Poisson和Cox回归模型在队列随访资料分析中的应用和对比

Ｐｏｉｓｓｏｎ与Ｃｏｘ回归模型是流行病学队列随访资料分析中常用的两类多变量分析方法。本文对有关这两类多变量回归模型的统计方法等问题进行了系统的回顾（相乘模型），并用一个实例的结果来说明两者的应用。从本文的结果和讨论来看，Ｐｏｉｓｓｏｎ和Ｃｏｘ回归模型均适合于队列随访资料的分析，但两者各有一些优势和不足。最后，笔者就目前两者的应用情况和相互比较提出了一些看法。此外，还讨论了其它形式的回归模型（相加模型）及在回归模型中如何引入外部对照率等。     

Cox比例风险模型对条件logistic回归参数估计原理和方法

医学研究中 ,为分析疾病和暴露之间关系 ,常常采用配对病例对照研究。条件ｌｏｇｉｓｔｉｃ回归分析是分析此类研究数据常用的方法〔1～ 3〕。近年来随着国内计算机应用的普及 ,统计软件的丰富 ,条件ｌｏｇｉｓｔｉｃ回归分析更被广泛应用到病例对照研究的数据分析中〔4〕。但目前广泛应用的统计软件如ＳＡＳ 6 12、ＳＰＳＳ 10 0等都没有直接提供用来处理 1∶ｎ ,和ｎ∶ｍ配对病例对照研究资料的条件ｌｏｇｉｓｔｉｃ回归分析过程。在处理这些数据时 ,国内有些文献作者直接用非条件ｌｏｇｉｓｔｉｃ回归过程来估计条件ｌｏｇｉｓｔｉｃ回…     

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...     

Cox比例风险模型在住院病例费用影响因素研究中的应用

掌握医疗费用的分布 ,对于科学确定参保职工住院费用的起付线和封顶线 ,确定保障水平 ,建立和完善补充保险等都有重要的参考作用。研究医疗费用的影响因素有利于降低医疗保险基金风险 ,还使定量地估计某项措施的控费力度成为可能。医疗费用的分布不服从正态分布 ,且费用的高低与多种因素有关 ,有不确定性 ,正因为这种不确定性 ,医疗高费用的发生可以看作是一种风险。医疗费用的影响因素多为分类变量 ,如 :性别、保险状况、入院情况、是否手术、是否做ＣＴ检查等。由于上述的原因 ,对住院病例费用及影响因素的分析不能用多元线性回归直接处理…     

Cox比例风险模型影响点的识别

目的 探讨Ｃｏｘ比例风险模型影响点的有效识别方法。方法 介绍了剩余残差、加权Ｓｃｏｒｅ残差、似然距离、最大影响曲率诊断量及相应的诊断图。结果 实例分析表明，上述诊断量可从不同角度识别Ｃｏｘ模型影响点。结论 影响分析应是Ｃｏｘ模型分析的一个重要组成部分。     

区间截尾Cox比例风险模型及其应用

Ｃｏｘ比例风险模型是生存分析中比较常用的一种方法 ,Ｃｏｘ比例风险模型假定说明变量的效果具有参数形式 ,但允许基准生存函数不具有特定的形式 ,所以应用范围非常广泛。但由于资料中常含有截尾数据(ｃｅｎｓｏｒｅｄｄａｔａ) ,使Ｃｏｘ比例风险模型更加复杂。根据个体生存时间与观察时间之间的关系可以分为 3类 :若个体的生存时间长于观察时间 ,称为右截尾数据 ;若个体的生存时间短于观察时间 ,称为左截尾数据 ;若个体的生存时间界于两次观察之间 ,则称为区间截尾数据。目前国内对左截尾和右截尾的Ｃｏｘ比例风险模型研究较多〔1,2〕,有…     

鞅残差在Cox回归模型诊断中的应用

目的：探讨Cox模型中某给定连续变量对生存效应的最佳函数形式。方法：不含该变量的Cox模型下的鞅残差对该协变量作图可揭示该变量在全模型中的函数形式。结果：实例分析表明,Loess平滑鞅残差图可用于Cox模型中协变量函数形式的确定。结论：建议分析者把鞅残差图纳入Cox模型分析中,对协变量的生存效应作出正确估计。     

Logistic和Cox回归模型在定群研究资料分析中的应用和对比

Ｌｏｇｉｓｔｉｃ和Ｃｏｘ回归模型在定群研究资料分析中的应用和对比项永兵，高玉堂，金凡Ｌｏｇｉｓｔｉｃ回归模型在流行病学研究资料分析中的应用众所周知￣［１，２］。Ｃｏｘ回归模型的应用也日益广泛，尤其在队列随访资料分析方面￣［３～１０］。因而，两者在定群...     

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.方法 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.     

Cox及其拓展模型在基于队列的依时暴露因素效应估计中的应用

队列研究的特点之一是暴露因素会随时间而改变,如何充分利用暴露因素及其协变量的变化及其相互关系,从而获得更真实的暴露因素与结局关系是目前的研究热点。本研究以开滦队列为例,探讨基于基线暴露状态、随时间变化的暴露信息以及同时控制依时混杂因素时,如何利用Cox比例风险回归及其拓展模型,包括依时Cox回归及边际结构模型,探讨FPG与肝癌的关系,概述并比较了上述拓展模型的基本原理、应用条件、估计结果及结果解释。     

手术类单病种费用影响因素的Cox回归分析

目的为了控制日益增长的医疗费用,通过Cox回归分析找出影响单病种费用的主要因素,为制定有针对性的费用控制政策提供参考依据。方法对3768例手术类单病种病人费用的影响因素进行Cox回归分析。结果提示手术类单病种发生高费用与病人性别、年龄、手术方式、麻醉方式、麻醉检测时间、药占比、病人付款方式密切相关。结论通过COX回归分析,明确了手术类单病种费用的主要影响因素,提出严格筛选病种、结合合理的临床路径和合理的花费开展费用控制工作。     

Efficiency of the logistic regression and Cox proportional hazards models in longitudinal studies

Both logistic regression and Cox proportional hazards models are used widely in longitudinal epidemiologic studies for analysing the relationship between several risk factors and a time-related dichotomous event. The two models yield similar estimates of regression coefficients in studies with short follow-up and low incidence of event occurrence. Further, with just one dichotomous covariate and identical censoring times for all subjects, the asymptotic relative efficiency of the two models is very close to 1 unless the duration of follow-up is extended. We generalize this result to several qualitative or quantitative covariates. This was motivated by the analysis of mortality data from a study where all subjects are followed up during the same fixed period without loss except by death. Logistic and Cox models were applied to these data. Similar results were obtained for the two models in shorter periods of follow-up of five years or less, but not in longer periods of ten years or more, where the survival rate was lower.     

On model specification and selection of the Cox proportional hazards model

Prognosis plays a pivotal role in patient management and trial design. A useful prognostic model should correctly identify important risk factors and estimate their effects. In this article, we discuss several challenges in selecting prognostic factors and estimating their effects using the Cox proportional hazards model. Although a flexible semiparametric form, the Cox's model is not entirely exempt from model misspecification. To minimize possible misspecification, instead of imposing traditional linear assumption, flexible modeling techniques have been proposed to accommodate the nonlinear effect. We first review several existing nonparametric estimation and selection procedures and then present a numerical study to compare the performance between parametric and nonparametric procedures. We demonstrate the impact of model misspecification on variable selection and model prediction using a simulation study and an example from a phase III trial in prostate cancer. Copyright © 2013 John Wiley & Sons, Ltd.     

金昌队列人群痛风发病危险因素的Cox回归分析

目的 了解金昌队列人群痛风的发病状况及影响因素,为制订痛风的防治措施提供科学依据。方法 采用前瞻性队列研究方法,以金昌队列基线资料中未患痛风的人群作为研究对象,于2013年1月24日至2015年11月24日完成随访问卷调查、体格检查和实验室检测。采用Cox 回归模型分析金昌队列人群中痛风发病的影响因素,并用对数线性模型分析各影响因素之间的交互作用。结果 33 153例随访人群中新发痛风病例277例,痛风发病率为0.8%,男性整体上高于女性,但在60岁以后男女性痛风发病率相当。多因素Cox 回归分析结果显示,年龄在40岁以上（40~59岁：HR=2.982, 95%CI：1.503~5.981; 60~91岁：HR=2.588, 95%CI：1.107~6.049）、大量酒精摄入（HR=2.234, 95%CI：1.128~4.427）、肥胖（HR=2.204, 95%CI：1.216~3.997）、糖尿病（HR=2.725, 95%CI：1.500~4.950）和高尿酸（HR=5.963, 95%CI：3.577~9.943）是痛风发病的危险因素,每周豆类摄入 ≥ 250 g（HR=0.528, 95%CI：0.345~0.808）和经常体育锻炼（HR=0.499, 95%CI：0.286~0.869）是痛风发病的保护性因素。对数线性模型交互作用分析结果显示,各影响因素之间存在二阶效应。结论 年龄、豆类、酒类、体育锻炼、肥胖、糖尿病和高尿酸是痛风发病的重要影响因素。培养良好的生活饮食习惯,定期进行体检,有利于预防和控制该职业人群痛风病的发生。     

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.     

Bootstrap investigation of the stability of a Cox regression model

We describe a bootstrap investigation of the stability of a Cox proportional hazards regression model resulting from the analysis of a clinical trial of azathioprine versus placebo in patients with primary biliary cirrhosis. We have considered stability to refer both to the choice of variables included in the model and, more importantly, to the predictive ability of the model. In stepwise Cox regression analyses of 100 bootstrap samples using 17 candidate variables, the most frequently selected variables were those selected in the original analysis, and no other important variable was identified. Thus there was no reason to doubt the model obtained in the original analysis. For each patient in the trial, bootstrap confidence intervals were constructed for the estimated probability of surviving two years. It is shown graphically that these intervals are markedly wider than those obtained from the original model.     

A Bayesian proportional hazards regression model with non-ignorably missing time-varying covariates

Missing covariate data are common in observational studies of time to an event, especially when covariates are repeatedly measured over time. Failure to account for the missing data can lead to bias or loss of efficiency, especially when the data are non-ignorably missing. Previous work has focused on the case of fixed covariates rather than those that are repeatedly measured over the follow-up period, hence, here we present a selection model that allows for proportional hazards regression with time-varying covariates when some covariates may be non-ignorably missing. We develop a fully Bayesian model and obtain posterior estimates of the parameters via the Gibbs sampler in WinBUGS. We illustrate our model with an analysis of post-diagnosis weight change and survival after breast cancer diagnosis in the Long Island Breast Cancer Study Project follow-up study. Our results indicate that post-diagnosis weight gain is associated with lower all-cause and breast cancer-specific survival among women diagnosed with new primary breast cancer. Our sensitivity analysis showed only slight differences between models with different assumptions on the missing data mechanism yet the complete-case analysis yielded markedly different results.     

The consequences of proportional hazards based model selection

For testing the efficacy of a treatment in a clinical trial with survival data, the Cox proportional hazards (PH) model is the well‐accepted, conventional tool. When using this model, one typically proceeds by confirming that the required PH assumption holds true. If the PH assumption fails to hold, there are many options available, proposed as alternatives to the Cox PH model. An important question which arises is whether the potential bias introduced by this sequential model fitting procedure merits concern and, if so, what are effective mechanisms for correction. We investigate by means of simulation study and draw attention to the considerable drawbacks, with regard to power, of a simple resampling technique, the permutation adjustment, a natural recourse for addressing such challenges. We also consider a recently proposed two‐stage testing strategy (2008) for ameliorating these effects. Copyright © 2013 John Wiley & Sons, Ltd.     

Objective Bayesian model selection for Cox regression

There is now a large literature on objective Bayesian model selection in the linear model based on the g‐prior. The methodology has been recently extended to generalized linear models using test‐based Bayes factors. In this paper, we show that test‐based Bayes factors can also be applied to the Cox proportional hazards model. If the goal is to select a single model, then both the maximum a posteriori and the median probability model can be calculated. For clinical prediction of survival, we shrink the model‐specific log hazard ratio estimates with subsequent calculation of the Breslow estimate of the cumulative baseline hazard function. A Bayesian model average can also be employed. We illustrate the proposed methodology with the analysis of survival data on primary biliary cirrhosis patients and the development of a clinical prediction model for future cardiovascular events based on data from the Second Manifestations of ARTerial disease (SMART) cohort study. Cross‐validation is applied to compare the predictive performance with alternative model selection approaches based on Harrell's c‐Index, the calibration slope and the integrated Brier score. Finally, a novel application of Bayesian variable selection to optimal conditional prediction via landmarking is described. Copyright © 2016 John Wiley & Sons, Ltd.