Survival Analysis Using Cox Proportional Hazards Regression for Pile Bridge Piles Under Wet Service Conditions

This paper studies the deterioration of bridge substructures utilizing the Long-Term Bridge Performance(LTBP)Program InfoBridge^(TM)and develops a survival model using Cox proportional hazards regression.The survival anal­ysis is based on the National Bridge Inventory(NBI)dataset.The study calculates the survival rate of reinforced and prestressed concrete piles on bridges under marine conditions over a 29-year span(from 1992 to 2020).The state of Maryland is the primary focus of this study,with data from three neighboring regions,the District of Columbia,Vir­ginia,and Delaware to expand the sample size.The data obtained from the National Bridge Inventory are condensed and filtered to acquire the most relevant information for model development.The Cox proportional hazards regres­sion is applied to the condensed NBI data with six parameters:Age,ADT,ADTT,number of spans,span length,and structural length.Two survival models are generated for the bridge substructures:Reinforced and prestressed concrete piles in Maryland and reinforced and prestressed concrete piles in wet service conditions in the District of Columbia,Maryland,Delaware,and Virginia.Results from the Cox proportional hazards regression are used to construct Markov chains to demonstrate the sequence of the deterioration of bridge substructures.The Markov chains can be used as a tool to assist in the prediction and decision-making for repair,rehabilitation,and replacement of bridge piles.Based on the numerical model,the Pile Assessment Matrix Program(PAM)is developed to facilitate the assessment and main­tenance of current bridge structures.The program integrates the NBI database with the inspection and research reports from various states’department of transportation,to serve as a tool for condition state simulation based on mainte­nance or rehabilitation strategies.

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.

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.

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 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.

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.

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.

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.

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。

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。

Cumulative effects of excess high-normal alanine aminotransferase levels in relation to new-onset metabolic dysfunction-associated fatty liver disease in China

BACKGROUND Within the normal range,elevated alanine aminotransferase(ALT)levels are associated with an increased risk of metabolic dysfunction-associated fatty liver disease(MAFLD).AIM To investigate the associations between repeated high-normal ALT measurements and the risk of new-onset MAFLD prospectively.METHODS A cohort of 3553 participants followed for four consecutive health examinations over 4 years was selected.The incidence rate,cumulative times,and equally and unequally weighted cumulative effects of excess high-normal ALT levels(ehALT)were measured.Cox proportional hazards regression was used to analyse the association between the cumulative effects of ehALT and the risk of new-onset MAFLD.RESULTS A total of 83.13%of participants with MAFLD had normal ALT levels.The incidence rate of MAFLD showed a linear increasing trend in the cumulative ehALT group.Compared with those in the low-normal ALT group,the multivariate adjusted hazard ratios of the equally and unequally weighted cumulative effects of ehALT were 1.651[95%confidence interval(CI):1.199-2.273]and 1.535(95%CI:1.119-2.106)in the third quartile and 1.616(95%CI:1.162-2.246)and 1.580(95%CI:1.155-2.162)in the fourth quartile,respectively.CONCLUSION Most participants with MAFLD had normal ALT levels.Long-term high-normal ALT levels were associated with a cumulative increased risk of new-onset MAFLD.

急性硬膜下血肿患者围术期继发颅内高压的Cox比例风险预测模型的建立及评价

目的构建急性硬膜下血肿(ASDH)患者围术期继发颅内高压的Cox比例风险预测模型,并对其效能进行验证。方法回顾性收集78例ASDH患者的临床资料,按围术期继发颅内高压情况将其分为继发组(25例,围术期继发颅内高压)和对照组(53例,围术期未继发颅内高压)。比较2组患者人口统计学指标、合并症、临床生化指标及影像学资料等因素的差异。应用Cox比例风险模型对ASDH患者围术期继发颅内高压的可能影响因素进行多因素分析。建立ASDH患者围术期继发颅内高压的预测模型并测算Harrell′s C指数以评估模型预测的准确度。通过列线图及校准曲线评估该模型预测风险概率与实际风险概率的符合程度。结果全组半年随访率为89.74%(70/78)。继发组年龄、吸烟史、高血压病、糖尿病、术前格拉斯哥昏迷量表(GCS)评分、格拉斯哥预后量表(GOS)评分、复合型血肿、颅内血肿体积、平均动脉压、糖化血红蛋白(HbA1c)、国际标准化比值(INR)、白细胞介素-6(IL-6)、降钙素原(PCT)与对照组比较,差异有统计学意义(P<0.05)。年龄(OR=2.895,95%CI:1.264~6.633,P=0.022)、吸烟史(OR=2.146,95%CI:1.029~4.475,P=0.036)、GOS评分(OR=0.288,95%CI:0.112~0.741,P=0.015)、HbA1c(OR=3.325,95%CI:1.243~8.894,P=0.028)、INR(OR=2.746,95%CI:1.203~6.267,P=0.027)、PCT(OR=3.426,95%CI:1.335~8.795,P=0.019)是ASDH患者围术期继发颅内高压的独立影响因素,Harrell′s C指数为0.812(95%CI:0.789~0.872)。列线图及校准曲线显示实际风险与模型预测风险存在较好的一致性。结论急性硬膜下血肿患者的Cox比例风险模型预测围术期继发颅内高压风险的准确度高,适宜临床推广。

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.

Influence of donor age on liver transplantation outcomes: A multivariate analysis and comparative study

BACKGROUND The growing disparity between the rising demand for liver transplantation(LT)and the limited availability of donor organs has prompted a greater reliance on older liver grafts.Traditionally,utilizing livers from elderly donors has been associated with outcomes inferior to those achieved with grafts from younger donors.By accounting for additional risk factors,we hypothesize that the utili-zation of older liver grafts has a relatively minor impact on both patient survival and graft viability.AIM To evaluate the impact of donor age on LT outcomes using multivariate analysis and comparing young and elderly donor groups.METHODS In the period from April 2013 to December 2018,656 adult liver transplants were performed at the University Hospital Merkur.Several multivariate Cox propor-tional hazards models were developed to independently assess the significance of donor age.Donor age was treated as a continuous variable.The approach involved univariate and multivariate analysis,including variable selection and assessment of interactions and transformations.Additionally,to exemplify the similarity of using young and old donor liver grafts,the group of 87 recipients of elderly donor liver grafts(≥75 years)was compared to a group of 124 recipients of young liver grafts(≤45 years)from the dataset.Survival rates of the two groups were estimated using the Kaplan-Meier method and the log-rank test was used to test the differences between groups.RESULTS Using multivariate Cox analysis,we found no statistical significance in the role of donor age within the constructed models.Even when retained during the entire model development,the donor age's impact on survival remained insignificant and transformations and interactions yielded no substantial effects on survival.Consistent insigni-ficance and low coefficient values suggest that donor age does not impact patient survival in our dataset.Notably,there was no statistical evidence that the five developed models did not adhere to the proportional hazards assumption.When comparing donor age groups,transplantation using elderly grafts showed similar early graft function,similar graft(P=0.92),and patient survival rates(P=0.86),and no significant difference in the incidence of postoperative complications.CONCLUSION Our center's experience indicates that donor age does not play a significant role in patient survival,with elderly livers performing comparably to younger grafts when accounting for other risk factors.

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.

多结局Cox模型在医学中的应用和Stata实现

目的 探讨生存分析中多结局风险比俐模型在实际研究中的应用。方法 采用多结局的比例风险模型,采用偏似然估计和饺正方差估计值,引入新的协变量,同一因素的不同结局的风险函数比(HR)不同。结果通过对实例的分析显示该方法在实际应用中较好地解决了同一因素对应不同结局风险函数比(HR)不同的问题。结论对于不同结局,定义协变量的相应取值,使多结局比例风险模型可估计和推断同一因素对应不同结局的风险函数比。

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 。