Product reliability assessment based on proportional hazard degradation model

In order to evaluate the reliability of long-lifetime products with degradation data, a new proportional hazard degradation model is proposed. By the similarity between time-degradation data and stress-accelerated lifetime, and the failure rate function of degradation data which is assumed to be proportional to the time covariate, the reliability assessment based on a proportional hazard degradation model is realized. The least squares method is used to estimate the model＇s parameters. Based on the failure rate of the degradation data and the proportion function of the known time, the failure rate and the reliability function under the given time and the predetermined failure threshold can be extrapolated. A long life GaAs laser is selected as a case study and its reliability is evaluated. The results show that the proposed method can accurately describe the degradation process and it is effective for the reliability assessment of long lifetime products.

Reliability estimation and remaining useful lifetime prediction for bearing based on proportional hazard model

As the central component of rotating machine,the performance reliability assessment and remaining useful lifetime prediction of bearing are of crucial importance in condition-based maintenance to reduce the maintenance cost and improve the reliability.A prognostic algorithm to assess the reliability and forecast the remaining useful lifetime(RUL) of bearings was proposed,consisting of three phases.Online vibration and temperature signals of bearings in normal state were measured during the manufacturing process and the most useful time-dependent features of vibration signals were extracted based on correlation analysis(feature selection step).Time series analysis based on neural network,as an identification model,was used to predict the features of bearing vibration signals at any horizons(feature prediction step).Furthermore,according to the features,degradation factor was defined.The proportional hazard model was generated to estimate the survival function and forecast the RUL of the bearing(RUL prediction step).The positive results show that the plausibility and effectiveness of the proposed approach can facilitate bearing reliability estimation and RUL prediction.

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.

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.

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.

Optimum design of equivalent accelerated life testing plans based on proportional hazards-proportional odds model

The optimum design of equivalent accelerated life testing plan based on proportional hazards-proportional odds model using D-optimality is presented. The defined equivalent test plan is the test plan that has the same value of the determinant of Fisher information matrix. The equivalent test plan of step stress accelerated life testing （SSALT） to a baseline optimum constant stress accelerated life testing （CSALT） plan is obtained by adjusting the censoring time of SSALT and solving the optimization problem for each case to achieve the same value of the determinant of Fisher information matrix as in the baseline optimum CSALT plan. Numer- ical examples are given finally which demonstrate the equivalent SSALT plan to the baseline optimum CSALT plan reduces almost half of the test time while achieving approximately the same estimation errors of model parameters.

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.

Reliability analysis of web server cluster systems based on proportional hazards model

An approach for web server cluster(WSC)reliability and degradation process analysis is proposed.The reliability process is modeled as a non-homogeneous Markov process(NHMH)composed of several non-homogeneous Poisson processes(NHPPs).The arrival rate of each NHPP corresponds to the system software failure rate which is expressed using Cox s proportional hazards model(PHM)in terms of the cumulative and instantaneous load of the software.The cumulative load refers to software cumulative execution time,and the instantaneous load denotes the rate that the users requests arrive at a server.The result of reliability analysis is a time-varying reliability and degradation process over the WSC lifetime.Finally,the evaluation experiment shows the effectiveness of the proposed approach.

Penalized Empirical Likelihood Via Adaptive LASSO for Cox＇s Proportional Hazards Model

Penalized empirical likelihood inferential procedure is proposed for Cox＇s pro- portional hazards model with adaptive LASSO（ALASSO）. Under reasonable conditions, we show that the proposed method has oracle property and the limiting distribution of a penal- ized empirical likelihood ratio via ALASSO is a chi-square distributions. The advantage of penalized empirical likelihood is illustrated in testing hypothesis and constructing confidence sets by simulation studies and a real example.

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.

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.

Exclusive Hypothesis Testing for Cox's Proportional Hazards Model

Exclusive hypothesis testing is a new and special class of hypothesis testing.This kind of testing can be applied in survival analysis to understand the association between genomics information and clinical information about the survival time.Besides,it is well known that Cox's proportional hazards model is the most commonly used model for regression analysis of failure time.In this paper,the authors consider doing the exclusive hypothesis testing for Cox's proportional hazards model with right-censored data.The authors propose the comprehensive test statistics to make decision,and show that the corresponding decision rule can control the asymptotic TypeⅠerrors and have good powers in theory.The numerical studies indicate that the proposed approach works well for practical situations and it is applied to a set of real data arising from Rotterdam Breast Cancer Data study that motivated this study.

Application of a 2 Parameter Weibull Distribution in Modeling of State Holding Time in HIV/AIDS Transition Dynamics

This study investigates the application of the two-parameter Weibull distribution in modeling state holding times within HIV/AIDS progression dynamics. By comparing the performance of the Weibull-based Accelerated Failure Time (AFT) model, Cox Proportional Hazards model, and Survival model, we assess the effectiveness of these models in capturing survival rates across varying gender, age groups, and treatment categories. Simulated data was used to fit the models, with model identification criteria (AIC, BIC, and R2) applied for evaluation. Results indicate that the AFT model is particularly sensitive to interaction terms, showing significant effects for older age groups (50 - 60 years) and treatment interaction, while the Cox model provides a more stable fit across all age groups. The Survival model displayed variability, with its performance diminishing when interaction terms were introduced, particularly in older age groups. Overall, while the AFT model captures the complexities of interactions in the data, the Cox model’s stability suggests it may be better suited for general analyses without strong interaction effects. The findings highlight the importance of model selection in survival analysis, especially in complex disease progression scenarios like HIV/AIDS.

全身炎症反应指数与缺血性脑卒中患者复发风险的关联性研究

背景全身炎症反应指数(SIRI)是一种较新的炎症生物标志物,其与缺血性脑卒中患者复发的关系尚不明确。目的探讨SIRI水平与缺血性脑卒中患者1年内复发的关联性。方法选取2019年3月—2021年3月在南昌大学第一附属医院、南昌大学第二附属医院、南昌市第二医院和南昌市第三医院住院且确诊为缺血性脑卒中的患者作为研究对象进入队列,并对其随访1年。收集患者入院后48 h内的基线信息、随访过程中的缺血性脑卒中复发情况。采用Cox比例风险回归模型、限制性立方样条、亚组分析探讨SIRI与缺血性脑卒中患者1年内复发之间的关联性。结果本研究纳入了1023例患者,在1年随访期间共107例(10.46%)复发。多因素Cox比例风险回归模型分析结果显示,在调整变量后,SIRI升高是缺血性脑卒中复发的危险因素(HR=1.06,95%CI=1.01~1.10,P<0.05)。将SIRI按四分位数分类时,与Q1亚组(256例)相比,Q4亚组(256例)有较高的缺血性脑卒中复发风险(HR=1.80,95%CI=1.08~3.00,P<0.05)。限制性立方样条分析结果显示,SIRI与缺血性脑卒中复发风险呈J型的剂量-反应关系(PNonlinear=0.025)。进一步按性别、年龄、既往脑卒中、入院时美国国立卫生研究院卒中量表(NIHSS)评分分层进行亚组分析,结果显示,SIRI和入院时NIHSS评分分层存在交互作用(P<0.001),在NIHSS评分为0~1分时,SIRI(HR=1.25,95%CI=1.04~1.51,P=0.020)与缺血性脑卒中复发存在相关关系;在NIHSS评分为5~15分时,SIRI(HR=1.20,95%CI=1.12~1.28,P<0.001)与缺血性脑卒中复发存在相关关系;在上述评分区间SIRI升高与缺血性脑卒中复发风险增加有关。结论较高的SIRI与缺血性脑卒中复发风险增加明显相关。在SIRI与缺血性脑卒中复发之间观察到J型关联,且在NIHSS评分为0~1、5~15分的缺血性脑卒中患者中,SIRI升高与缺血性脑卒中复发风险增加有关。

脑血管病急性期血尿酸/血肌酐比值与脑血管事件复发及死亡的关系:一项前瞻性队列研究

背景脑卒中在世界各地有较高的死亡率和复发率。血尿酸(SUA)是嘌呤代谢的产物,已被认为是心脑血管病的危险因素。血尿酸/血肌酐比值(SUA/Scr)是代表肾功能标准化的SUA,目前有关SUA/Scr在急性脑血管病中的作用仍有争议。目的探讨脑血管病急性期SUA/Scr与脑血管事件复发和死亡的关系。方法本研究为前瞻性队列研究,选取2006年9月—2019年9月天津市环湖医院连续收治的首次发生脑血管事件的13313例患者为研究队列,并对患者进行随访,随访截至2020年9月。随访方式为门诊及电话相结合。随访主要终点事件为全因死亡,次要终点事件为脑血管事件复发、心血管事件复发、其他血管事件发生(如下肢动静脉栓塞)。采用Cox比例风险回归模型探究SUA/Scr与脑血管事件复发与死亡的关系。结果根据脑血管病急性期SUA/Scr四分位数,将患者分为Q1组(SUA/Scr≤3.16,n=3520)、Q2组(3.16<SUA/Scr≤3.94,n=3280)、Q3组(3.94<SUA/Scr≤4.92,n=3270)、Q4组(SUA/Scr>4.92,n=3243)。截至随访结束,774例(5.8%)患者死亡,2064例(15.5%)患者复发脑血管事件。脑血管病急性期SUA/Scr位于Q1~Q4的患者中,男性复发脑血管病的例数依次为302、375、408、337例,女性依次为99、125、169、249例;男性复发脑梗死的例数依次为261、314、345、283例,女性依次为90、101、142、205例;男性复发大动脉粥样硬化型脑梗死的例数依次为154、191、214、183例,女性依次为58、52、45、31例;男性全因死亡的例数依次为165、128、131、88例,女性依次为57、63、62、80例;男性因脑梗死死亡的例数依次为93、72、70、46例,女性依次为31、33、36、44例;男性因大动脉粥样硬化型脑梗死死亡的例数依次为58、52、45、31例,女性依次为17、18、27、24例。调整多项混杂因素后,SUA/Scr位于Q4相较于Q1是男性急性脑梗死复发的影响因素(HR=0.690,95%CI=0.500~0.953,P=0.026);SUA/Scr位于Q4相较于Q1是男性脑梗死亚组患者大动脉粥样硬化型脑梗死复发的影响因素(HR=0.740,95%CI=0.578~0.947,P=0.017)。SUA/Scr位于Q4相较于Q1是男性全因死亡、因脑梗死死亡的影响因素(HR=0.575,95%CI=0.368~0.901,P=0.003;HR=0.610,95%CI=0.353~0.814,P=0.011)。SUA/Scr位于Q3、Q4相较于Q1是男性出院后死亡的影响因素(HR=0.656,95%CI=0.476~0.904,P=0.010;HR=0.582,95%CI=0.409~0.829,P=0.001)。SUA/Scr位于Q4相较于Q1是男性脑梗死亚组患者因大动脉粥样硬化型脑梗死死亡的影响因素(HR=0.580,95%CI=0.386~0.873,P=0.007)。结论一定范围内,脑血管病急性期SUA/Scr升高对男性患者脑血管事件复发及死亡有一定的保护作用,低SUA/Scr与男性大动脉粥样硬化型脑梗死的死亡和复发风险升高有关,但与小动脉闭塞型脑梗死和心源性卒中复发和死亡无关。在女性患者中没有观察到SUA/Scr与脑血管事件复发及死亡的关系。

石家庄市老年人轻度认知障碍的危险因素分析及风险预测模型的构建

目的 识别老年人轻度认知障碍(mild cognitive impairment, MCI)的相关危险因素并建立MCI风险的列线图,为临床早期识别和干预提供参考。方法 选取2021年9月-2022年7月于石家庄市社区体检的322例老年人作为研究对象,采集一般资料、临床检测指标以及日常休闲活动现状,采用单因素分析和多因素Logistic回归分析确定老年人患MCI风险的独立危险因素,建立列线图预测模型,并用受试者工作曲线(receiver operating characteristic, ROC)曲线、拟合优度Hosmer-Lemeshow(H-L)检验以及校准曲线评价列线图模型的区分度和校准度。结果 多因素Logistic回归分析显示,高龄、低教育程度、低认知活动参与以及携带载脂蛋白E(apolipoprotein E,ApoE)ε4风险基因是MCI的独立危险因素。建立列线图预测模型,预测MCI的ROC曲线下面积=0.887(95%CI:0.834~0.939,P<0.001),H-L检验P=0.675。校准曲线Brier值为0.078,绝对误差为0.013,校准曲线极其接近理想参考线。结论 基于年龄、教育程度、认知活动指数、ApoE ε4风险基因四项风险因素的列线图模型能够有效预测石家庄市老年人MCI风险,可进一步开展外部验证研究。

基于比例失效模型的开关柜电缆接头状态评估

电缆接头是开关柜内的薄弱环节,为保证开关柜的稳定运行,需要对电缆接头状态进行准确评估。结合开关柜内电缆接头的实际运行特点,有必要考虑开关柜负载率对电缆接头状态的影响。因此,提出了一种基于比例失效模型的电缆接头状态评估方法。首先利用开关柜电缆接头的历史故障数据和温度数据,并结合开关柜的负载率构建比例失效函数。然后基于比例失效函数定义决策量和告警阈值函数,其中决策量表示电缆接头的综合运行状态,告警阈值函数由电缆接头处于损耗故障期且状态协变量均为危险值时确定;当电缆接头状态决策量的值大于其告警阈值函数值时,此时对电缆接头进行状态告警,并实施检修。最后由仿真分析结果,评估模型判断的结果与实际观测的现象一致,验证了该评估方法的有效性。

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.

肿瘤患者发生利奈唑胺诱导血小板减少的临床预测模型研究

目的:通过建立Cox比例风险回归模型,探究肿瘤患者发生利奈唑胺诱导血小板减少(LIT)的危险因素,并建立相关血小板减少预测风险评分系统。方法:纳入2020年1月至2024年3月某三级甲等医院使用利奈唑胺抗感染治疗的肿瘤患者,回顾性收集相关资料,包括年龄、性别、体重、基础疾病、联合用药信息和实验室检查指标(包括用药前血液学参数、肝肾功能等),以及用药期间和用药后的血小板计数等。根据是否发生血小板减少,将患者分为血小板减少组与非血小板减少组,通过多因素Cox回归分析明确LIT发生的独立危险因素,建立Cox比例风险回归模型并构建肿瘤患者发生LIT的风险评分系统。结果:共纳入85例患者,其中30例发生LIT,LIT发生率为35.3%。血小板减少组与非血小板减少组患者用药前的红细胞计数、红细胞压积、血红蛋白和碱性磷酸酶水平,血小板基线值分级、是否合并脑血管疾病、是否合并低蛋白血症、肾功能分级等指标的差异均有统计学意义(P<0.05)。将单因素分析中P<0.1的变量纳入多因素Cox回归分析,建立Cox比例风险回归模型并构建风险评分系统,结果表明,血小板基线值<50×109/L和合并脑血管疾病是LIT的独立危险因素。通过进一步构建Kaplan-Meier生存曲线验证了该模型能够有效预测LIT的发生风险。结论:肿瘤患者发生LIT的危险因素为血小板基线值<50×109/L和合并脑血管疾病,基于Cox比例风险回归模型的风险评分系统在预测LIT方面具有较高的有效性,有助于临床优化用药方案。

应用Cox's模型研究根治性贲门癌的长期生存因素

目的 :研究影响贲门癌的预后因素。方法 :对 15 8例贲门癌根治术后患者作随访调查 ,应用统计软件对影响其术后的 16项可能因素作如下分析 :(1)单因素分析 Kruskal- wallis检验 ;(2 ) Cox's模型的多因素分析。结果 :确定了淋巴结转移总数、浸润深度、年龄、组织学分型为贲门癌根治术后的预后因子。结论 :根据 Cox's模型筛选的影响贲门癌预后的因子 ,帮助临床医师选择合理治疗方案 。