Cox回归模型在肝癌病人生存分析中应用的研究

生存时间是癌症患者和临床医师共同关心的焦点,也是临床癌症诊治工作的重要指标之一．生存分析是研究多种因素与生存时间的关系以及关系程度的大小．Cox回归模型是生存分析中常用的方法之一．本文利用Cox回归模型对786名肝癌患者进行生存分析,确定影响肝癌患者预后的主要因素是癌栓、肝癌部位、治疗方式、肝脏储备功能、端粒酶活性、细胞增殖活性、γ-GT(γ-谷氮酰转肽酶)、术后复发等．为临床研究延长肝癌病人的生存期,提高其生存率提供了有力的依据．     

A Note on the Theil-Sen Regression Estimator When the Regressor Is Random and the Error Term Is Heteroscedastic

In simple regression, two serious problems with the ordinary least squares (OLS) estimator are that its efficiency can be relatively poor when the error term is normal but heteroscedastic, and the usual confidence interval for the slope can have highly unsatisfactory probability coverage. When the error term is nonnormal, these problems become exacerbated. Two other concerns are that the OLS estimator has an unbounded influence function and a breakdown point of zero. Wilcox (1996) compared several estimators when there is heteroscedasticity and found two that have relatively good efficiency and simultaneously provide protection against outliers: an M-estimator with Schweppe weights and an estimator proposed by Cohen, Dalal and Tukey (1993). However, the M-estimator can handle only one outlier in the X-domain or among the Y values, and among the methods considered by Wilcox for computing confidence intervals for the slope, none performed well when working with the Cohen-Dalal-Tukey estimator. This note points out that the small-sample efficiency of theTheil-Sen estimator competes well with the estimators considered by Wilcox, and a method for computing a confidence interval was found that performs well in simulations. The Theil-Sen estimator has a reasonably high breakdown point, a bounded influence function, and in some cases its small-sample efficiency offers a substantial advantage over all of the estimators compared in Wilcox (1996).     

Median Regression Model with Interval Censored Data

Quantile regression methods have been used to estimate upper and lower quantile reference curves as the function of several covariates. Especially, in survival analysis, median regression models to the right‐censored data are suggested with several assumptions. In this article, we consider a median regression model for interval‐censored data and construct an estimating equation based on weights derived from interval‐censored data. In a simulation study, the performances of the proposed method are evaluated for both symmetric and right‐skewed distributed failure times. A well‐known breast cancer data are analyzed to illustrate the proposed method.     

The Analysis of Life Table and Follow-up Data with Covariates Using Poisson Regression Model

The Poisson regression model for the analysis of life table and follow-up data with covariates is presented. An example is presented to show how this technique can be used to construct a parsimonious model which describes a set of survival data. All parameters in the model, the hazard and survival functions are estimated by maximum likelihood.     

Regression modeling of competing crude failure probabilities

In a randomized trial of tamoxifen therapy for breast cancer, women can experience tumor recurrence or die from competing causes. One goal of analysis is to describe the effect of tamoxifen on the probabilities of recurrence or death from other causes. To this end, we propose a semi-parametric transformation model for the crude failure probabilities of a competing risk, conditional on covariates. The model is developed as an extension of the standard approach to survival data with independent right censoring. Estimation of the regression coefficients is achieved with a rank-based least squares criterion. Simulations show that the procedure works well with practical sample sizes. A separate estimating function is developed for the baseline parameter. Prediction of covariate-adjusted failure probabilities is considered. The methodology is motivated and illustrated with data from the tamoxifen trial.     

Analysis of Rates Using a Generalized Poisson Regression Model

In this paper a generalization of the Poisson regression model indexed by a shape parameter is proposed for the analysis of life table and follow-up data with concomitant variables. The model is suitable for analysis of extra-Poisson variation data. The model is used to fit the survival data given in Holford (1980). The model parameters, the hazard and survival functions are estimated by the method of maximum likelihood. The results obtained from this study seem to be comparable to those obtained by Chen (1988). Approximate tests of the dispersion and goodness-of-fit of the data to the model are also discussed.     

基于支持向量回归的酚类化合物QSAR建模

目的：采用定量构效关系（QSAR）方法探索酚类化合物的毒性与分子结构参数的关系。方法：基于支持向量回归（SVR）、依均方误差最小原则选择最优核函数,对酚类化合物及其衍生物进行了QSAR研究。结果：不同数据集选取的最优核函数有异,对小样本、非线性等问题,SVR具有较优的稳定性及预测能力,在酚类化合物及其衍生物的QSAR研究中得到了优于原文献方法的独立预测结果。结论：SVR模型具有较好的预测能力,在QSAR及相关研究中可得到更广泛应用。     

Biplots in Reduced-Rank Regression

Regression problems with a number of related response variables are typically analyzed by separate multiple regressions. This paper shows how these regressions can be visualized jointly in a biplot based on reduced-rank regression. Reduced-rank regression combines multiple regression and principal components analysis and can therefore be carried out with standard statistical packages. The proposed biplot highlights the major aspects of the regressions by displaying the least-squares approximation of fitted values, regression coefficients and associated t-ratios. The utility and interpretation of the reduced-rank regression biplot is demonstrated with an example using public health data that were previously analyzed by separate multiple regressions.     

Randomized Blocks Analysis for the Exponential Distribution

A procedure for analyzing randomized blocks experiments for uncensored exponential random variables is presented. Its small sample behavior is studied in several simulations. Sample size requirements are given.     

Relating Cox's Proportional Hazard Model to the Exponential Model for Survival

An approximate representation is given for the partial likelihood estimate of the regression coefficient in Cox's proportional hazard model which indicates how it measures the association between survival time and covariate. The case of a single covariate is concentrated on. The representation is closely related to the first step of a Newton-Raphson iteration, i.e. to the score test. A similar representation for the Feigl-Zelen exponential model shows that a similar type of association is being measured, if observed lifetimes are interpreted as expected lifetimes of ordered exponentials. Necessary and sufficient conditions for the existence of Cox's estimate in the simple case are also written down.     

时滞传染病模型的指数稳定性

利用分析技巧研究了一类SEIRS传染病模型的动力学行为.结论表明如果再生数小于1,则带变时滞的传染病模型的无病平衡点是全局指数渐近稳定的,如果再生数大于1,得到传染病平衡点局部指数稳定的充分条件,同时给出了例子说明结论的有效性.     

Estimation of Exponential Parameters in the Presence of Outliers

In the present paper we discuss the estimation of the parameter and survival function of an exponential population. It is assumed that the sample based on which the estimation is done, contains k outliers that are also exponentially distributed with parameter, a constant multiple of that of the original distribution.     

饱和试验设计资料的逐步回归分析

对饱和试验设计资料,一次最小二乘分析是不合理的,采用逐步回归分析法,在选择适当的理论F值前提下,不仅可以检验每个回归系数的显著性,而且能够获得最优回归方程．     

Efron-type measures of prediction error for survival analysis

Estimates of the prediction error play an important role in the development of statistical methods and models, and in their applications. We adapt the resampling tools of Efron and Tibshirani (1997, Journal of the American Statistical Association92, 548-560) to survival analysis with right-censored event times. We find that flexible rules, like artificial neural nets, classification and regression trees, or regression splines can be assessed, and compared to less flexible rules in the same data where they are developed. The methods are illustrated with data from a breast cancer trial.     

Some Tests for k£2 Upper Outliers in an Exponential Sample

The sequential procedure for testing up to k upper outliers proposed by Kimber (1982) for one-parameter exponential distribution is modified to a two-parameter exponential distribution. Further null distributions of some test statistics for an upper outlier-pair in a complete or censored sample from a two-parameter exponential distribution are given. Percentage points of the statistic T₁ are tabulated.     

Novel statistical approaches to identify risk factors for soil-transmitted helminth infection in Timor-Leste

Soil-transmitted helminths (STHs) are parasitic intestinal worms that infect almost a fifth of the global population. Sustainable control of STHs requires understanding the complex interaction of factors contributing to transmission. Identifying risk factors has mainly relied on logistic regression models where the underlying assumption of independence between variables is not always satisfied. Previously demonstrated risk factors including water, sanitation and hygiene (WASH) access and behaviours, and socioeconomic status are intrinsically linked. Similarly, environmental factors including climate, soil and land attributes are often strongly correlated. Alternative methods such as recursive partitioning and Bayesian networks can handle correlated variables, but there are no published studies comparing these methods with logistic regression in the context of STH risk factor analysis. Baseline cross-sectional data from school-aged children in the (S)WASH-D for Worms study were used to compare risk factors identified from modelling the same data using three different statistical techniques. Outcomes of interest were infection with Ascaris spp. and any hookworm species (Necator americanus, Ancylostoma duodenale, and Ancylostoma ceylanicum). Mixed-effects logistic regression identified the fewest risk factors. Recursive partitioning identified the most WASH and demographic risk factors, while Bayesian networks identified the most environmental risk factors. Recursive partitioning produced classification trees that visualised potentially at-risk population sub-groups. Bayesian networks helped visualise relationships between variables and enabled interactive modelling of outcomes based on different scenarios for the predictor variables of interest. Model performance was similar across all techniques. Risk factors identified across all techniques were vegetation for Ascaris spp., and cleaning oneself with water after defecating for hookworm. This study adds to the limited body of evidence exploring alternative data modelling approaches in identifying risk factors for STH infections. Our findings suggest these approaches can provide novel insights for more robust interpretation.