzle JE.Analysis of tables having ordered response categoriesJournal of the American Statistical Association, 1972,67:53-64
[22] Simon G.Alternative analysis for singly ordered contingency tables.Journal of the American Statistical Association, 1974,69:971-976
[23] Gibbons RD,Bock RD.Trends in correlated proportions.Psychometrika, 1987(52)
[24] Peterson B,Harrell FE.Partial Proportional Odds Models for Ordinal Response Variables.Applied Statistics,1990,39(2):205-217
[25]Terza JV.Ordinal probit:a generalization.Communications in Statistical Theory and Methods, 1985,14(1-11)
[26] Hedeker D.A mixed-effects multinomial logistic regression model.Stat Med,2003,22:1433-1446
[27] Goldstein H. Multilevel Statistical Models.2nd edn. New York: Halstead Press, 1995
[28] Sheiner LB, Rosenberg B,Marathe W.Estimation of population characteristics of pharmacokinetic parameters from routine clinical data.J Pharmacokinet Biopharm,1977,5(5):445-479
[29] Beal SL.Population pharmacokinetic data and parameter estimation based on their first two statistical moments.Drug Metabolism Reviews,1984,15:173-193
[30] Sheiner LB.The population approach to pharmacokinetic data analysis: rationale and standard data analysis methods.Drug Metabolism Reviews, 1984,15:153-171
[31]Lindstrom MJ,Bates DM.Nonlinear mixed effects models for repeated measures data.Biometrics, 1990,46(3):673-687
[32]Vonesh EF,Carter RL.Mixed-effects nonlinear regression for unbalanced repeated measures.Biometrics, 1992,48:1 -17
[33] Davidian M,Giltinan DM. Nonlinear Models for Measurement Data. London: Chapman & Hall, 1995
[34] Pinheiro JC,Bates DM Model Building for Nonlinear Mixed-Effects Models. Technical Report 91 In: Department of Biostatistics, University of Wisconsin- Madison, 1995.
[35] Ke C,Wang Y.Semiparametric nonlinear mixed models and their applications.Journal of the American statistical asociation,2001,96:1272-1298
[36] Vonesh EF, Chinchilli VM,Pu KW.Goodness-Of-Fit in Generalized Nonlinear Mixed-Effects Models.Biometrics,1996,52:572-587
[37] Vonesh EG, Wang H, Nie L, et al.Conditional Second-Order Generalized Estimating Equations for Generalized Linear and Nonlinear Mixed-Effects Models.Journal of the American Statistical Association,2002,97:271 -283
[38]Vonesh EF,Schork MA.Sample Size in the multivariate analysis of repeated measurements.Biometrics, 1986,42:601-610
[39]Rochon J.Sample size calculation for two-group repeated-measures experiments Biometrics,1991,17:1383-1398
[40] Overall JE, Shobaki G,Anderson CB.Comparative Evaluation of Two Models for Estimating Sample Sizes for Tests on Trends across Repeated Measurements.Statistics in Medicine,1998,17:1643-1658
[41] Nelson WB. Recurrent Events Data Analysis for Product Repairs,Disease Recurrences, and Other Applications: The ASA-SIAM Series on Statistics and Applied Probability, 2003
[42] Prentice RL, Williams BJ,Peterson AV.On the regression analysis of multivariate failure time data.Biometrika,1981,68:373-379
[43] Andersen PK,Gill RD.Cox's regression model for counting processes: a large sample study.Annals of Statistics, 1982,10:1100-1120
[44] Wei LJ, Lin DY,Weissfeld L.Regression analysis of multivariate incomplete failure time data by modeling marginal distributions.Journal of the American Statistical Association, 1989,84:1065-1073
[45] Lee EW, Wei LJ,Amato DA.COX-type regression analysis for large number of small groups of correlated failure time observations Kulwer Academic Publishers,Dordrecht, 1992:237-247
[46] Greenwood M,Yule GU.An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents.Journal of the Royal Statistical Society, 1920,83:255-279
[47] Vaupel JW, Manton KG,Stallard E.The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality.Demography, 1979,16:439-454
[48] Clayton DGA model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence.Biometrika, 1978,65:141-151
[49] Hougaard P. Analysis of Multivariate Survival Data. New York Springer-Verlag, 2000
[50] Hougaard P.A class of multivariate failure time distributions.Biometrika,1986b,73:671-678
[51]Hougaard P.Survival models for heterogeneous populations derived from stable distributions.Biometrika, 1986a,73:671 -678
[52] Yashin AI, Vaupel JW,Iachine IA.Correlated individual frailty:an advantageous approach to survival analysis of bivariate data.Mathematical Population Studies, 1995,5:145-159
[53] Akaike H.a new look at th estatistical model identification.lEEE Transaction on Automatic Control, 1974,AC-19:716-723
[54] Schwarz G. Estimating the Dimension of a model.Annal of Statistics, 1978,6(2):461 - 464
[55] McCullagh P,Nelder JA. Generalized Linear Models. London: Chapman and Hall, 1989
[56] Cox DR.Partial Likelihood.Biometrika,1975,66:188-190
[57]Pan W.Akaike's information criterion in generalized estimating equations.Biometrics,2001,57(1): 120-125
[58] Pan W.Model selection in estimating equations.Biometrics,2001,57(2):529-534
[59] Lin X,Breslow NE.Bias correction in generalized linear mixed models with multiple components of dispersion.Journal of Amrican Statistical Assosiation, 1996,91:1007-1016
[60] Vonesh EF, Wang H, Nie L, et al.Conditional second-order generalized estimating equations for generalized linear and nonlinear mixed-effects models.Journai of the American Statistical Association,2002,96:282-291
[61] Zeger SL,Karim MR.Generalized linear models with random effects-a Gibbs sampling approach Journal of the American Statistical Association, 1991,86:79-86
[62]Steele BM.A modified EM algorithm for estimation in generalized mixed models.Biometrics, 1996,52(4): 1295-1310
[63] McCulloch CE.Maximum Likelihood Variance Components Estimation for Binary Data Journal of the American Statistical Association, 1994,89:330-335
[64] McCulloch CE.Maximum likelihood algorithms for generalized linear mixed models. J. Amer. Statist. Assoc.,1997,92:162-170
[65] Kuk AYC.Laplace importance sampling for generalized linear mixed models.Journai of Statistical Computation and Simulation, 1999,63:143-158
[66] Hobert JP.Hierarchical models: A current computational perspective.Journal of the American Statistical Association,2000,95:1312-1316
[67] Tanner M. Tools for statistical inference. New York: Springer, 1993
[68] Booth JG,Hobert JP.Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm.Journal of the Royal Statistical Society, Series B, 1999,61:265-285
[69] Zhu HT,Lee SY.Analysis of generalized linear mixed models via a stochastic approximation algorithm with Markov chain Monte-Carlo method Statistics and Computing,2002,12(2): 175-183
[70] Geman S,Geman D.Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images.IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984,6:721-741
[71] Metropolis N, Rosenbluth A, W., Rosenbluth MN, et al.Equations of state calculations by fast computing machines.Journal of Chemical Physics, 1953,21 (1087-1092)
[72]Hostings WK.Monte Carlo sampling methods using Markov chains and their applications.Biometrika, 1970,57(97-109)
[73] Gelman A,Meng XL.SimuIating normalizing constant:from importance sampling to bridge sampling to path sampling.Statistical Science, 1998,13:163-185
[74] Meng XL,Wong WH.Simulating ratios of normalizing constants via a simple identity:a theoretical exploration.Statistica Sinica,1996,6(821-860)
[75]Song XY,Lee SY.Model comparison of generalized linear mixed models.Stat Med,2006,25(10):1685-1698
[76]Cai B,Dunson DB.Bayesian covariance selection in generalized linear mixed models.Biometrics,2006,62(2):446-457
[77] Cook,Weisberg. An Introduction to Regression Graphics. New York: Wiley, 1994
[78] Lin DY, Wei LJ,Ying Z.Checking the Cox Model with Cumulative Sums of Martingale-Based Residuals.Biometrika, 1993,80:557-572
[79]Lin D, Wei L,Ying Z.Model-Checking Techniques Based on Cumulative Residuals.Biometrics,2002,58:1 -12
[80] Su JQ,Wei LJ.A lack-of-fit test for the mean function in a genralized linear model.Joumal of the American Statistical Association, 1991,86:420-426
[81]Pan Z,Lin DY.Goodness-of-fit methods for generalized linear mixed models.Biometrics,2005,61 (4): 1000-1009