样条Cox回归在随访资料分析中的应用

介绍借助R软件应用样条Cox回归分析不满足Cox比例风险模型两个基本假定条件的随访资料的方法,可同时估计非线性效应和时协效应.结果表明文中实例涉及的连续型协变量多不符合线性假定,3个变量不符合比例风险假定,应用样条Cox回归控制多个协变量后,踝臂指数每降低0.1,全因死亡的风险比(HR)为1.071.随访资料在不满足比例风险Cox回归模型的应用条件时,可选择应用样条Cox回归进行分析.     

条件Logistic回归模型拟合方法简介

正1概念条件Logistic回归模型又称配对Logistic回归模型,适用于配对(配伍)方法收集的应变量为二分类资料的Logistic回归分析。包括SPSS和SAS在内的多数统计软件都没有为条件Logistic回归模型提供直接拟合的程序,但根据模型原理,对数据格式略加变换后,可采用Cox比例风险回归模型(Cox回归模型)进行拟合[1]。Cox回归模型是半参数型的多因素生存分析方法[2],具有比例风险性,即在协变量固定的情形下,     

利用三次样条函数考察Cox模型比例风险假定

目的 介绍一种检查Cox模型比例风险假定的假设检验方法。方法 利用时间的三次样条函数评价Cox比例风险回归模型中的时协变量交互作用项。结果 该法灵活有效，并且提供LHRF的点估计和区间估计。结论 三次样条回归作为一种检验方法，可与其他检验方法或图法结合使用，以考察Cox模型比例风险假定。     

Aalen模型在医学研究中的应用

<正>Cox比例风险模型[1]是生存分析中最常用的模型,很多实际问题中的协变量并不满足比例风险,而且协变量的效应可能随时间变化。基于这些情况的考虑,Aalen提出了加法危险率模型[2-3],Aalen模型是Cox模型的补充。Aalen模型一个重要的特征就是其回归系数是随时间变化的函数,这种函数没有特定的形式,也不依赖任何参数假定。相对于Cox模型的半参数本质,Aalen模型是非参的,适合用于模型中含随     

Cox回归模型比例风险假定的检验方法研究

正生存分析(survival analysis)是一系列处理"事件发生时间"变量的统计方法总称~([1]),常用于研究疾病的发生、转归、痊愈和死亡。Cox比例风险回归模型(Cox proportional hazards regression model)~([2])作为生存分析中最重要的多因素分析方法之一,被广泛应用于临床随访资料的危险因素筛选及预测。Cox回归模型将风险函数表达为基准风险函数与相应协变量函数的乘积,通过描述不同人群在不同时刻的风险,来探索各危险因素对生存的影响。其基本     

参数混合模型在长期生存者资料分析中的应用

目的介绍长期生存者资料分析的参数混合模型。方法以急性骨髓性白血病患者数据为例阐述参数混合模型原理与方法 ,并与传统生存分析方法 log-rank检验的结果进行比较。结果参数混合模型得到不同处理组之间的生存差别有统计学意义,而log-rank检验未发现该差别。结论对有长期生存者存在(删失严重)的数据分析时,不宜用传统的生存分析方法。选用恰当的参数混合模型分析,不仅可以得到合理的结果而且可从多角度提供更多有价值的信息。参数混合模型是一种适用范围广,实用性强的长期生存者资料统计分析方法 。     

Aalen模型在医学研究中的应用北大核心CSCD

Cox比例风险模型是生存分析中最常用的模型,很多实际问题中的协变量并不满足比例风险,而且协变量的效应可能随时间变化。基于这些情况的考虑,Aalen提出了加法危险率模型,Aalen模型是Cox模型的补充。Aalen模型一个重要的特征就是其回归系数是随时间变化的函数,这种函数没有特定的形式,也不依赖任何参数假定。     

随机生存森林在大规模基因分型肺癌预后关联性研究中的降维作用

目的 探索随机生存森林在大规模测序肺癌随访研究资料中的降维效果,为进一步建立预后预测模型提供依据.方法 利用随机生存森林法对120位肺癌患者399个单核苷酸多态性(single nucleotide polymorphisms,SNPs)位点进行降维分析,筛选出重要性评分较高且错分率较低的SNPs子集,再对该子集建立多元Cox比例风险模型,并利用交叉验证法评价模型的预测效果.结果 随机生存森林法筛选出25个重要的SNPs,控制临床协变量(临床分期、是否手术、组织病理学类型)的多元Cox比例风险模型显示有4个位点有统计学意义.交叉验证结果表明,该模型的平均准确度达83.63％.结论 对高维关联性研究数据利用随机生存森林法先去噪降维,再作进一步分析,有助于后续预后预测模型的建立.     

限制性立方样条在Cox比例风险回归模型中的应用

限制性立方样条Cox比例风险回归模型分析是流行病学多因素生存分析的重要方法。本研究通过对典型Cox比例风险回归模型和限制性立方样条Cox比例风险回归模型比较,阐述了典型Cox比例风险回归模型的局限性,以及限制性立方样条Cox比例风险回归模型基本原理与实现过程。在随访数据不满足典型Cox比例风险回归模型应用条件时,可采用该方法实现连续性暴露与结局之间的关联分析。     

非随机化医学研究中风险比的一种估计方法

目的提出一种适用于非随机化医学研究的,结合倾向指数与非参数生存分析估计风险比的方法.方法首先对倾向指数进行估计,然后对倾向指数分布分层以消除比较两组间协变量分布的不均衡.其次对分层样本用非参数生存分析的方法估计两组间发病或死亡的风险比.最后比较本法与常用的Cox模型方法并探讨其适用性.结果将本法应用于一项评价某降血脂新药效果的4期临床试验数据后显示:(1)对倾向指数分布分层后基本上消除了由于随机分组方案失败导致的新药组与传统药物组之间协变量分布的不均衡性,使得非参数生存分析方法得以应用;(2)由本法得到的新药效果的估计-风险比与由Cox模型得到的结果基本一致.结论对于非随机化医学研究,结合倾向指数进行非参数生存分析是一种新的可选择的统计方法.     

A general semiparametric hazards regression model: efficient estimation and structure selection

We consider a general semiparametric hazards regression model that encompasses the Cox proportional hazards model and the accelerated failure time model for survival analysis. To overcome the nonexistence of the maximum likelihood, we derive a kernel‐smoothed profile likelihood function and prove that the resulting estimates of the regression parameters are consistent and achieve semiparametric efficiency. In addition, we develop penalized structure selection techniques to determine which covariates constitute the accelerated failure time model and which covariates constitute the proportional hazards model. The proposed method is able to estimate the model structure consistently and model parameters efficiently. Furthermore, variance estimation is straightforward. The proposed estimation performs well in simulation studies and is applied to the analysis of a real data set. Copyright © 2013 John Wiley & Sons, Ltd.     

Dynamic regression hazards models for relative survival

A natural way of modelling relative survival through regression analysis is to assume an additive form between the expected population hazard and the excess hazard due to the presence of an additional cause of mortality. Within this context, the existing approaches in the parametric, semiparametric and non-parametric setting are compared and discussed. We study the additive excess hazards models, where the excess hazard is on additive form. This makes it possible to assess the importance of time-varying effects for regression models in the relative survival framework. We show how recent developments can be used to make inferential statements about the non-parametric version of the model. This makes it possible to test the key hypothesis that an excess risk effect is time varying in contrast to being constant over time. In case some covariate effects are constant, we show how the semiparametric additive risk model can be considered in the excess risk setting, providing a better and more useful summary of the data. Estimators have explicit form and inference based on a resampling scheme is presented for both the non-parametric and semiparametric models. We also describe a new suggestion for goodness of fit of relative survival models, which consists on statistical and graphical tests based on cumulative martingale residuals. This is illustrated on the semiparametric model with proportional excess hazards. We analyze data from the TRACE study using different approaches and show the need for more flexible models in relative survival.     

Parametric models for accelerated and long-term survival: a comment on proportional hazards

The Cox proportional hazards model (CPH) is routinely used in clinical trials, but it may encounter serious difficulties with departures from the proportional hazards assumption, even when the departures are not readily detected by commonly used diagnostics. We consider the Gamel-Boag (GB) model, a log-normal model for accelerated failure in which a proportion of subjects are long-term survivors. When the CPH model is fit to simulated data generated from this model, the results can range from gross overstatement of the effect size, to a situation where increasing follow-up may cause a decline in power. We implement a fitting algorithm for the GB model that permits separate covariate effects on the rapidity of early failure and the fraction of long-term survivors. When effects are detected by both the CPH and GB methods, the attribution of the effect to long-term or short-term survival may change the interpretation of the data. We believe these examples motivate more frequent use of parametric survival models in conjunction with the semi-parametric Cox proportional hazards model.     

Estimating the proportion of cured patients in a censored sample

There has been a recurring interest in modelling survival data which hypothesize subpopulations of individuals highly susceptible to some types of adverse events while other individuals are assumed to be at much less risk, like recurrence of breast cancer. A binary random effect is assumed in this article to model the susceptibility of each individual. We propose a simple multiple imputation algorithm for the analysis of censored data which combines a binary regression formulation for the probability of occurrence of an event, say recurrence of the breast cancer tumour, and a Cox's proportional hazards regression model for the time to occurrence of the event if it does. The model distinguishes the effects of the covariates on the probability of cure and on the time to recurrence of the disease. A SAS macro has been written to implement the proposed multiple imputation algorithm so that sophisticated programming effort can be rendered into a user-friendly application. Simulation results show that the estimates are reasonably efficient. The method is applied to analyse the breast cancer recurrence data. The proposed method can be modified easily to accommodate more general random effects other than the binary random effects so that the random effects not only affect the probability of occurrence of the event, but also the heterogeneity of the time to recurrence of the event among the uncured patients.     

Analysis of linear transformation models with covariate measurement error and interval censoring

Among several semiparametric models, the Cox proportional hazard model is widely used to assess the association between covariates and the time-to-event when the observed time-to-event is interval-censored. Often, covariates are measured with error. To handle this covariate uncertainty in the Cox proportional hazard model with the interval-censored data, flexible approaches have been proposed. To fill a gap and broaden the scope of statistical applications to analyze time-to-event data with different models, in this paper, a general approach is proposed for fitting the semiparametric linear transformation model to interval-censored data when a covariate is measured with error. The semiparametric linear transformation model is a broad class of models that includes the proportional hazard model and the proportional odds model as special cases. The proposed method relies on a set of estimating equations to estimate the regression parameters and the infinite-dimensional parameter. For handling interval censoring and covariate measurement error, a flexible imputation technique is used. Finite sample performance of the proposed method is judged via simulation studies. Finally, the suggested method is applied to analyze a real data set from an AIDS clinical trial.     

Semiparametric accelerated failure time cure rate mixture models with competing risks

Modern medical treatments have substantially improved survival rates for many chronic diseases and have generated considerable interest in developing cure fraction models for survival data with a non‐ignorable cured proportion. Statistical analysis of such data may be further complicated by competing risks that involve multiple types of endpoints. Regression analysis of competing risks is typically undertaken via a proportional hazards model adapted on cause‐specific hazard or subdistribution hazard. In this article, we propose an alternative approach that treats competing events as distinct outcomes in a mixture. We consider semiparametric accelerated failure time models for the cause‐conditional survival function that are combined through a multinomial logistic model within the cure‐mixture modeling framework. The cure‐mixture approach to competing risks provides a means to determine the overall effect of a treatment and insights into how this treatment modifies the components of the mixture in the presence of a cure fraction. The regression and nonparametric parameters are estimated by a nonparametric kernel‐based maximum likelihood estimation method. Variance estimation is achieved through resampling methods for the kernel‐smoothed likelihood function. Simulation studies show that the procedures work well in practical settings. Application to a sarcoma study demonstrates the use of the proposed method for competing risk data with a cure fraction.     

Nonproportional hazards and unobserved heterogeneity in clustered survival data: When can we tell the difference?

Multivariate survival data are frequently encountered in biomedical applications in the form of clustered failures (or recurrent events data). A popular way of analyzing such data is by using shared frailty models, which assume that the proportional hazards assumption holds conditional on an unobserved cluster-specific random effect. Such models are often incorporated in more complicated joint models in survival analysis. If the random effect distribution has finite expectation, then the conditional proportional hazards assumption does not carry over to the marginal models. It has been shown that, for univariate data, this makes it impossible to distinguish between the presence of unobserved heterogeneity (eg, due to missing covariates) and marginal nonproportional hazards. We show that time-dependent covariate effects may falsely appear as evidence in favor of a frailty model also in the case of clustered failures or recurrent events data, when the cluster size or number of recurrent events is small. When true unobserved heterogeneity is present, the presence of nonproportional hazards leads to overestimating the frailty effect. We show that this phenomenon is somewhat mitigated as the cluster size grows. We carry out a simulation study to assess the behavior of test statistics and estimators for frailty models in such contexts. The gamma, inverse Gaussian, and positive stable shared frailty models are contrasted using a novel software implementation for estimating semiparametric shared frailty models. Two main questions are addressed in the contexts of clustered failures and recurrent events: whether covariates with a time-dependent effect may appear as indication of unobserved heterogeneity and whether the additional presence of unobserved heterogeneity can be detected in this case. Finally, the practical implications are illustrated in a real-world data analysis example.     

Flexible multistate models for interval‐censored data: Specification,estimation, and an application to ageing research

Continuous‐time multistate survival models can be used to describe health‐related processes over time. In the presence of interval‐censored times for transitions between the living states, the likelihood is constructed using transition probabilities. Models can be specified using parametric or semiparametric shapes for the hazards. Semiparametric hazards can be fitted using P‐splines and penalised maximum likelihood estimation. This paper presents a method to estimate flexible multistate models that allow for parametric and semiparametric hazard specifications. The estimation is based on a scoring algorithm. The method is illustrated with data from the English Longitudinal Study of Ageing.     

Semiparametric linear transformation models: Effect measures,estimators, and applications

Semiparametric linear transformation models form a versatile class of regression models with the Cox proportional hazards model being the most well-known member. These models are well studied for right censored outcomes and are typically used in survival analysis. We consider transformation models as a tool for situations with uncensored continuous outcomes where linear regression is not appropriate. We introduce the probabilistic index as a uniform effect measure for the class of transformation models. We discuss and compare three estimators using a working Cox regression model: the partial likelihood estimator, an estimator based on binary generalized linear models and one based on probabilistic index model estimating equations. The latter has a superior performance in terms of bias and variance when the working model is misspecified. For the purpose of illustration, we analyze data that were collected at an urban alcohol and drug detoxification unit.     

Likelihood approaches for proportional likelihood ratio model with right‐censored data

Regression methods for survival data with right censoring have been extensively studied under semiparametric transformation models such as the Cox regression model and the proportional odds model. However, their practical application could be limited because of possible violation of model assumption or lack of ready interpretation for the regression coefficients in some cases. As an alternative, in this paper, the proportional likelihood ratio model introduced by Luo and Tsai is extended to flexibly model the relationship between survival outcome and covariates. This model has a natural connection with many important semiparametric models such as generalized linear model and density ratio model and is closely related to biased sampling problems. Compared with the semiparametric transformation model, the proportional likelihood ratio model is appealing and practical in many ways because of its model flexibility and quite direct clinical interpretation. We present two likelihood approaches for the estimation and inference on the target regression parameters under independent and dependent censoring assumptions. Based on a conditional likelihood approach using uncensored failure times, a numerically simple estimation procedure is developed by maximizing a pairwise pseudo‐likelihood. We also develop a full likelihood approach, and the most efficient maximum likelihood estimator is obtained by a profile likelihood. Simulation studies are conducted to assess the finite‐sample properties of the proposed estimators and compare the efficiency of the two likelihood approaches. An application to survival data for bone marrow transplantation patients of acute leukemia is provided to illustrate the proposed method and other approaches for handling non‐proportionality. The relative merits of these methods are discussed in concluding remarks. Copyright © 2014 John Wiley & Sons, Ltd.