光滑误差项分布的加速失效时间模型及其医学应用

目的介绍光滑误差项分布的加速失效时间模型并探讨其在医学中的应用。方法通过惩罚最大似然的方法对模型中的参数做出估计,以"伪方差估计"的方法做进一步推断,以实例说明模型的实际应用并与Cox模型结果相比较。结果资料不满足Cox模型比例风险假定时,加速失效时间模型的结果优于Cox模型。结论光滑误差项分布的加速失效时间模型不需要知道误差项的基准分布,也不需要满足比例风险假定,是Cox模型很好的替代模型。     

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。     

区间截尾Cox比例风险模型在健康教育中的应用

目的 介绍区间截尾型Cox比例风险模型及其在健康教育中的应用。结果 采用区间截尾型Cox比例风险模型评价健康教育对降低HIV转阳的作用。结果 接受健康教育对象HIV阳性的危险比未接受的降低了41．6％。结论 区间截尾型Cox比例风险模型在健康教育研究中是可行的。     

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.     

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。     

队列研究资料分析中Cox比例风险回归模型的时间尺度选择和应用

Cox比例风险回归模型（Cox模型）是时间-事件数据分析中常用的多因素分析方法，拟合Cox模型时一个关键问题是如何选择合适的与结局事件发生相关的时间尺度。目前国内开展的队列研究在资料分析中较少关注Cox模型的时间尺度选择问题。本研究对文献报道中常见的几种时间尺度选择策略进行简要介绍和比较；并利用上海女性健康队列资料，以中心性肥胖与肝癌发病风险的关联为例，说明选择不同时间尺度的Cox模型对数据分析结果的影响；在此基础上提出几点Cox模型时间尺度选择上的建议，以期为队列研究资料的分析提供参考。     

限制平均生存时间回归模型在生存分析中的应用

目的 探讨限制平均生存时间(restricted mean survival time,RMST)回归模型在生存数据分析中的应用。 方法 运用伪值估计方法对医学数据进行限制平均生存时间回归模型实例分析,并与常见生存分析模型进行比较。 结果 RMST回归模型无特定模型假设,适用于不满足比例风险假定的生存数据;实例分析显示,RMST模型构建灵活,可通过设定多个τ值在多个时间段内进行估计;犯第一类错误的概率低于Cox比例风险模型,模型估算结果容易解释,能够提供在临床实践中更为实用的结论。 结论 在不满足比例风险假定且生存曲线有较大交叉的情形下,限制性平均生存时间模型能够提供稳定有效且易于解释的效应估计,在生存分析领域具有优良的适用性,可以作为Cox比例风险模型分析结果的补充。     

半参数治愈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生存分析模型与方法 .方法 以SARS病人为例阐述半参数治愈模型原理与方法 ,并将长期生存者资料半参数治愈模型与Cox回归模型得到的结果 进行对比分析.结果 Cox比例风险回归模型得到四个协变量有统计学意义;半参数治愈模型比例风险回归部分得到一个有意义的协变量,logistic回归部分得到三个协变量有统计学意义.结论 在对长期生存者存在的资料分析时,半参数治愈模型比传统的Cox比例风险回归模型更具优势,不仅模型形式简明,参数估计解释合理,而且可从多角度提供更多有价值的信息,是一种适用范围更广,实用性更强的统计分析方法 .     

基于Cox模型的美沙酮维持治疗患者脱失预测研究

目的 构建Cox比例风险模型预测美沙酮维持治疗门诊患者脱失概率,及时识别患者脱失风险,实施个体化干预,提高患者维持治疗率。方法 收集福田区和南山区2009-2014年所有美沙酮维持治疗患者相关信息,将样本分为训练样本和测试样本,训练样本用来拟合Cox比例风险预测模型,测试样本用来评估模型信度和效度。结果 经拟合模型,筛选出8个变量对脱失预测有统计学意义（P<0.05）,经测试样本评估,模型的灵敏度为82.24%,特异度为80.76%,一致率为81.76%,说明模型预测结果和实际脱失情况具有较高的一致性。结论 Cox比例风险模型可以用于美沙酮维持治疗门诊患者的脱失预测。     

衢州市手足口病再感染风险分析——基于Cox比例风险回归模型

目的 采用Cox比例风险回归模型，分析2017—2022年衢州市手足口病(hand, foot, and mouth disease, HFMD)患者再感染的风险，为HFMD防控提供依据。方法 选取中国疾病预防控制信息系统导出的2017—2022年衢州市HFMD重复个案为研究对象，收集人口学资料、再感染时间和实验室结果资料，采用Kaplan-Meier法比较不同性别、年龄组、人群类型、地区、实验室结果的首次再感染的累计危险概率；采用Cox比例风险回归模型对HFMD再感染风险进行单变量和多变量分析。结果 2017—2022年衢州市HFMD再感染率为6.23%(1 506/24 185)。再感染病例1 506人，2次感染1 471人(97.68%),3次感染33人(2.19%),4次感染2人(0.13%)。首次感染后20个月内，再感染风险急剧增加，其再感染率(18.58%)达到最高值。Kaplan-Meier曲线显示，柯萨奇病毒A16型(CV-A16)首次感染、3岁以下、男童、城市地区、散居儿童再感染危险性较高。Cox比例风险回归模型显示，男童(HR=1.394,95%CI:1.250～1...     

检验Cox模型成比例危险性假设的探讨

目的：探讨如何对Cox模型成比例危险性假设进行检验,以及协变量与危险函数之间非成比例危险性的解决方法。方法：以Ⅲc期卵巢浆液性囊腺癌数据为例,用图形法对影响Ⅲc期卵巢浆液怀囊腺癌生存时间的预后因素。做了成比例危险性假设的检验。结果：术前一般状态这一 后因素违背了成比例危险性假设。结论：在应用Cox模型时,检验预后因素是否违背成比例危险性假设应当引起重视。     

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.     

Generating survival times to simulate Cox proportional hazards models

Simulation studies present an important statistical tool to investigate the performance, properties and adequacy of statistical models in pre-specified situations. One of the most important statistical models in medical research is the proportional hazards model of Cox. In this paper, techniques to generate survival times for simulation studies regarding Cox proportional hazards models are presented. A general formula describing the relation between the hazard and the corresponding survival time of the Cox model is derived, which is useful in simulation studies. It is shown how the exponential, the Weibull and the Gompertz distribution can be applied to generate appropriate survival times for simulation studies. Additionally, the general relation between hazard and survival time can be used to develop own distributions for special situations and to handle flexibly parameterized proportional hazards models. The use of distributions other than the exponential distribution is indispensable to investigate the characteristics of the Cox proportional hazards model, especially in non-standard situations, where the partial likelihood depends on the baseline hazard. A simulation study investigating the effect of measurement errors in the German Uranium Miners Cohort Study is considered to illustrate the proposed simulation techniques and to emphasize the importance of a careful modelling of the baseline hazard in Cox models.     

The restricted cubic spline as baseline hazard in the proportional hazards model with step function time-dependent covariables

We incorporate a cubic spline function where the tails are linearly constrained, as the baseline hazard, into the proportional hazards model. We show estimation of covariable coefficients and survival probabilities with this model to be as efficient statistically as with the Cox proportional hazards model when covariables are fixed. Examples show that the inclusion of time-dependent covariables defined as step functions into the restricted cubic spline proportional hazards model reduces computation time by a factor of 213 over the Cox model. Advantages of the spline model also include flexibility of the hazard, smooth survival curves, and confidence limits for the survival and hazard estimates when there are time-dependent covariables present.     

Bayesian random threshold estimation in a Cox proportional hazards cure model

In this paper, we develop a Bayesian approach to estimate a Cox proportional hazards model that allows a threshold in the regression coefficient, when some fraction of subjects are not susceptible to the event of interest. A data augmentation scheme with latent binary cure indicators is adopted to simplify the Markov chain Monte Carlo implementation. Given the binary cure indicators, the Cox cure model reduces to a standard Cox model and a logistic regression model. Furthermore, the threshold detection problem reverts to a threshold problem in a regular Cox model. The baseline cumulative hazard for the Cox model is formulated non‐parametrically using counting processes with a gamma process prior. Simulation studies demonstrate that the method provides accurate point and interval estimates. Application to a data set of oropharynx cancer patients suggests a significant threshold in age at diagnosis such that the effect of gender on disease‐specific survival changes after the threshold. Copyright © 2013 John Wiley & Sons, Ltd.     

Comparing alternative models: log vs Cox proportional hazard?

Health economists often use log models (based on OLS or generalized linear models) to deal with skewed outcomes such as those found in health expenditures and inpatient length of stay. Some recent studies have employed Cox proportional hazard regression as a less parametric alternative to OLS and GLM models, even when there was no need to correct for censoring. This study examines how well the alternative estimators behave econometrically in terms of bias when the data are skewed to the right. Specifically we provide evidence on the performance of the Cox model under a variety of data generating mechanisms and compare it to the estimators studied recently in Manning and Mullahy (2001). No single alternative is best under all of the conditions examined here. However, the gamma regression model with a log link seems to be more robust to alternative data generating mechanisms than either OLS on ln(y) or Cox proportional hazards regression. We find that the proportional hazard assumption is an essential requirement to obtain consistent estimate of the E(y|x) using the Cox model.     

Estimation of treatment effect under non‐proportional hazards and conditionally independent censoring

In clinical trials with time‐to‐event outcomes, it is common to estimate the marginal hazard ratio from the proportional hazards model, even when the proportional hazards assumption is not valid. This is unavoidable from the perspective that the estimator must be specified a priori if probability statements about treatment effect estimates are desired. Marginal hazard ratio estimates under non‐proportional hazards are still useful, as they can be considered to be average treatment effect estimates over the support of the data. However, as many have shown, under non‐proportional hazard, the ‘usual’ unweighted marginal hazard ratio estimate is a function of the censoring distribution, which is not normally considered to be scientifically relevant when describing the treatment effect. In addition, in many practical settings, the censoring distribution is only conditionally independent (e.g., differing across treatment arms), which further complicates the interpretation. In this paper, we investigate an estimator of the hazard ratio that removes the influence of censoring and propose a consistent robust variance estimator. We compare the coverage probability of the estimator to both the usual Cox model estimator and an estimator proposed by Xu and O'Quigley (2000) when censoring is independent of the covariate. The new estimator should be used for inference that does not depend on the censoring distribution. It is particularly relevant to adaptive clinical trials where, by design, censoring distributions differ across treatment arms. Copyright © 2012 John Wiley & Sons, Ltd.     

Dealing with competing risks: testing covariates and calculating sample size

It is universally agreed that Kaplan-Meier estimates overestimate the probability of the event of interest in the presence of competing risks. Kalbfleisch and Prentice recommend using the cumulative incidence as an estimate of the probability of an event of interest. However, there is no consensus on how to test the effect of a covariate in the presence of competing risks. Using simulations, this paper illustrates that the Cox proportional hazards model gives valid results when employed in testing the effect of a covariate on the hazard rate and when estimating the hazard ratio. A method to calculate the sample size for testing the effect of a covariate on outcome in the presence of competing risks is also provided.     

Relative risk estimation and inference using a generalized logrank statistic.

When comparing two survival distributions with proportional hazard functions, the logrank test is optimal for testing the null hypothesis that the constant hazard ratio (relative risk) is one. In this paper, we focus on (i) testing for departures from a relative risk other than one, and (ii) estimation of the relative risk. The standard tool to address both (i) and (ii) is the Cox proportional hazards model. However, the performance of the Cox model can be less than optimal with small samples. We show why this is the case, and propose a simple alternative method of estimation and inference based on a generalized logrank (GLR) statistic. While the GLR and Cox model approaches are asymptotically similar, empirical results reveal that the GLR approach is notably more efficient than the Cox model when the number of subjects is small (< 100 subjects per treatment group). An example based on survival times of cervical cancer patients is used to illustrate the proposed methodology.     

Analysis of time‐to‐event for observational studies: Guidance to the use of intensity models

This paper provides guidance for researchers with some mathematical background on the conduct of time‐to‐event analysis in observational studies based on intensity (hazard) models. Discussions of basic concepts like time axis, event definition and censoring are given. Hazard models are introduced, with special emphasis on the Cox proportional hazards regression model. We provide check lists that may be useful both when fitting the model and assessing its goodness of fit and when interpreting the results. Special attention is paid to how to avoid problems with immortal time bias by introducing time‐dependent covariates. We discuss prediction based on hazard models and difficulties when attempting to draw proper causal conclusions from such models. Finally, we present a series of examples where the methods and check lists are exemplified. Computational details and implementation using the freely available R software are documented in Supplementary Material. The paper was prepared as part of the STRATOS initiative.