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.

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.

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 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.

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.

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.

Risk prediction model for cutaneous squamous cell carcinoma in adult cardiac allograft recipients

BACKGROUND Heart transplant recipients are at higher risk of developing skin cancer than the general population due to the long-term immunosuppression treatment.Cancer has been reported as one of the major causes of morbidity and mortality for patients after heart transplantation.Among different types of skin cancers,cutaneous squamous cell carcinoma(cSCC)is the most common one,which requires timely screening and better management.AIM To identify risk factors and predict the incidence of cSCC for heart transplant recipients.METHODS We retrospectively analyzed adult heart transplant recipients between 2000 and 2015 extracted from the United Network for Organ Sharing registry.The whole dataset was randomly divided into a derivation set(80%)and a validation set(20%).Uni-and multivariate Cox regression were done to identify significant risk factors associated with the development of cSCC.Receiver operating characteristics curves were generated and area under the curve(AUC)was calculated to assess the accuracy of the prediction model.Based on the selected risk factors,a risk scoring system was developed to stratify patients into different risk groups.A cumulative cSCC-free survival curve was generated using the Kaplan-Meier method for each group,and the log-rank test was done to compare the intergroup cSCC rates.RESULTS There were 23736 heart-transplant recipients during the study period,and 1827 of them have been reported with cSCC.Significant predictors of post-transplant cSCC were older age,male sex,white race,recipient and donor human leukocyte antigen(HLA)mismatch level,malignancy at listing,diagnosis with restrictive myopathy or hypertrophic myopathy,heart re-transplant,and induction therapy with OKT3 or daclizumab.The multivariate model was used to predict the 5-,8-and 10-year incidence of cSCC and respectively provided AUC of 0.79,0.78 and 0.77 in the derivation set and 0.80,0.78 and 0.77 in the validation set.The risk scoring system assigned each patient with a risk score within the range of 0-11,based on which they were stratified into 4 different risk groups.The predicted and observed 5-year probability of developing cSCC match well among different risk groups.In addition,the log-rank test indicated significantly different cSCCfree survival across different groups.CONCLUSION A risk prediction model for cSCC among heart-transplant recipients has been generated for the first time.It offers a c-statistic of≥0.77 in both derivation and validation sets.

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.

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.

Prediction models for development of hepatocellular carcinoma in chronic hepatitis B patients

Chronic hepatitis B(CHB)-related hepatocellular carcinoma(HCC)is a major health problem in Asian-Pacific regions.Antiviral therapy reduces,but does not completely prevent,HCC development.Thus,there is a need for accurate risk prediction to assist prognostication and decisions on the need for antiviral therapy and HCC surveillance.A few risk scores have been developed to predict the occurrence of HCC in CHB patients.Initially,the scores were derived from untreated CHB patients.With the development and extensive clinical application of nucleos(t)ide analog(s)(NA),the number of risk scores based on treated CHB patients has increased gradually.The components included in risk scores may be categorized into host factors and hepatitis B virus factors.Hepatitis activities,hepatitis B virus factors,and even liver fibrosis or cirrhosis are relatively controlled by antiviral therapy.Therefore,variables that are more dynamic during antiviral therapy have since been included in risk scores.However,host factors are more difficult to modify.Most existing scores derived from Asian populations have been confirmed to be accurate in predicting HCC development in CHB patients from Asia,while these scores have not offered excellent predictability in Caucasian patients.These findings support that more relevant variables should be considered to provide individualized predictions that are easily applied to CHB patients of different ethnicities.CHB patients should receive different intensities of HCC surveillance according to their risk category.

Transformation Models for Survival Data Analysis with Applications

When the event of interest never occurs for a proportion of subjects during the study period, survival models with a cure fraction are more appropriate in analyzing this type of data. Considering the non-linear relationship between response variable and covariates, we propose a class of generalized transformation models motivated by Zeng et al. [1] transformed proportional time cure model, in which fractional polynomials are used instead of the simple linear combination of the covariates. Statistical properties of the proposed models are investigated, including identifiability of the parameters, asymptotic consistency, and asymptotic normality of the estimated regression coefficients. A simulation study is carried out to examine the performance of the power selection procedure. The generalized transformation cure rate models are applied to the First National Health and Nutrition Examination Survey Epidemiologic Follow-up Study (NHANES1) for the purpose of examining the relationship between survival time of patients and several risk factors.

Multivariate analysis by Cox Proportional Hazards Model on pro gnoses of patients with bile duct carcinoma after resection

OBJECTIVE: To evaluate the influence of various clinicopathologic factors on the survival of patients with bile duct carcinoma after curative resection. METHODS: A retrospective analysis was performed on 86 cases of bile duct carcinoma treated from January 1981 to September 1995. Fifteen clinicopathologic factors that could possibly influence survival were selected. A multivariate analysis of these individuals was performed using the Cox Proportional Hazards Model. RESULTS: The overall cumulative survival rate was 73% for 1 year, 32% for 3 years and 19% for 5 years. The results of univariate analysis showed that the major significant prognostic factors for influencing survival of these patients were type of histological lesion, lymph node metastasis, pancreatic invasion, duodenal invasion, perineural invasion, macroscopic vessel involvement, resected surgical margin and depth of cancer invasion (P

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.

SICA for Cox's Proportional Hazards Model with a Diverging Number of Parameters

The smooth integration of counting and absolute deviation （SICA） penalized variable selection procedure for high-dimensional linear regression models is proposed by Lv and Fan （2009）. In this article, we extend their idea to Cox＇s proportional hazards （PH） model by using a penalized log partial likelihood with the SICA penalty. The number of the regression coefficients is allowed to grow with the sample size. Based on an approximation to the inverse of the Hessian matrix, the proposed method can be easily carried out with the smoothing quasi-Newton （SQN） algorithm. Under appropriate sparsity conditions, we show that the resulting estimator of the regression coefficients possesses the oracle property. We perform an extensive simulation study to compare our approach with other methods and illustrate it on a well known PBC data for predicting survival from risk factors.

Optimal Generalized Case-Cohort Analysis with Cox's Proportional Hazards Model

Generalized case-cohort design has been proved to be a cost-effective way to enhance the efficiency of large epidemiological cohort. In this article, we propose an inference procedure for estimating the unknown parameters in Cox＇s proportional hazards model in generalized case-cohort design and establish an optimal sample size allocation to achieve the maximum power at a given budget. The finite sample performance of the proposed method is evaluated through simulation studies. The proposed method is applied to a real data set from the National Wilm＇s Tumor Study Group.

The Proportional Hazards Model for Multiple Type Recurrent Gap Times

Recurrent events data and gap times between recurrent events are frequently encountered in many clinical and observational studies,and often more than one type of recurrent events is of interest.In this paper,we consider a proportional hazards model for multiple type recurrent gap times data to assess the effect of covaxiates on the censored event processes of interest.An estimating equation approach is used to obtain the estimators of regression coefficients and baseline cumulative hazard functions.We examine asymptotic properties of the proposed estimators.Finite sample properties of these estimators are demonstrated by simulations.

Jackknifed random weighting for Cox proportional hazards model

The Cox proportional hazards model is the most used statistical model in the analysis of survival time data.Recently,a random weighting method was proposed to approximate the distribution of the maximum partial likelihood estimate for the regression coefficient in the Cox model.This method was shown not as sensitive to heavy censoring as the bootstrap method in simulation studies but it may not be second-order accurate as was shown for the bootstrap approximation.In this paper,we propose an alternative random weighting method based on one-step linear jackknife pseudo values and prove the second accuracy of the proposed method.Monte Carlo simulations are also performed to evaluate the proposed method for fixed sample sizes.

Maximum Likelihood Estimator for the Proportional Hazards Model with Incomplete Information

Right randomly censored data with incomplete infor-mation are frequently met in practice.Although much study about right randomly censored data has been seen in the proportional hazards model,relatively little is known about the inference of regression parameters for right randomly censored data with in-complete information in such model.In particular,theoretical properties of the maximum likelihood estimator of the regression parameters have not been proven yet in that model.In this paper,we show the consistency and asymptotic normality of the maxi-mum likelihood estimator of unknown regression parameters.

High Cycle Fatigue Life Prediction and Reliability Analysis of Aeroengine Blades

Based on the nonlinear continuum damage model （CDM） developed by Chaboehe, a modified model for high cycle fatigue of TC4 alloy was proposed. Unsymmetrical cycle fatigue tests were conducted on rod specimens at room temperature. Then the material parameters needed in the CDM were obtained by the fatigue tests, and the stress distribution of the specimen was calculated by FE method. Compared with the linear damage model （LDM）, the dam- age results and the life prediction of the CDM show a better agreement with the test and they are more precise than the LDM. By applying the CDM developed in this study to the life prediction of aeroengine blades, it is concluded that the root is the most dangerous region of the whole blade and the shortest life is 58 211 cycles. Finally, the Cox propor- tional hazard model of survival analysis was applied to the analysis of the fatigue reliability. The Cox model takes the covariates into consideration, which include diameter, weight, mean stress and tensile strength. The result shows that the mean stress is the only factor that accelerates the fracture process.