A Software Reliability Model for OSS Including Various Fault Data Based on Proportional Hazard-Rate Model

The software reliability model is the stochastic model to measure the software reliability quantitatively. A Hazard-Rate Model is the well-known one as the typical software reliability model. We propose Hazard-Rate Models Considering Fault Severity Levels (CFSL) for Open Source Software (OSS). The purpose of this research is to make the Hazard-Rate Model considering CFSL adapt to baseline hazard function and 2 kinds of faults data in Bug Tracking System (BTS), i.e., we use the covariate vectors in Cox proportional Hazard-Rate Model. Also, we show the numerical examples by evaluating the performance of our proposed model. As the result, we compare the performance of our model with the Hazard-Rate Model CFSL.

Clinical Study on the Impact of Long-term Survival Quality in 204 Postoperative Patients with Breast Cancer by Cox Proportional Hazard Models

The aim of study was to evaluate clinical characteristics, social support and the association with the prognosis of breast cancer patients. A total of 204 participants were followed from 2003 until the end of 2008. Information about patients with breast cancer was submitted by investigators. Data were analyzed by Cox’s proportional hazard model. The clinical staging of breast cancer we used was the TNM classification. A 'T' score is based upon the size and/or extent of invasion. The 'N' score indicates the extent of lymph node involvement. Age at diagnose was associated with protective factors (HR=0.972;95%CI (0.834-1.130)), T staging (HR=2.075;95%CI (1.424-3.022)), N staging (HR=1.513;95%CI (1.066-2.148)), were associated with risk factor. Two survival graphs of nodes with negative effects by histology and nodes with positive effects by histology was analyzed by log-rank test, there was statistically significant relationship between two survival graphs (χ2 =136.8467, p <.0001). Age at diagnoses, Clinical stage tumor and node could contribute to the development of breast cancer and disease free survival in Chinese women.

A Cox Proportional Hazard Model Approach to Age at First Sexual Intercourse in Nigeria

Early age at first sexual intercourse comes with many negative sexual outcomes namely: having unprotected sex on first sexual intercourse, condom misuse, high rate of sexually transmitted infections (STIs), teenage pregnancy, increased number of sexual partners, etc. In this paper, we considered some socio-demographic and cultural factors and their relationship with age at first sexual intercourse so as to reduce the numerous negative sexual outcomes of early age at first sexual intercourse using the 2018 Nigerian Demographic and Health Survey data. The analysis was made using the Cox proportional hazard model and the Kaplan-Meier plot. The result shows that some respondents started having their first sexual intercourse at the age of 8 years and about 54.4% of the respondents had their first sexual intercourse before age 17 years. The median age of first sexual intercourse is 16 years which implies that about 50% of the respondents had their first sexual intercourse on or before their 16th birthday. Education, religion, region and residence significantly affects the age of first sexual intercourse while circumcision has no significant effect.

Comparison of Cox proportional hazards model,Cox proportional hazards with time-varying coefficients model,and lognormal accelerated failure time model:Application in time to event analysis of melioidosis patients

Objective:To compare the prognostic factors of mortality among melioidosis patients between lognormal accelerated failure time(AFT),Cox proportional hazards(PH),and Cox PH with time-varying coefficient(TVC)models.Methods:A retrospective study was conducted from 2014 to 2019 among 453 patients who were admitted to Hospital Sultanah Bahiyah,Kedah and Hospital Tuanku Fauziah,Perlis in Northern Malaysia due to confirmed-cultured melioidosis.The prognostic factors of mortality from melioidosis were obtained from AFT survival analysis,and Cox’s models and the findings were compared by using the goodness of fit methods.The analyses were done by using Stata SE version 14.0.Results:A total of 242 patients(53.4%)survived.In this study,the median survival time of melioidosis patients was 30.0 days(95%CI 0.0-60.9).Six significant prognostic factors were identified in the Cox PH model and Cox PH-TVC model.In AFT survival analysis,a total of seven significant prognostic factors were identified.The results were found to be only a slight difference between the identified prognostic factors among the models.AFT survival showed better results compared to Cox's models,with the lowest Akaike information criteria and best fitted Cox-snell residuals.Conclusions:AFT survival analysis provides more reliable results and can be used as an alternative statistical analysis for determining the prognostic factors of mortality in melioidosis patients in certain situations.

Cox Proportional Hazard Model for Survival Time of Neonatal Mortality in Neonatal Intensive Care Unit of Hospitals in River Nile State-Sudan

Cox Proportional Hazard model is a popular statistical technique for exploring the relationship between the survival time of neonates and several explanatory variables. It provides an estimate of the study variables’ effect on survival after adjustment for other explanatory variables, and allows us to estimate the hazard (or risk) of death of newborn in NICU of hospitals in River Nile State-Sudan for the period (2018-2020). Study Data represented (neonate gender, mode of delivery, birth type, neonate weight, resident type, gestational age, and survival time). Kaplan-Meier method is used to estimate survival and hazard function for survival times of newborns that have not completed their first month. Of 700 neonates in the study area, 25% of them died during 2018-2020. Variables of interest that had a significant effect on neonatal death by Cox Proportional Hazard Model analysis were neonate weight, resident type, and gestational age. In Cox Proportional Hazard Model analysis all the variables of interest had an effect on neonatal death, but the variables with a significant effect included, weight of neonate, resident type and gestational age.

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。

A Statistical Model with Non-Linear Effects and Non-Proportional Hazards for Breast Cancer Survival Analysis

The Cox proportional hazard model is being used extensively in oncology in studying the relationship between survival times and prognostic factors. The main question that needs to be addressed with respect to the applicability of the Cox PH model is whether the proportional hazard assumption is met. Failure to justify the subject assumption will lead to misleading results. In addition, identifying the correct functional form of the continuous covariates is an important aspect in the development of a Cox proportional hazard model. The purpose of this study is to develop an extended Cox regression model for breast cancer survival data which takes non-proportional hazards and non-linear effects that exist in prognostic factors into consideration. Non-proportional hazards and non-linear effects are detected using methods based on residuals. An extended Cox model with non-linear effects and time-varying effects is proposed to adjust the Cox proportional hazard model. Age and tumor size were found to have nonlinear effects. Progesterone receptor assay status and age violated the proportional hazard assumption in the Cox model. Quadratic effect of age and progesterone receptor assay status had hazard ratio that changes with time. We have introduced a statistical model to overcome the presence of the proportional hazard assumption violation for the Cox proportional hazard model for breast cancer data. The proposed extended model considers the time varying nature of the hazard ratio and non-linear effects of the covariates. Our improved Cox model gives a better insight on the hazard rates associated with the breast cancer risk factors.

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。

基于Cox比例风险模型的交通违法间隔时间研究

为探寻驾驶员因素和时间因素对城市道路机动车交通违法间隔时间的影响,收集机动车驾驶员交通违法的间隔时间和驾驶员年龄、累计积分等数据,清洗后得到包含10个影响因素的基础数据;基于生存分析算法,采用Cox比例风险回归模型,从各变量对再次发生交通违法间隔时间的影响方面,研究驾驶员交通违法的间隔时间差异,以及影响驾驶员发生再次违法的关键因素。结果表明:交通违法时间间隔受年龄、累计积分、月份3个因素显著影响;33~44岁的驾驶者再次违法率最大,大于60岁的驾驶者再次违法率最小;驾驶员累计积分与生存曲线陡峭程度为正相关关系,累计积分与驾驶者再次违法率为正相关关系;相同间隔时间下,11月生存率最高,1月生存率最短。

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。

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。

Analysis of Length of Stay (LOS) Data from the Medical Records of Tertiary Care Hospital in Saudi Arabia for Five Diagnosis Related Groups: Application of Cox Prediction Model

Background: One of the main objectives of hospital managements is to control the length of stay (LOS). Successful control of LOS of inpatients will result in reduction in the cost of care, decrease in nosocomial infections, medication side effects, and better management of the limited number of available patients’ beds. The length of stay (LOS) is an important indicator of the efficiency of hospital management by improving the quality of treatment, and increased hospital profit with more efficient bed management. The purpose of this study was to model the distribution of LOS as a function of patient’s age, and the Diagnosis Related Groups (DRG), based on electronic medical records of a large tertiary care hospital. Materials and Methods: Information related to the research subjects were retrieved from a database of patients admitted to King Faisal Specialist Hospital and Research Center hospital in Riyadh, Saudi Arabia between January 2014 and December 2016. Subjects’ confidential information was masked from the investigators. The data analyses were reported visually, descriptively, and analytically using Cox proportional hazard regression model to predict the risk of long-stay when patients’ age and the DRG are considered as antecedent risk factors. Results: Predicting the risk of long stay depends significantly on the age at admission, and the DRG to which a patient belongs to. We demonstrated the validity of the Cox regression model for the available data as the proportionality assumption is shown to be satisfied. Two examples were presented to demonstrate the utility of the Cox model in this regard.

限制性立方样条Cox比例风险模型在肿瘤预后分析中的应用

目的探讨限制性立方样条Cox比例风险模型在肿瘤预后分析中的应用。方法应用限制性立方样条Cox比例风险模型分析686名原发性乳腺癌患者预后情况,比较限制性立方样条Cox比例风险模型与传统Cox比例风险模型的一致性指数(concordance index,C-index)、净重分类改善指标(net reclassification improvement,NRI)、综合判别指数(integrated discrimination improvement,IDI)以及校准度(calibration)。结果初次手术年龄、阳性淋巴结数、孕激素受体及雌激素受体与乳腺癌复发之间存在非线性关联。当预测时间小于511天时,传统Cox比例风险模型的C-index优于限制性立方样条Cox比例风险模型;当预测时间大于511天时,限制性立方样条Cox比例风险模型的C-index优于传统Cox比例风险模型。限制性立方样条Cox比例风险模型在NR、IDI以及校准度均优于传统Cox比例风险模型,且未出现过度拟合现象,在原发性乳腺癌患者的预后分析中具有较好的预测价值。结论尽管限制性立方样条受到样条函数节点个数及位置的影响,且高次项的存在会影响模型的可解释性,但当随访数据不满足传统Cox比例风险模型的对数线性假定时,限制性立方样条Cox比例风险模型拟合自变量的非线性关系在肿瘤预后分析中仍表现出优势。

原发性肝癌切除术后预后因素的Cox模型分析

目的探讨影响原发性肝癌切除术后预后因素,为其临床综合治疗及判断预后提供依据。方法回顾性分析广西医科大学第一附属医院经根治性手术切除的145例原发性肝癌的临床病理资料,对可能影响预后的各种因素进行单因素分析,将单因素分析中可能影响预后的指标依次引入Cox比例风险模型进行多因素分析。结果全组1、3、5年复发率分别为39.3%、68.3%和82.8%,总生存率分别为76.6%、39.3%和24.1%。单因素分析显示,年龄、肿瘤包膜形成、肿瘤包膜浸润、门脉癌栓、微血管浸润、肿瘤直径和肿瘤早期复发对预后有影响(P<0.05)。多因素分析表明肿瘤早期复发、门脉癌栓、微血管浸润为影响肝癌预后的独立因素。结论原发性肝细胞癌的预后是由多种因素决定的,肿瘤早期复发、门脉癌栓、微血管浸润是影响其预后的最主要因素。及早发现、早期规范的治疗是提高肝癌患者预后的关键。

晚期非小细胞肺癌化疗预后因素的COX回归分析

背景与目的:非小细胞肺癌(NSCLC)是肺癌最常见的组织学类型,晚期非小细胞肺癌患者化疗后预后有较大差异。本研究结合临床资料探讨化疗后晚期非小细胞肺癌患者的独立预后因素。方法:回顾性分析1998年2月—2006年7月间山东省立医院肿瘤中心收治的204例晚期非小细胞肺癌行化疗治疗患者资料,单因素分析采用Kaplan-Meier法及Log-rank时序分析;多因素分析采用COX比例风险回归模型。结果:本组患者整体中位生存时间为12.2个月,1年生存率为54.9%。单因素分析显示TNM分期(P=0.0075)、KPS评分(P=0.0151)、化疗方式(P=0.0325)、化疗周期数(P=0.0298)以及近期疗效(P=0.0061)是影响预后的因素,多因素分析显示KPS评分(P=0.019)、TNM分期(P=0.011)及近期疗效(P=0.009)是影响预后的相关因素。结论:TNM分期、KPS评分及化疗的近期疗效是化疗后晚期非小细胞肺癌患者的独立预后因素。

基于Cox比例风险模型的电力电缆故障影响因素分析

电力电缆故障信息的深层次挖掘可提高对电缆故障影响因素的分析。因此,针对某供电公司10 k V电力电缆故障数据,运用统计学模型—Cox比例风险模型,定量分析了电缆故障影响因素,用以指导电缆采购、施工、运行和维护。为确保数据分析的准确性,提出了电缆数据预处理原则,探讨了合适的样本量大小。运用Cox比例风险模型对电缆故障影响因素进行单因素分析;运用Logistic回归模型确定了电缆故障影响因素类别,并统计计算了各电缆故障影响因素对应的电缆故障率,确定了各影响因素组成元素的相对危险程度,最终证明了Cox比例风险模型分析结果的正确性。结果表明:本体生产厂家M1、附件生产厂家N1、施工单位I3对应的电缆故障率最高分别为0.33、0.29、0.218,企业在进行电缆采购、施工、维护时应着重关注这3家单位。

基于Cox模型的农户对政策性森林保险支付意愿研究

以首批政策性森林保险试点省份湖南、福建、江西三省农户为研究对象,采用多界二分选择文件方式的条件评估法(CVM)共获取364份有效问卷,计算出湖南、福建和江西三省农户对政策性森林保险的支付意愿值分别为3.61元/亩、2.18元/亩、1元/亩;在此基础上,利用Cox比例风险模型分析了影响农户支付意愿值的因素.研究发现:已接受森林保险的农户对目前的支付价格基本满意;其次,家庭规模越大、土壤产量状况越低、林地面积越大、对森林保险的重视程度越高,农户对政策性森林保险的支付意愿就越高,且男性比女性的支付意愿高.最后,提出了相关政策建议:加大政策性森林保险宣传力度;结合各省的实际情况,改善政策性森林保险的制度设计;同时提高保险公司服务水平,加强保险市场的监管工作;加强推进农村金融体系建设.

Cox比例风险模型在原发性肝癌患者凝血功能分析中的应用

目的应用Cox比例风险模型探讨原发性肝癌的临床分期和患者生存期与凝血功能的相关性,为临床治疗和预后提供可靠的评价指标。方法对228例原发性肝癌患者、52例普通肝病患者和52例健康对照者进行了血浆凝血功能检测,并观察肝癌分期与凝血功能的关系;进行随访并收集相关的预后资料。采用Cox比例风险模型分析凝血指标和原发性肝癌晚期患者生存期及血栓性疾病的关系。结果原发性肝癌患者凝血指标变化不仅与健康对照组的差异显著,而且随着肝癌分期程度的加重,凝血功能障碍加剧(P<0.05);D-聚体(D-dimer)、纤维蛋白原降解产物(FDP)、纤维蛋白原(FIB)和血小板(PLT)水平与晚期肝癌患者的远期生存呈负相关。结论凝血功能指标的检测能从多方面及时、准确地反映肝癌患者肝脏的损害程度及危险程度,动态地观察凝血功能指标有利于对肝癌患者的病情进行更好的监测和治疗。

基于变量聚类和COX比例风险模型的企业财务预警研究

以沪深两市A股上市的制造企业为样本,运用变量聚类方法,从32个财务与非财务指标中选取11个指标作为财务预警典型指标,在此基础上,建立COX比例风险模型。通过COX比例风险模型实证研究发现:速动比率、股东权益相对年初增长率、资产负债率为危险因素,增加了发生财务困境的危险性;总资产周转率、独立董事比例为保护因素,降低了发生财务困境的危险性。通过COX比例风险模型的判别能力检验,COX模型针对训练样本和测试样本的综合识别准确率均达到80%以上。研究结果证实,COX比例风险模型具有较好的财务预警判别能力。