Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.

Analysis of risk factors leading to anxiety and depression in patients with prostate cancer after castration and the construction of a risk prediction model

BACKGROUND Cancer patients often suffer from severe stress reactions psychologically,such as anxiety and depression.Prostate cancer(PC)is one of the common cancer types,with most patients diagnosed at advanced stages that cannot be treated by radical surgery and which are accompanied by complications such as bodily pain and bone metastasis.Therefore,attention should be given to the mental health status of PC patients as well as physical adverse events in the course of clinical treatment.AIM To analyze the risk factors leading to anxiety and depression in PC patients after castration and build a risk prediction model.METHODS A retrospective analysis was performed on the data of 120 PC cases treated in Xi'an People's Hospital between January 2019 and January 2022.The patient cohort was divided into a training group(n=84)and a validation group(n=36)at a ratio of 7:3.The patients’anxiety symptoms and depression levels were assessed 2 wk after surgery with the Self-Rating Anxiety Scale(SAS)and the Selfrating Depression Scale(SDS),respectively.Logistic regression was used to analyze the risk factors affecting negative mood,and a risk prediction model was constructed.RESULTS In the training group,35 patients and 37 patients had an SAS score and an SDS score greater than or equal to 50,respectively.Based on the scores,we further subclassified patients into two groups:a bad mood group(n=35)and an emotional stability group(n=49).Multivariate logistic regression analysis showed that marital status,castration scheme,and postoperative Visual Analogue Scale(VAS)score were independent risk factors affecting a patient's bad mood(P<0.05).In the training and validation groups,patients with adverse emotions exhibited significantly higher risk scores than emotionally stable patients(P<0.0001).The area under the curve(AUC)of the risk prediction model for predicting bad mood in the training group was 0.743,the specificity was 70.96%,and the sensitivity was 66.03%,while in the validation group,the AUC,specificity,and sensitivity were 0.755,66.67%,and 76.19%,respectively.The Hosmer-Lemeshow test showed aχ^(2) of 4.2856,a P value of 0.830,and a C-index of 0.773(0.692-0.854).The calibration curve revealed that the predicted curve was basically consistent with the actual curve,and the calibration curve showed that the prediction model had good discrimination and accuracy.Decision curve analysis showed that the model had a high net profit.CONCLUSION In PC patients,marital status,castration scheme,and postoperative pain(VAS)score are important factors affecting postoperative anxiety and depression.The logistic regression model can be used to successfully predict the risk of adverse psychological emotions.

Development and validation of a predictive model for acute-onchronic liver failure after transjugular intrahepatic portosystemic shunt

BACKGROUND Transjugular intrahepatic portosystemic shunt(TIPS)is a cause of acute-onchronic liver failure(ACLF).AIM To investigate the risk factors of ACLF within 1 year after TIPS in patients with cirrhosis and construct a prediction model.METHODS In total,379 patients with decompensated cirrhosis treated with TIPS at Nanjing Drum Tower Hospital from 2017 to 2020 were selected as the training cohort,and 123 patients from Nanfang Hospital were included in the external validation cohort.Univariate and multivariate logistic regression analyses were performed to identify independent predictors.The prediction model was established based on the Akaike information criterion.Internal and external validation were conducted to assess the performance of the model.RESULTS Age and total bilirubin(TBil)were independent risk factors for the incidence of ACLF within 1 year after TIPS.We developed a prediction model comprising age,TBil,and serum sodium,which demonstrated good discrimination and calibration in both the training cohort and the external validation cohort.CONCLUSION Age and TBil are independent risk factors for the incidence of ACLF within 1 year after TIPS in patients with decompensated cirrhosis.Our model showed satisfying predictive value.

Development of a machine learning-based model for predicting risk of early postoperative recurrence of hepatocellular carcinoma

BACKGROUND Surgical resection is the primary treatment for hepatocellular carcinoma(HCC).However,studies indicate that nearly 70%of patients experience HCC recurrence within five years following hepatectomy.The earlier the recurrence,the worse the prognosis.Current studies on postoperative recurrence primarily rely on postoperative pathology and patient clinical data,which are lagging.Hence,developing a new pre-operative prediction model for postoperative recurrence is crucial for guiding individualized treatment of HCC patients and enhancing their prognosis.AIM To identify key variables in pre-operative clinical and imaging data using machine learning algorithms to construct multiple risk prediction models for early postoperative recurrence of HCC.METHODS The demographic and clinical data of 371 HCC patients were collected for this retrospective study.These data were randomly divided into training and test sets at a ratio of 8:2.The training set was analyzed,and key feature variables with predictive value for early HCC recurrence were selected to construct six different machine learning prediction models.Each model was evaluated,and the bestperforming model was selected for interpreting the importance of each variable.Finally,an online calculator based on the model was generated for daily clinical practice.RESULTS Following machine learning analysis,eight key feature variables(age,intratumoral arteries,alpha-fetoprotein,preoperative blood glucose,number of tumors,glucose-to-lymphocyte ratio,liver cirrhosis,and pre-operative platelets)were selected to construct six different prediction models.The XGBoost model outperformed other models,with the area under the receiver operating characteristic curve in the training,validation,and test datasets being 0.993(95%confidence interval:0.982-1.000),0.734(0.601-0.867),and 0.706(0.585-0.827),respectively.Calibration curve and decision curve analysis indicated that the XGBoost model also had good predictive performance and clinical application value.CONCLUSION The XGBoost model exhibits superior performance and is a reliable tool for predicting early postoperative HCC recurrence.This model may guide surgical strategies and postoperative individualized medicine.

Inference for accelerated bivariate dependent competing risks model based on Archimedean copulas under progressive censoring

Dependent competing risks model is a practical model in the analysis of lifetime and failure modes.The dependence can be captured using a statistical tool to explore the re-lationship among failure causes.In this paper,an Archimedean copula is chosen to describe the dependence in a constant-stress accelerated life test.We study the Archimedean copula based dependent competing risks model using parametric and nonparametric methods.The parametric likelihood inference is presented by deriving the general expression of likelihood function based on assumed survival Archimedean copula associated with the model parameter estimation.Combining the nonparametric estimation with progressive censoring and the non-parametric copula estimation,we introduce a nonparametric reliability estimation method given competing risks data.A simulation study and a real data analysis are conducted to show the performance of the estimation methods.

Designing a risk prognosis model based on natural killer cell-linked genes to accurately evaluate the prognosis of gastric cancer

Background:This study was aimed at identifying natural killer(NK)cell-related genes to design a risk prognosis model for the accurate evaluation of gastric cancer(GC)prognosis.Methods:We obtained NK cell-related genes from various databases,followed by Cox regression analysis and molecular typing to identify prognostic genes.Various immune algorithms and enrichment analyses were used to investigate the mutations,immune status,and pathway variations among different genotypes.The key prognostic genes were assessed using the least absolute shrinkage and selection operator(Lasso)regression analysis and univariate Cox regression analysis.Thereafter,the risk score(RS)prognosis model was constructed based on the selected important prognostic genes.A Receiver Operating Characteristics(ROC)curve was plotted for analyzing the robustness of the model.Subsequently,the decision and calibration curves were used for assessing the reliability and prediction accuracy of the proposed model.The‘pRRophetic’R software package was utilized for predicting the half-maximal inhibitory concentration(IC50)of immunotherapy and chemotherapy drugs.Results:We screened 21 prognostic genes and three molecular subtypes and found that the C1 subtype had the worst prognosis.Further,the pathways promoting tumor proliferation,such as epithelial-mesenchymal transition were significantly up-regulated.The results also showed that the macrophages in the M2 stage were significantly infiltrated in the C1 subtype,and there was significant overexpression in the C1 subtype,accompanied by a severe inflammatory reaction.The C1 was highly sensitive to drugs like 5-fluorouracil and paclitaxel.The ROC,calibration curve,and decision curve showed that the risk model was robust and strongly reliable.Conclusion:Overall,our proposed NK cell-related RS model can be used as a more accurate prediction index for GC patients,providing a valuable contribution to personalized medicine.

Preoperative risk modelling for oesophagectomy: A systematic review

BACKGROUND Oesophageal cancer is a frequently observed and lethal malignancy worldwide.Surgical resection remains a realistic option for curative intent in the early stages of the disease.However,the decision to undertake oesophagectomy is significant as it exposes the patient to a substantial risk of morbidity and mortality.Therefore,appropriate patient selection,counselling and resource allocation is important.Many tools have been developed to aid surgeons in appropriate decision-making.AIM To examine all multivariate risk models that use preoperative and intraoperative information and establish which have the most clinical utility.METHODS A systematic review of the MEDLINE,EMBASE and Cochrane databases was conducted from 2000-2020.The search terms applied were((Oesophagectomy)AND(Risk OR predict OR model OR score)AND(Outcomes OR complications OR morbidity OR mortality OR length of stay OR anastomotic leak)).The applied inclusion criteria were articles assessing multivariate based tools using exclusively preoperatively available data to predict perioperative patient outcomes following oesophagectomy.The exclusion criteria were publications that described models requiring intra-operative or post-operative data and articles appraising only univariate predictors such as American Society of Anesthesiologists score,cardiopulmonary fitness or pre-operative sarcopenia.Articles that exclusively assessed distant outcomes such as long-term survival were excluded as were publications using cohorts mixed with other surgical procedures.The articles generated from each search were collated,processed and then reported in accordance with PRISMA guidelines.All risk models were appraised for clinical credibility,methodological quality,performance,validation,and clinical effectiveness.RESULTS The initial search of composite databases yielded 8715 articles which reduced to 5827 following the deduplication process.After title and abstract screening,197 potentially relevant texts were retrieved for detailed review.Twenty-seven published studies were ultimately included which examined twenty-one multivariate risk models utilising exclusively preoperative data.Most models examined were clinically credible and were constructed with sound methodological quality,but model performance was often insufficient to prognosticate patient outcomes.Three risk models were identified as being promising in predicting perioperative mortality,including the National Quality Improvement Project surgical risk calculator,revised STS score and the Takeuchi model.Two studies predicted perioperative major morbidity,including the predicting postoperative complications score and prognostic nutritional index-multivariate models.Many of these models require external validation and demonstration of clinical effectiveness.CONCLUSION Whilst there are several promising models in predicting perioperative oesophagectomy outcomes,more research is needed to confirm their validity and demonstrate improved clinical outcomes with the adoption of these models.

Combined and intraoperative risk modelling for oesophagectomy:A systematic review

BACKGROUND Oesophageal cancer is the eighth most common malignancy worldwide and is associated with a poor prognosis.Oesophagectomy remains the best prospect for a cure if diagnosed in the early disease stages.However,the procedure is associated with significant morbidity and mortality and is undertaken only after careful consideration.Appropriate patient selection,counselling and resource allocation is essential.Numerous risk models have been devised to guide surgeons in making these decisions.AIM To evaluate which multivariate risk models,using intraoperative information with or without preoperative information,best predict perioperative oesophagectomy outcomes.METHODS A systematic review of the MEDLINE,EMBASE and Cochrane databases was undertaken from 2000-2020.The search terms used were[(Oesophagectomy)AND(Model OR Predict OR Risk OR score)AND(Mortality OR morbidity OR complications OR outcomes OR anastomotic leak OR length of stay)].Articles were included if they assessed multivariate based tools incorporating preoperative and intraoperative variables to forecast patient outcomes after oesophagectomy.Articles were excluded if they only required preoperative or any post-operative data.Studies appraising univariate risk predictors such as preoperative sarcopenia,cardiopulmonary fitness and American Society of Anesthesiologists score were also excluded.The review was conducted following the preferred reporting items for systematic reviews and meta-analyses model.All captured risk models were appraised for clinical credibility,methodological quality,performance,validation and clinical effectiveness.RESULTS Twenty published studies were identified which examined eleven multivariate risk models.Eight of these combined preoperative and intraoperative data and the remaining three used only intraoperative values.Only two risk models were identified as promising in predicting mortality,namely the Portsmouth physiological and operative severity score for the enumeration of mortality and morbidity(POSSUM)and POSSUM scores.A further two studies,the intraoperative factors and Esophagectomy surgical Apgar score based nomograms,adequately forecasted major morbidity.The latter two models are yet to have external validation and none have been tested for clinical effectiveness.CONCLUSION Despite the presence of some promising models in forecasting perioperative oesophagectomy outcomes,there is more research required to externally validate these models and demonstrate clinical benefit with the adoption of these models guiding postoperative care and allocating resources.

Development and application of hepatocellular carcinoma risk prediction model based on clinical characteristics and liver related indexes

BACKGROUND Hepatocellular carcinoma(HCC)is difficult to diagnose with poor therapeutic effect,high recurrence rate and has a low survival rate.The survival of patients with HCC is closely related to the stage of diagnosis.At present,no specific serolo-gical indicator or method to predict HCC,early diagnosis of HCC remains a challenge,especially in China,where the situation is more severe.AIM To identify risk factors associated with HCC and establish a risk prediction model based on clinical characteristics and liver-related indicators.METHODS The clinical data of patients in the Affiliated Hospital of North Sichuan Medical College from 2016 to 2020 were collected,using a retrospective study method.The results of needle biopsy or surgical pathology were used as the grouping criteria for the experimental group and the control group in this study.Based on the time of admission,the cases were divided into training cohort(n=1739)and validation cohort(n=467).Using HCC as a dependent variable,the research indicators were incorporated into logistic univariate and multivariate analysis.An HCC risk prediction model,which was called NSMC-HCC model,was then established in training cohort and verified in validation cohort.RESULTS Logistic univariate analysis showed that,gender,age,alpha-fetoprotein,and protein induced by vitamin K absence or antagonist-II,gamma-glutamyl transferase,aspartate aminotransferase and hepatitis B surface antigen were risk factors for HCC,alanine aminotransferase,total bilirubin and total bile acid were protective factors for HCC.When the cut-off value of the NSMC-HCC model joint prediction was 0.22,the area under receiver operating characteristic curve(AUC)of NSMC-HCC model in HCC diagnosis was 0.960,with sensitivity 94.40%and specificity 95.35%in training cohort,and AUC was 0.966,with sensitivity 90.00%and specificity 94.20%in validation cohort.In early-stage HCC diagnosis,the AUC of NSMC-HCC model was 0.946,with sensitivity 85.93%and specificity 93.62%in training cohort,and AUC was 0.947,with sensitivity 89.10%and specificity 98.49%in validation cohort.CONCLUSION The newly NSMC-HCC model was an effective risk prediction model in HCC and early-stage HCC diagnosis.

Predicting lymph node metastasis in colorectal cancer:An analysis of influencing factors to develop a risk model

BACKGROUND Colorectal cancer(CRC)is a significant global health issue,and lymph node metastasis(LNM)is a crucial prognostic factor.Accurate prediction of LNM is essential for developing individualized treatment strategies for patients with CRC.However,the prediction of LNM is challenging and depends on various factors such as tumor histology,clinicopathological features,and molecular characteristics.The most reliable method to detect LNM is the histopathological examination of surgically resected specimens;however,this method is invasive,time-consuming,and subject to sampling errors and interobserver variability.AIM To analyze influencing factors and develop and validate a risk prediction model for LNM in CRC based on a large patient queue.METHODS This study retrospectively analyzed 300 patients who underwent CRC surgery at two Peking University Shenzhen hospitals between January and December 2021.A deep learning approach was used to extract features potentially associated with LNM from primary tumor histological images while a logistic regression model was employed to predict LNM in CRC using machine-learning-derived features and clinicopathological variables as predictors.RESULTS The prediction model constructed for LNM in CRC was based on a logistic regression framework that incorporated machine learning-extracted features and clinicopathological variables.The model achieved high accuracy(0.86),sensitivity(0.81),specificity(0.87),positive predictive value(0.66),negative predictive value(0.94),area under the curve for the receiver operating characteristic(0.91),and a low Brier score(0.10).The model showed good agreement between the observed and predicted probabilities of LNM across a range of risk thresholds,indicating good calibration and clinical utility.CONCLUSION The present study successfully developed and validated a potent and effective risk-prediction model for LNM in patients with CRC.This model utilizes machine-learning-derived features extracted from primary tumor histology and clinicopathological variables,demonstrating superior performance and clinical applicability compared to existing models.The study provides new insights into the potential of deep learning to extract valuable information from tumor histology,in turn,improving the prediction of LNM in CRC and facilitate risk stratification and decision-making in clinical practice.

Risk Assessment of Deep-Water Horizontal X-Tree Installation

Due to the high potential risk and many influencing factors of subsea horizontal X-tree installation,to guarantee the successful completion of sea trials of domestic subsea horizontal X-trees,this paper established a modular risk evaluation model based on a fuzzy fault tree.First,through the analysis of the main process oftree down and combining the Offshore&Onshore Reliability Data(OREDA)failure statistics and the operation procedure and the data provided by the job,the fault tree model of risk analysis of the tree down installation was established.Then,by introducing the natural language of expert comprehensive evaluation and combining fuzzy principles,quantitative analysis was carried out,and the fuzzy number was used to calculate the failure probability of a basic event and the occurrence probability of a top event.Finally,through a sensitivity analysis of basic events,the basic events of top events significantly affected were determined,and risk control and prevention measures for the corresponding high-risk factors were proposed for subsea horizontal X-tree down installation.

Validation and performance of three scoring systems for predicting primary non-function and early allograft failure after liver transplantation

Background: Primary non-function(PNF) and early allograft failure(EAF) after liver transplantation(LT) seriously affect patient outcomes. In clinical practice, effective prognostic tools for early identifying recipients at high risk of PNF and EAF were urgently needed. Recently, the Model for Early Allograft Function(MEAF), PNF score by King's College(King-PNF) and Balance-and-Risk-Lactate(BAR-Lac) score were developed to assess the risks of PNF and EAF. This study aimed to externally validate and compare the prognostic performance of these three scores for predicting PNF and EAF. Methods: A retrospective study included 720 patients with primary LT between January 2015 and December 2020. MEAF, King-PNF and BAR-Lac scores were compared using receiver operating characteristic(ROC) and the net reclassification improvement(NRI) and integrated discrimination improvement(IDI) analyses. Results: Of all 720 patients, 28(3.9%) developed PNF and 67(9.3%) developed EAF in 3 months. The overall early allograft dysfunction(EAD) rate was 39.0%. The 3-month patient mortality was 8.6% while 1-year graft-failure-free survival was 89.2%. The median MEAF, King-PNF and BAR-Lac scores were 5.0(3.5–6.3),-2.1(-2.6 to-1.2), and 5.0(2.0–11.0), respectively. For predicting PNF, MEAF and King-PNF scores had excellent area under curves(AUCs) of 0.872 and 0.891, superior to BAR-Lac(AUC = 0.830). The NRI and IDI analyses confirmed that King-PNF score had the best performance in predicting PNF while MEAF served as a better predictor of EAD. The EAF risk curve and 1-year graft-failure-free survival curve showed that King-PNF was superior to MEAF and BAR-Lac scores for stratifying the risk of EAF. Conclusions: MEAF, King-PNF and BAR-Lac were validated as practical and effective risk assessment tools of PNF. King-PNF score outperformed MEAF and BAR-Lac in predicting PNF and EAF within 6 months. BAR-Lac score had a huge advantage in the prediction for PNF without post-transplant variables. Proper use of these scores will help early identify PNF, standardize grading of EAF and reasonably select clinical endpoints in relative studies.

A risk assessment method considering risk attributes and work safety informational needs and its application

The technological revolution has spawned a new generation of industrial systems,but it has also put forward higher requirements for safety management accuracy,timeliness,and systematicness.Risk assessment needs to evolve to address the existing and future challenges by considering the new demands and advancements in safety management.The study aims to propose a systematic and comprehensive risk assessment method to meet the needs of process system safety management.The methodology first incorporates possibility,severity,and dynamicity(PSD)to structure the“51X”evaluation indicator system,including the inherent,management,and disturbance risk factors.Subsequently,the four-tier(risk point-unit-enterprise-region)risk assessment(RA)mathematical model has been established to consider supervision needs.And in conclusion,the application of the PSD-RA method in ammonia refrigeration workshop cases and safety risk monitoring systems is presented to illustrate the feasibility and effectiveness of the proposed PSD-RA method in safety management.The findings show that the PSD-RA method can be well integrated with the needs of safety work informatization,which is also helpful for implementing the enterprise's safety work responsibility and the government's safety supervision responsibility.

Clinical risk factors for preterm birth and evaluating maternal psychology in the postpartum period

BACKGROUND Although the specific pathogenesis of preterm birth(PTB)has not been thoroughly clarified,it is known to be related to various factors,such as pregnancy complications,maternal socioeconomic factors,lifestyle habits,reproductive history,environmental and psychological factors,prenatal care,and nutritional status.PTB has serious implications for newborns and families and is associated with high mortality and complications.Therefore,the prediction of PTB risk can facilitate early intervention and reduce its resultant adverse consequences.AIM To analyze the risk factors for PTB to establish a PTB risk prediction model and to assess postpartum anxiety and depression in mothers.METHODS A retrospective analysis of 648 consecutive parturients who delivered at Shenzhen Bao’an District Songgang People’s Hospital between January 2019 and January 2022 was performed.According to the diagnostic criteria for premature infants,the parturients were divided into a PTB group(n=60)and a full-term(FT)group(n=588).Puerperae were assessed by the Self-rating Anxiety Scale(SAS)and Self rating Depression Scale(SDS),based on which the mothers with anxiety and depression symptoms were screened for further analysis.The factors affecting PTB were analyzed by univariate analysis,and the related risk factors were identified by logistic regression.RESULTS According to univariate analysis,the PTB group was older than the FT group,with a smaller weight change and greater proportions of women who underwent artificial insemination and had gestational diabetes mellitus(P<0.05).In addition,greater proportions of women with reproductive tract infections and greater white blood cell(WBC)counts(P<0.05),shorter cervical lengths in the second trimester and lower neutrophil percentages(P<0.001)were detected in the PTB group than in the FT group.The PTB group exhibited higher postpartum SAS and SDS scores than did the FT group(P<0.0001),with a higher number of mothers experiencing anxiety and depression(P<0.001).Multivariate logistic regression analysis revealed that a greater maternal weight change,the presence of gestational diabetes mellitus,a shorter cervical length in the second trimester,a greater WBC count,and the presence of maternal anxiety and depression were risk factors for PTB(P<0.01).Moreover,the risk score of the FT group was lower than that of the PTB group,and the area under the curve of the risk score for predicting PTB was greater than 0.9.CONCLUSION This study highlights the complex interplay between postpartum anxiety and PTB,where maternal anxiety may be a potential risk factor for PTB,with PTB potentially increasing the incidence of postpartum anxiety in mothers.In addition,a greater maternal weight change,the presence of gestational diabetes mellitus,a shorter cervical length,a greater WBC count,and postpartum anxiety and depression were identified as risk factors for PTB.

GIS Application in Urban Flood Risk Analysis: Midar as a Case Study

The significance of this study lies in its exploration of the advanced applications of Geographic Information Systems (GIS) in assessing urban flood risks, with a specific focus on Midar, Morocco. This research is pivotal as it showcases that GIS technology is not just a tool for mapping, but a critical component in urban planning and emergency management strategies. By meticulously identifying and mapping flood-prone areas in Midar, the study provides invaluable insights into the potential vulnerabilities of urban landscapes to flooding. Moreover, this research demonstrates the practical utility of GIS in mitigating material losses, a significant concern in flood-prone urban areas. The proactive approach proposed in this study, centered around the use of GIS, aims to safeguard Midar’s population and infrastructure from the devastating impacts of floods. This approach serves as a model for other urban areas facing similar challenges, highlighting the indispensable role of GIS in disaster preparedness and response. Overall, the study underscores the transformative potential of GIS in enhancing urban resilience, making it a crucial tool in the fight against natural disasters like floods.

Navigating breast cancer brain metastasis:Risk factors,prognostic indicators,and treatment perspectives

In this editorial,we comment on the article by Chen et al.We specifically focus on the risk factors,prognostic factors,and management of brain metastasis(BM)in breast cancer(BC).BC is the second most common cancer to have BM after lung cancer.Independent risk factors for BM in BC are:HER-2 positive BC,triplenegative BC,and germline BRCA mutation.Other factors associated with BM are lung metastasis,age less than 40 years,and African and American ancestry.Even though risk factors associated with BM in BC are elucidated,there is a lack of data on predictive models for BM in BC.Few studies have been made to formulate predictive models or nomograms to address this issue,where age,grade of tumor,HER-2 receptor status,and number of metastatic sites(1 vs>1)were predictive of BM in metastatic BC.However,none have been used in clinical practice.National Comprehensive Cancer Network recommends screening of BM in advanced BC only when the patient is symptomatic or suspicious of central nervous system symptoms;routine screening for BM in BC is not recommended in the guidelines.BM decreases the quality of life and will have a significant psychological impact.Further studies are required for designing validated nomograms or predictive models for BM in BC;these models can be used in the future to develop treatment approaches to prevent BM,which improves the quality of life and overall survival.

Storage reliability assessment model based on competition failure of multi-components in missile

The degradation data of multi-components in missile is derived by periodical testing. How to use these data to assess the storage reliability (SR) of the whole missile is a difficult problem in current research. An SR assessment model based on competition failure of multi-components in missile is proposed. By analyzing the missile life profile and its storage failure feature, the key components in missile are obtained and the characteristics voltage is assumed to be its key performance parameter. When the voltage testing data of key components in missile are available, a state space model (SSM) is applied to obtain the whole missile degradation state, which is defined as the missile degradation degree (DD). A Wiener process with the time-scale model (TSM) is applied to build the degradation failure model with individual variability and nonlinearity. The Weibull distribution and proportional risk model are applied to build an outburst failure model with performance degradation effect. Furthermore, a competition failure model with the correlation between degradation failure and outburst failure is proposed. A numerical example with a set of missiles in storage is analyzed to demonstrate the accuracy and superiority of the proposed model.

ON THE EXPECTED DISCOUNTED PENALTY FUNCTION IN A MARKOV-DEPENDENT RISK MODEL WITH CONSTANT DIVIDEND BARRIER

This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.

RUIN PROBABILITY IN A SEMI-MARKOV RISK MODEL WITH CONSTANT INTEREST FORCE AND HEAVY-TAILED CLAIMS

In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.

DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL

We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.