SURVIVAL ANALYSIS OF GASTRIC CANCER PATIENTS BY COX REGRESSION MODEL

Mortality rate of gastric cancer is about 20.93/100000 which is the highest malignancy in China. The scientist of our country are at present interested in studying the postoperative survival model by multivariate analysis method just as stepwise regression model. The proportional hazard model initiated by Cox (1972) is more advanced than other regression method which is unneccessary to suppose the distribution of survival time and easy to analyse censoring data (the latter is difficult). This paper presented the first time application of Cox model in survival analysis of gastric cancer in China. The survival analysis system (SAS-Ⅰ) software complied by the author includes multivariate anlysis by Cox model, PV analysis and estimation of survival function which could provide useful information to surgeon for treatment of cancer patients.

Sequential Shrinkage Estimate for COX Regression Models with Uncertain Number of Effective Variables

In the applications of COX regression models, we always encounter data sets that contain too many variables that only a few of them contribute to the model. Therefore, it will waste much more samples to estimate the “noneffective” variables in the inference. In this paper, we use a sequential procedure for constructing the fixed size confidence set for the “effective” parameters to the model based on an adaptive shrinkage estimate such that the “effective” coefficients can be efficiently identified with the minimum sample size. Fixed design is considered for numerical simulation. The strong consistency, asymptotic distributions and convergence rates of estimates under the fixed design are obtained. In addition, the sequential procedure is shown to be asymptotically optimal in the sense of Chow and Robbins (1965).

Cox Regression模型在交通事件持续时间研究中的应用

有效的交通事件管理要求交通管理者全面了解交通事件的各种特征才能准确估计事件持续时间,从而及时地疏导交通拥堵。利用某高速公路应急指挥中心管理系统中记录的近3 a的交通事件持续时间数据,建立Cox Regression模型探索影响持续时间的危险因素并评价其作用强度和方向。研究表明,日夜、报警方式、事件类型、占用车道数、涉及车辆数、涉及死亡、救护车、牵引车、吊车、驳车、涉及货车等11项是交通事件持续时间的显著影响因素,因此,交通管理者对这些因素进行改善可有效提高交通事件管理效率和安全性。

基于Cox Regression的生存分析

本文利用Cox回归模型对137位癌症患者的生存数据进行了分析,并对相应变量进行了检验,从而找出不同癌症患者生存时间长短的原因.

Log-normal censored regression model detecting prognostic factors in gastric cancer:A study of 3018 cases

AIM:To investigate the efficiency of Cox proportional hazard model in detecting prognostic factors for gastric cancer.METHODS:We used the log-normal regression model to evaluate prognostic factors in gastric cancer and compared it with the Cox model.Three thousand and eighteen gastric cancer patients who received a gastrectomy between 1980 and 2004 were retrospectively evaluated.Clinic-pathological factors were included in a log-normal model as well as Cox model.The akaike information criterion (AIC) was employed to compare the efficiency of both models.Univariate analysis indicated that age at diagnosis,past history,cancer location,distant metastasis status,surgical curative degree,combined other organ resection,Borrmann type,Lauren's classification,pT stage,total dissected nodes and pN stage were prognostic factors in both log-normal and Cox models.RESULTS:In the final multivariate model,age at diagnosis,past history,surgical curative degree,Borrmann type,Lauren's classification,pT stage,and pN stage were significant prognostic factors in both log-normal and Cox models.However,cancer location,distant metastasis status,and histology types were found to be significant prognostic factors in log-normal results alone.According to AIC,the log-normal model performed better than the Cox proportional hazard model (AIC value:2534.72 vs 1693.56).CONCLUSION:It is suggested that the log-normal regression model can be a useful statistical model to evaluate prognostic factors instead of the Cox proportional hazard model.

基于贝叶斯Cox风险比例回归的兰州市HIV感染者/AIDS患者死亡影响因素分析

[目的]了解兰州市HIV/AIDS报告病例相关特征的构成情况,分析艾滋病相关死亡的影响因素。[方法]通过收集兰州市2011-2019年HIV/AIDS报告病例信息,采用生存分析方法,构建贝叶斯Cox风险比例回归模型分析影响死亡的相关因素。[结果]本研究共选取2312例HIV/AIDS患者,其中艾滋病相关死亡45例。多因素回归结果显示,患者年龄越大,死亡风险越高;确诊时为AIDS患者的死亡风险是HIV感染者的13.91倍;与未接受CD4检测的患者相比,接受CD4检测的患者的死亡风险降低;进行抗病毒治疗者的死亡风险是未进行抗病毒治疗者的0.22倍。[结论]确诊时年龄、病程阶段、是否接受抗病毒治疗是兰州市HIV/AIDS患者艾滋病相关死亡的影响因素,因此要加强艾滋病相关人群健康教育,提倡早发现、早诊断、早治疗,扩大艾滋病检测与治疗的覆盖面,延长艾滋病患者的生存时间。

Marginal Distribution Plots for Proportional Hazards Models with Time-Dependent Covariates or Time-Varying Regression Coefficients

Given a sample of regression data from (Y, Z), a new diagnostic plotting method is proposed for checking the hypothesis H0: the data are from a given Cox model with the time-dependent covariates Z. It compares two estimates of the marginal distribution FY of Y. One is an estimate of the modified expression of FY under H0, based on a consistent estimate of the parameter under H0, and based on the baseline distribution of the data. The other is the Kaplan-Meier-estimator of FY, together with its confidence band. The new plot, called the marginal distribution plot, can be viewed as a test for testing H0. The main advantage of the test over the existing residual tests is in the case that the data do not satisfy any Cox model or the Cox model is mis-specified. Then the new test is still valid, but not the residual tests and the residual tests often make type II error with a very large probability.

Identifying the dependency pattern of daily rainfall of Dhaka station in Bangladesh using Markov chain and logistic regression model

Bangladesh is a subtropical monsoon climate characterized by wide seasonal variations in rainfall, moderately warm temperatures, and high humidity. Rainfall is the main source of irrigation water everywhere in the Bangladesh where the inhabitants derive their income primarily from farming. Stochastic rainfall models were concerned with the occurrence of wet day and depth of rainfall for different regions to model the daily occurrence of rainfall and achieved satisfactory results around the world. In connection to the Markov chain of different order, logistic regression is conducted to visualize the dependence of current rainfall upon the rainfall of previous two-time period. It had been shown that wet day of the previous two time period compared to the dry day of previous two time period influences positively the wet day of current time period, that is the dependency of dry-wet spell for the occurrence of rain in the rainy season from April to September in the study area. Daily data are collected from meteorological department of about 26 years on rainfall of Dhaka station during the period January 1985-August 2011 to conduct the study. The test result shows that the occurrence of rainfall follows a second order Markov chain and logistic regression also tells that dry followed by dry and wet followed by wet is more likely for the rainfall of Dhaka station and also the model could perform adequately for many applications of rainfall data satisfactorily.

Customer Retention: Behaviour Perspective Model of Ghanaian Telecommunication Industry Using Multinomial Regression Analysis

To stay competitive, the mobile telecommunication companies spend millions of Ghana cedi each year on building long-term relationships with their customers. Marketing managers are constantly challenged with the problem of where to channel the limited resources in order to retain existing customers. This study approaches the customer retention problem in the mobile phone sector from a behavioural perspective, applying the Behavioural Perspective Model as the main analytical framework and further exploits some other factors that influence customer retention. The model includes a set of pre-behaviour and post-behaviour factors to study consumer choice, and explains its relevant drivers in a viable and comprehensive way, grounded in radical behaviourism. Data for the analysis were collected from tertiary students from Accra and Takoradi. Data collected were analysed using the multinomial regression technique. Analysis of the data revealed that the Behaviour setting factor is the only significant element in Behaviour Perspective Model. Further exploitation of behaviour situation revealed that the number of networks a customer uses, previous experience of a customer and customer’s intention are significant factors in determining customer retention in Ghana’s mobile telecommunication industry.

Quasi-Negative Binomial: Properties, Parametric Estimation, Regression Model and Application to RNA-SEQ Data

Background: The Poisson and the Negative Binomial distributions are commonly used to model count data. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial has a variance larger than the mean and therefore both models are appropriate to model over-dispersed count data. Objectives: A new two-parameter probability distribution called the Quasi-Negative Binomial Distribution (QNBD) is being studied in this paper, generalizing the well-known negative binomial distribution. This model turns out to be quite flexible for analyzing count data. Our main objectives are to estimate the parameters of the proposed distribution and to discuss its applicability to genetics data. As an application, we demonstrate that the QNBD regression representation is utilized to model genomics data sets. Results: The new distribution is shown to provide a good fit with respect to the “Akaike Information Criterion”, AIC, considered a measure of model goodness of fit. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling count data exhibiting overdispersion, arising in various fields of scientific investigation such as genomics and biomedicine.

App Store Analysis: Using Regression Model for App Downloads Prediction

App store provides rich information for software vendors and customers to understand the market of mobile applications. However, app store analysis don’t consider some vital factors such as version number, app description and app name currently. In this paper we propose an approach that App Store Analysis can be used to predict app downloads. We use data mining to extract app name and description and app rank information etc. from the Wandoujia App Store and AppCha App Store. We use questionnaire and sentimentanalysis to quantify some app nonnumeric information. We revealed strong correlations app name score, app rank, app rating with app downloads by Spearman’s rank correlation analysis respectively. Finally, we establish a multiple nonlinear regression model which app downloads defined as dependent variable and three relevant attributes defined as independent variable. On average, 59.28 % of apps in Wandoujia App Store and 66.68 % of apps in AppCha App Store can be predicted accurately within threshold which error rate is 25 %. One can observe the more detailed classification of app store, the more accurate for regression modeling to predict app downloads. Our approach can help app developers to notice and optimize the vital factors which influence app downloads.

Stratified Cox Regression Analysis of Survival under CIMAvax^(■)EGF Vaccine

Background: The Center of Molecular Immunology (CIM) is a center in Cuba devoted to the research, development and manufacturing of biotechnological products. CIMAvax?EGF is a vaccine for the treatment of non-small cell lung cancer patients (NSCL). Purpose: The aim of this work is to evaluate the effects of some potential prognostic factors on the overall survival of patients treated with CIMAvax?EGF vaccine, based on data collected in a phase II and a phase III clinical trials. Methods: The stratified Cox regression model is used to evaluate the effects of these prognostic factors, based on separate analysis for each trial, and on the combined data from both trials. Results: Patients with Performance status 0 or 1, with IV stage of tumor and male under 60 years obtain more benefit in terms of overall survival if they receive CIMAvax?EGF. Conclusions: Vaccinated group has a better performance if patients have a performance status 0 or 1, stage IV and age under 60 years. These prognostic factors influence overall survival in a positive way for those patients that received CIMAvax?EGF.

糖尿病肾脏疾病预后影响因素的COX比例风险回归模型分析

目的基于COX比例风险回归模型分析糖尿病肾脏疾病(diabetic kidney disease,DKD)预后的影响因素,为临床早期评估和防治DKD提供科学的依据。方法收集多中心(河南中医药大学第一附属医院、河南中医药大学第三附属医院、河南省中医院及郑州市人民医院)2010—2021年就诊治疗的DKD患者资料,包括一般资料、实验室指标、中医辨证分型及中医药治疗,以肾小球滤过率(eGFR)下降≥50%、血肌酐(Scr)翻倍、DKD 5期、死亡为结局指标,随访其发生时间及情况,利用COX比例风险回归模型分析筛选DKD预后影响因素。结果本研究最终纳入1947例患者,随访时间为4.65(4.557~4.746)年,发生复合终点事件305例(15.67%)。单因素COX回归分析结果表明,不同年龄、DKD病程≥4年、饮酒史、吸烟史、高血压、冠心病、脑血管病、糖尿病足、糖尿病眼病、糖化血红蛋白(HbA1c)、血尿酸(SUA)、Scr、24 h尿蛋白定量(24 h-UTP)、eGFR、湿热血瘀证、脾肾气虚兼湿聚血瘀证、脾肾阳虚兼血瘀证、中药熏洗、服用中药患者DKD预后情况比较,差异有统计学意义(P<0.05)。多因素COX回归分析结果表明,年龄[HR(95%CI)=2.52(1.92,3.30)]、DKD病程[HR(95%CI)=1.62(1.09,2.42)]、吸烟史[HR(95%CI)=1.61(1.13,2.29)]、饮酒史[HR(95%CI)=1.41(1.01,1.95)]、脑血管病[HR(95%CI)=1.33(1.01,1.75)]、糖尿病眼病[HR(95%CI)=1.43(1.13,1.82)]、SUA[HR(95%CI)=1.72(1.26,2.33)]、24 h-UTP[HR(95%CI)=1.48(1.14,1.91)]、脾肾气虚兼湿聚血瘀证[HR(95%CI)=2.22(1.44,3.43)]与DKD发生终点事件的风险关系密切(P<0.05),服用中药[HR(95%CI)=2.57(2.00,3.31)]能够减少终点事件的发生(P<0.05)。结论年龄、DKD病程、吸烟史、饮酒史、脑血管病、糖尿病眼病、SUA、24 h-UTP、脾肾气虚兼湿聚血瘀证是影响DKD患者预后的危险因素,而服用中药治疗为其保护因素。

老年原发性肝癌微波消融术后复发危险因素的多元COX回归分析

目的按探讨老年原发性肝癌微波消融术后复发多元COX回归模型。方法去选择我院于2018年9月至2021年9月收治的原发性肝癌患者183例,均行微波消融术治疗。所有患者均随访至2023年9月,定期门诊、住院随访,于微波消融术后前3个月内,每月进行1次随访,之后以每3个月进行1次随访,随访终点为患者出现肿瘤复发。以完全消融术后肝内重复出现肝癌或者远处发生转移为复发。采用多元COX回归模型分析影响老年原发性肝癌微波消融术后复发危险因素。结果随访末,微波消融术治疗原发性肝癌患者183例中,复发患者39例,复发率为21.31%。单因素COX回归分析,不同性别、不同年龄、家族史、合并肝硬化、Chlid-Pugh分级、AST、ALT、HBVDNA阳性、腹水、脾大和消融次数复发率比较无明显差异(P>0.05);肿瘤直径>3cm复发率高于肿瘤直径≤3cm,AFP>400ng/ml复发率高于AFP≤400ng/ml(P<0.05)。经多元C0X回归模型分析显示,肿瘤直径>3cm和血清AFP>400ng/ml为影响微波消融术后复发危险因素。结论老年原发性肝癌微波消融术后复发率较高,而肿瘤直径和血清AFP为其危险因素.

The burden of upper motor neuron involvement is correlated with the bilateral limb involvement interval in patients with amyotrophic lateral sclerosis:a retrospective observational study

Amyotrophic lateral sclerosis is a rare neurodegenerative disease characterized by the involvement of both upper and lower motor neurons.Early bilateral limb involvement significantly affects patients'daily lives and may lead them to be confined to bed.However,the effect of upper and lower motor neuron impairment and other risk factors on bilateral limb involvement is unclear.To address this issue,we retrospectively collected data from 586 amyotrophic lateral sclerosis patients with limb onset diagnosed at Peking University Third Hospital between January 2020 and May 2022.A univariate analysis revealed no significant differences in the time intervals of spread in different directions between individuals with upper motor neuron-dominant amyotrophic lateral sclerosis and those with classic amyotrophic lateral sclerosis.We used causal directed acyclic graphs for risk factor determination and Cox proportional hazards models to investigate the association between the duration of bilateral limb involvement and clinical baseline characteristics in amyotrophic lateral sclerosis patients.Multiple factor analyses revealed that higher upper motor neuron scores(hazard ratio[HR]=1.05,95%confidence interval[CI]=1.01–1.09,P=0.018),onset in the left limb(HR=0.72,95%CI=0.58–0.89,P=0.002),and a horizontal pattern of progression(HR=0.46,95%CI=0.37–0.58,P<0.001)were risk factors for a shorter interval until bilateral limb involvement.The results demonstrated that a greater degree of upper motor neuron involvement might cause contralateral limb involvement to progress more quickly in limb-onset amyotrophic lateral sclerosis patients.These findings may improve the management of amyotrophic lateral sclerosis patients with limb onset and the prediction of patient prognosis.

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。

基于SPSS因子分析的肝细胞癌预后因素的Cox比例风险回归模型

目的探讨基于SPSS因子分析的肝细胞癌(肝癌)预后因素的Cox比例风险回归模型的可行性。方法采用SPSS13.0统计软件及Microsoft Office Excel 2007对140例肝癌患者以及44个预后因素进行分析,比较传统Cox比例风险回归模型与基于因子分析的Cox比例风险回归模型分析结果的优缺点。结果传统Cox比例风险回归模型中,44个预后因素中经单因素分析后有25个进入多因素分析,多因素分析中有5个因素进入Cox比例风险回归模型方程,其中因素X5在单因素分析和多因素分析中的结论相反,提示预后因素存在多重共线性。因子分析提取了13个公因子,利用提取的公因子进行Cox比例风险回归模型分析,结果有7个公因子进入Cox比例风险回归模型方程,对方程中的公因子重新命名后符合专业实际,便于解释。结论基于SPSS因子分析的肝癌预后因素的Cox比例风险回归模型能很好地解决因素间存在的多重共线性问题。

卵巢癌术后患者Cox比例风险模型的构建与验证

目的基于常规临床资料构建卵巢癌术后患者预后模型,初步探讨影响生存的因素,为预后评估提供参考。方法回顾性分析293例卵巢癌术后患者的临床资料及随访结局,通过Cox比例风险回归法构建预后模型,采用受试者工作特征(ROC)曲线评价模型的预测效能,基于模型分值的P_(25)和P_(75)为界点将具有完整随访结局的患者分为低、中、高风险组,Kaplan-Meier法进行生存分析以验证模型的预后分类能力。结果(1)多因素Cox回归分析显示:年龄、FIGO分期、肿瘤直径、淋巴结转移、远处转移、腹水、术前PLT与患者生存预后独立相关(P<0.05)。以上述指标构建Cox比例风险模型,计算公式:风险指数(risk index,RI)=0.452年龄(50-60)岁+0.799年龄(>60岁)+0.297FIGO分期+0.281淋巴结转移+0.774远处转移+0.473腹水+0.239肿瘤直径+0.402术前PLT(≥300×10^(9)/L)。(2)ROC分析显示:RI预测3年死亡的ROC曲线下面积(AUC)是0.71(95%CI:0.646-0.774),以RI=1.869为截断点(Youden指数最大),预测的敏感性和特异性分别0.754和0.589。RI预测5年死亡的AUC是0.753(95%CI:0.679-0.827),当RI=1.767时,敏感性为0.737,特异性为0.750。(3)生存分析显示,低风险组、中风险组和高风险组的生存曲线无交叉平行下移,三组中位生存时间分别为44(95%CI:35.433-52.567)个月、36(95%CI:29.745-42.255)个月和23(95%CI:13.171-32.829)个月,累积生存率有显著统计学差异(χ^(2)=23.762,P=0.000)。结论本研究构建的Cox比例风险模型对卵巢癌术后患者预后预测具有良好的效能,有助于卵巢癌患者预后分层和高风险人群的识别。

不同MMSE评分下阿尔兹海默病发病风险因素的贝叶斯分位数回归联合模型分析

目的:探讨校正简易精神状态检查(MMSE)评分轨迹后的阿尔兹海默病(AD)发病风险影响因素,阐明不同MMSE评分人群AD发病的风险因素。方法:基于AD神经成像计划数据库收集2005—2016年的随访数据,经筛选后最终纳入425名随访者的随访数据,采用LASSO方法对变量进行筛选;采用贝叶斯分位数回归模型分析MMSE评分在不同分位数上的影响因素,采用Cox模型和贝叶斯分位数回归联合模型方法分析影响AD发病的主要风险因素。结果:经筛选后,纳入的变量包括白蛋白、总胆固醇和血糖浓度等10个变量。贝叶斯分位数回归联合模型的纵向子模型分析,在MMSE评分的不同分位数处,影响MMSE评分轨迹变化的因素相同,均为白蛋白、血糖浓度、年龄、性别、载脂蛋白E4 (APOE4)基因、种族和教育评分。联合模型的Cox回归子模型分析,种族和APOE4基因在所有分位数上均对AD发病有影响,其中APOE4基因在4个分位数上的风险比分别为2.188 (95%CI:1.775,2.620)、1.751 (95%CI:1.422,2.042)、1.706 (95%CI:1.391,2.102)和2.056 (95%CI:1.439,3.206)。总胆固醇水平和家族史仅在部分分位数上对AD发病有影响。结论:不同MMSE评分分布的人群,AD发病的风险因素不同,影响程度也有差异。有APOE4基因和白种人在不同分位数上均是AD发病的风险因素,总胆固醇水平和家族史仅在部分分位数上是AD发病的风险因素。

机器学习模型和Cox回归模型预测食管胃结合部腺癌预后的效能

目的探讨机器学习和传统Cox回归模型在预测食管胃结合部腺癌(AEG)患者术后生存能力中的应用价值。方法选取2015年9月~2020年10月本院收治的287例AEG患者,排除失访及临床资料缺失者,共筛选出203例患者的临床病理资料,经过对数据的赋值等处理,转换成满足R语言分析数据的要求的数据。将203例患者数据使用随机数表法按照3∶1的比例划分为训练集和验证集,对两组数据分别进行Cox比例风险模型构建和4种机器学习模型的构建,绘制出ROC曲线、校准曲线和临床决策曲线(DCA)。为评估4种机器学习模型之间的预测效能,进行机器学习模型的内部验证。通过曲线下面积(AUC)评价模型预测的性能,校准曲线反映模型的拟合情况,并通过DAC判断其临床意义。结果Cox等比例风险回归、极端梯度提升、随机森林、支持向量机、多层感知机验证集中3年生存率的AUC值分别为0.870、0.901、0.791、0.832、0.725,验证集中5年生存率的AUC值分别为0.915、0.916、0.758、0.905、0.737。4种机器学习模型内部验证分别是:极端梯度提升(AUC=0.818)、随机森林(AUC=0.772)、支持向量机(AUC=0.804)、多层感知机(AUC=0.745)。结论机器学习模型对于AEG患者生存率预测的表现优于Cox等比例风险回归模型,尤其在不满足等比例假设或线性回归模型下,并能够包含较多的影响变量。在内部验证中,XGBoost模型的预测效能最好,支持向量机次之,随机森林出现过拟合,多层感知机受数据量影响可能拟合效果较差。