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.

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.

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.

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.

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.

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.

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.

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.

Fibrinogen-to-albumin ratio predicts overall survival of hepatocellular carcinoma

BACKGROUND Fibrinogen-to-albumin ratio(FAR)has been found to be of prognostic significance for several types of malignant tumors.However,less is known about the association between FAR and survival outcomes in hepatocellular carcinoma(HCC)patients.AIM To explore the association between FAR and prognosis and survival in patients with HCC.METHODS A total of 366 histologically confirmed HCC patients diagnosed between 2013 and 2018 in a provincial cancer hospital in southwestern China were retrospectively selected.Relevant data were extracted from the hospital information system.The optimal cutoff for baseline serum FAR measured upon disease diagnosis was established using the receiver operating characteristic(ROC)curve.Univariate and multivariate Cox proportional hazards models were used to determine the crude and adjusted associations between FAR and the overall survival(OS)of the HCC patients while controlling for various covariates.The restricted cubic spline(RCS)was applied to estimate the dose-response trend in the FAR-OS association.RESULTS The optimal cutoff value for baseline FAR determined by the ROC was 0.081.Multivariate Cox proportional hazards model revealed that a lower baseline serum FAR level was associated with an adjusted hazard ratio of 2.43(95%confidence interval:1.87–3.15)in the OS of HCC patients,with identifiable dose-response trend in the RCS.Subgroup analysis showed that this FAR-OS association was more prominent in HCC patients with a lower baseline serum aspartate aminotransferase or carbohydrate antigen 125 level.CONCLUSION Serum FAR is a prominent prognostic indicator for HCC.Intervention measures aimed at reducing FAR might result in survival benefit for HCC patients.

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.

Prognostic Factors in Patients with Pancreatic Carcinoma

Objective: To evaluate the major prognostic factors in patients with pancreatic carcinoma. Methods:113 cases of a particular disease were retrospectively analysed and 9 factors for prognosis were studied by multivaritate analysis with Cox proportional hazards survival model.Survival rate was calculated by Kaplan-Meier estimation. Results:In this group,survival time was 0.1 to 82 months,and the median survival time was 3 months.Overall survival rates at month 6,12,18,36 were 35.6%,20.3%,15.9% and 6.2%,respectively.Multivariate analyses revealed significant prognostic factors as follows:jaundice,metastasis,therapy method and synthetic therapy. Conclusion: The prognosis of pancreatic carcinoma is determined by various factors.Jaundice and metastasis are independent predictors of poor survival.Radical operation and synthetic therapy will improve the prognosis.

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.

Prognostic analysis of patients with thymoma after resection

Objective: To explore the prognostic factors influencing the long term survival rate of thymoma after resection. Methods: Sixty nine patients with thymoma surgically treated in our department from 1973 to 2000 were retrospectively studied. The possible prognostic factors were analyzed by univariate analysis and multivariate analysis with Kaplan Meiter method and Cox proportional hazard model respectively. Results: Overall patients survival rates were 83.3%, 67.4%, 48.3% at 5, 10, 15 years. The significant prognostic factors ( P <0 05) demonstrated by univariate analysis included age, Masaoka staging, WHO histological classification, resection method and Rosai/Levine classification. According to multivariate analysis, the independent prognostic factors included Masaoka stage ( P <0 01), resection method ( P <0 05) and age ( P <0 05). Conclusion: Complete surgical resection of thymomas helps increase the long term survival rate.

Retrospective analysis of clinical characteristics and prognostic factors for pathologic fracture in 44 patients with extremity osteosarcoma

Objective: The aim of this study was to identify the clinical features and prognostic factors associated with extremity osteosarcoma with pathologic fracture. Methods: The clinical records of 271 patients with extremity osteosarcomas were retrospectively reviewed. The data obtained covered the period from October 2003 to May 2012, and included sex, age, tumor site etc. The mean follow-up time was 25.2 months(ranged from 1 to 117). Chi-square method and Kaplan-Meier method were used to compare clinical differences and overall survival between patients with or without pathologic fracture, respectively. The univariate analysis was used to determine the prognostic factors related with survival rate by log-rank test. The multivariate analysis of prognosis was performed by COX proportional hazards regression model. Results: The proportions of patients having a tumor's diameter of 10 cm or more(P = 0.038), locating upper limbs(P = 0.004) and receiving amputation surgery(P = 0.02) were significantly higher with pathological fracture group than without pathological fracture group. The local recurrence rate(P = 0.000) was also significantly higher in the pathological fracture group. The median survival time of patients with or without pathological fracture was 16(95% confidence interval: 14.6–17.4) months and 22(95% confidence interval: 19.8–24.1) months(P = 0.002). The Log-rank univariate analysis indicated that the tumor size, Enneking's surgical staging, Karnofsky performance status(KPS) score, cycles of adjuvant chemotherapy, local recurrence and metastasis were significantly related to overall survival. Multivariate Cox regression analysis revealed KPS score, cycles of adjuvant chemotherapy and metastasis were independent prognostic factors(P < 0.05). Conclusion: Compared with the patients without pathological fracture, a higher proportion of patients receiving amputation surgery or having larger tumor size, humeral osteosarcoma or local recurrence was observed in patients with pathological fracture, and the prognosis of these patients was poor. The independent prognostic factors of extremity osteosarcoma with pathologic fracture were the KPS score, cycles of adjuvant chemotherapy and metastasis.

Study for Prognosis and Survival Rate of Ovarian Cancer

In this paper, we analyze ovarian cancer cases from six hospitals in China, screen the prognostic factors and predict the survival rate. The data has the feature that all the covariates are categorical. We use three methods to estimate the survival rate–the traditional Cox regression, the two-step Cox regression and a method based on conditional inference tree. By comparison, we know that they are all effective and can predict the survival curve reasonably. The analysis results show that the survival rate is determined by a combination of risk factors, where clinical stage is the most important prognosis factor.

An evaluation of treatments and survival rates for pancreatic adenocarcinoma through survival analysis with inverse probability of treatment weighting:a population-based study

Objective:This study conducted inverse probability of treatment weighting(IPTW)survival analysis to examine survival in pancreatic adenocarcinoma patients.Methods:In this population-based study,data from the Surveillance,Epidemiology,and End Results program of the United States were analyzed to identify patients diagnosed with adenocarcinoma of the pancreas 2004 to 2014.Differences in survival rates were examined among patients who underwent pancreatectomy alone,radiotherapy alone,and those who had pancreatectomy plus adjuvant radiotherapy.Kaplan-Meier estimates and Cox proportional hazards models with the IPTW were performed to determine the effect of different treatments on overall and cancer-specific survival.This study was approved by the Ethics Review Board of Weifang Medical University.Results:A total of 8191 patients were included,with 3409 taking pancreatectomy only,2865 taking radiotherapy only,and 1917 taking pancreatectomy plus adjuvant radiotherapy.Patients who received surgery plus adjuvant radiotherapy had statistically a higher survival rate than those who received the other 2 treatments.Survival analysis with the IPTW for the 3 different groups showed that the difference in median overall survival time among these patient groups was significant.Conclusion:Using IPTW survival analysis,the present study shows that surgery with adjuvant radiotherapy is significantly associated with improved overall and cancer-specific survival among patients with pancreatic adenocarcinoma.