生存资料回归模型分析——基于MCMC过程构建生存资料Cox非比例风险回归模型

本文目的是介绍采用PHREG过程及MCMC过程且基于贝叶斯统计思想分别构建Cox非比例风险回归模型的相关内容及其SAS软件实现。在MCMC过程中,有两种构建模型的方法:一是对观测值进行转置之后,在MODEL语句中使用GENERAL函数;二是不对观测值进行转置,使用MCMC过程中的JOINTMODEL选项。两个过程所得计算结果基本一致。     

生存资料回归模型分析--Cox比例风险假设的图形检验法

本文目的是介绍目前使用图形检验比例风险的常用方法。经典的Cox比例风险回归模型要求生存资料满足比例风险假设,而在临床资料中,这个假设往往并不成立。鉴于此,本文首先阐述了比例风险假设的概念;然后介绍了一些检验比例风险假设是否成立的常用图示方法,主要包括Kaplan-Meier生存曲线图、ln[-ln(St)]生存时间关系图、缩放Schoenfeld残差与时间的关系图、SAS软件PHREG过程中ACCESS语句的PH和RESAMPLE选项产生的模拟路径图;最后,基于SAS软件并通过实例演示上述方法的实现。     

生存资料回归模型分析——生存资料参数回归模型分析基础

本文目的是介绍生存资料参数回归模型有关的基础知识。首先,介绍了构建三个常见的生存资料参数回归模型的基本原理,包括指数分布回归模型、Weibull分布回归模型和Log-logistic分布回归模型;其次,介绍了基于图示法判断生存时间服从何种概率分布的方法;最后,介绍了基于最大似然估计法求解参数回归模型中的参数和两个参数回归模型拟合优度的比较。得到如下结论:①当资料中的生存时间服从特定概率分布时,应选用相应的参数回归模型;②图示法可用于粗略判断生存时间服从何种概率分布;③似然比检验可用于包含不同参数数目的两个参数回归模型之间拟合优度的比较。     

生存资料回归模型分析——生存资料参数回归模型分析SAS实现

本文目的是介绍生存资料参数回归模型的SAS实现,包括创建SAS数据集、依据图示法选择模型、拟合参数模型和似然比检验。利用SAS中的LIFEREG过程绘制生存函数关于生存时间的关系图,拟合对应的参数分布回归模型,通过拟合优度检验选择最优的参数回归模型,最后对相关结果进行解释。     

生存资料回归模型分析——生存资料Cox比例风险回归模型分析

本文目的是介绍生存资料Cox比例风险回归模型分析的概念、作用及使用SAS软件实现计算的方法。首先介绍相关基本概念,包括"Cox比例风险回归模型简介""模型假定及其检验""参数解释"和"参数估计与假设检验";然后通过一个实例并基于SAS软件演示如何实施生存资料Cox比例风险回归模型分析,内容包括"产生SAS数据集""绘制生存曲线图""判断PH假定是否成立"和"算出参数估计值与假设检验结果"。结果表明:当生存资料满足PH假定时,Cox比例风险回归模型可用于生存资料影响因素分析、校正混杂因素后的组间比较以及对每个个体进行预后指数和生存率的预测。     

生存资料回归模型分析——生存资料及其统计分析方法概述

本文目的是全面介绍生存资料的特点及其常用统计分析方法。生存资料具有以下四个特点:①同时具有生存结局和生存时间;②生存时间可能含有删失数据或截尾数据;③生存时间的分布通常不服从正态分布,常呈指数分布、Weibull分布、对数正态分布;④影响生存时间的因素较复杂且不易控制。生存资料统计分析方法涉及统计描述、差异性分析和回归分析三大类,其中,统计描述主要有Kaplan-Meier(卡普兰-迈耶)估计法和Life table(寿命表)估计法;差异性分析主要有对数秩检验(log-rank test)和威尔考克森检验(Wilcoxon test);而回归分析主要有Cox比例和非比例风险回归模型、参数回归模型。在对生存资料进行统计分析时,需要合理选择统计分析方法,方可全面而又深入地揭示生存资料的内在变化规律。     

非配对设计多值有序资料一水平多重Logistic回归分析

本文目的是介绍非配对设计多值有序资料一水平多重logistic回归模型的构建与求解方法。本文详细介绍了构建累积logistic回归模型的原理和具体方法,并结合实例介绍如何使用SAS软件中的LOGISTIC过程来拟合此回归模型,并对逐步回归法的输出结果进行了解释;其次讨论了有关构建累积logistic回归模型的过程中自变量筛选、模型评价以及拟合模型时需注意的问题。     

非配对设计二值资料多水平多重Logistic回归分析

本文目的是介绍非配对设计二值资料多水平多重logistic回归模型的构建与求解方法。首先介绍模型的有关概念及模型的构建原理,基于实例使用SAS软件对列联表资料进行分析,以proc glimmix和proc nlmixed过程构建和求解模型,并对相关结果进行解释和比较。     

一般计数资料Poisson分布模型回归分析

本文目的是介绍一般计数资料Poisson分布模型回归分析。首先,介绍一般计数资料及其Poisson分布模型构建原理,包括"一般计数资料Poisson分布回归模型的形式"和"一般计数资料Poisson分布回归模型的求解";其次,介绍"一般计数资料Poisson分布回归模型的SAS实现",包括"创建SAS数据集""求出因变量Y的均值和方差""检验因变量是否存在过离散现象""对过离散进行校正"和"基于全部自变量对因变量Y构建多重Poisson分布回归模型"。本文结果提示,在"过离散"不十分严重的情况下,通过在GENMOD过程的"model语句"中增加选项"dist=poisson"和"scale=deviance",可以较好地校正"过离散"导致的不良后果。     

非配对设计多值名义资料多水平多重Logistic回归模型

本文目的是介绍非配对设计多值名义资料多水平多重logistic回归模型的构建与求解方法。首先介绍了有关的基本概念,涉及“多值名义结果变量”“分层或多水平数据结构”和“扩展的多重logistic回归模型”;其次,呈现了一个具有二水平结构的横断面调查资料,该资料涉及多个影响因素和一个多值有序的结果变量（在本文中,将其视为多值名义结果变量）;最后,借助SAS中的两个过程（即GLIMMIX和NLMIXED）对给定的资料进行统计分析,即构建和求解“非配对设计多值名义资料多水平多重logistic回归模型”,并对相关结果进行比较和解释。     

Assessing principal component regression prediction of neurochemicals detected with fast-scan cyclic voltammetry

Principal component regression is a multivariate data analysis approach routinely used to predict neurochemical concentrations from in vivo fast-scan cyclic voltammetry measurements. This mathematical procedure can rapidly be employed with present day computer programming languages. Here, we evaluate several methods that can be used to evaluate and improve multivariate concentration determination. The cyclic voltammetric representation of the calculated regression vector is shown to be a valuable tool in determining whether the calculated multivariate model is chemically appropriate. The use of Cook's distance successfully identified outliers contained within in vivo fast-scan cyclic voltammetry training sets. This work also presents the first direct interpretation of a residual color plot and demonstrated the effect of peak shifts on predicted dopamine concentrations. Finally, separate analyses of smaller increments of a single continuous measurement could not be concatenated without substantial error in the predicted neurochemical concentrations due to electrode drift. Taken together, these tools allow for the construction of more robust multivariate calibration models and provide the first approach to assess the predictive ability of a procedure that is inherently impossible to validate because of the lack of in vivo standards.     

Effects of ignoring clustered data structure in confirmatory factor analysis of ordered polytomous items: a simulation study based on PANSS

Statistical theory indicates that hierarchical clustering by interviewers or raters needs to be considered to avoid incorrect inferences when performing any analyses including regression, factor analysis (FA) or item response theory (IRT) modelling of binary or ordinal data. We use simulated Positive and Negative Syndrome Scale (PANSS) data to show the consequences (in terms of bias, variance and mean square error) of using an analysis ignoring clustering on confirmatory factor analysis (CFA) estimates. Our investigation includes the performance of different estimators, such as maximum likelihood, weighted least squares and Markov Chain Monte Carlo (MCMC). Our simulation results suggest that ignoring clustering may lead to serious bias of the estimated factor loadings, item thresholds, and corresponding standard errors in CFAs for ordinal item response data typical of that commonly encountered in psychiatric research. In addition, fit indices tend to show a poor fit for the hypothesized structural model. MCMC estimation may be more robust against clustering than maximum likelihood and weighted least squares approaches but further investigation of these issues is warranted in future simulation studies of other datasets. Copyright © 2015 John Wiley & Sons, Ltd.     

Many regression algorithms,one unified model: A review

Regression is the process of learning relationships between inputs and continuous outputs from example data, which enables predictions for novel inputs. The history of regression is closely related to the history of artificial neural networks since the seminal work of Rosenblatt (1958). The aims of this paper are to provide an overview of many regression algorithms, and to demonstrate how the function representation whose parameters they regress fall into two classes: a weighted sum of basis functions, or a mixture of linear models. Furthermore, we show that the former is a special case of the latter. Our ambition is thus to provide a deep understanding of the relationship between these algorithms, that, despite being derived from very different principles, use a function representation that can be captured within one unified model. Finally, step-by-step derivations of the algorithms from first principles and visualizations of their inner workings allow this article to be used as a tutorial for those new to regression.