Retrospective Analysis of Radiofrequency Ablation in Patients with Small Solitary Hepatocellular Carcinoma:Survival Outcomes and Development of a Machine Learning Prognostic Model

Background and Objective The effectiveness of radiofrequency ablation(RFA)in improving long-term survival outcomes for patients with a solitary hepatocellular carcinoma(HCC)measuring 5 cm or less remains uncertain.This study was designed to elucidate the impact of RFA therapy on the survival outcomes of these patients and to construct a prognostic model for patients following RFA.Methods This study was performed using the Surveillance,Epidemiology,and End Results(SEER)database from 2004 to 2017,focusing on patients diagnosed with a solitary HCC lesion≤5 cm in size.We compared the overall survival(OS)and cancer-specific survival(CSS)rates of these patients with those of patients who received hepatectomy,radiotherapy,or chemotherapy or who were part of a blank control group.To enhance the reliability of our findings,we employed stabilized inverse probability treatment weighting(sIPTW)and stratified analyses.Additionally,we conducted a Cox regression analysis to identify prognostic factors.XGBoost models were developed to predict 1-,3-,and 5-year CSS.The XGBoost models were evaluated via receiver operating characteristic(ROC)curves,calibration plots,decision curve analysis(DCA)curves and so on.Results Regardless of whether the data were unadjusted or adjusted for the use of sIPTWs,the 5-year OS(46.7%)and CSS(58.9%)rates were greater in the RFA group than in the radiotherapy(27.1%/35.8%),chemotherapy(32.9%/43.7%),and blank control(18.6%/30.7%)groups,but these rates were lower than those in the hepatectomy group(69.4%/78.9%).Stratified analysis based on age and cirrhosis status revealed that RFA and hepatectomy yielded similar OS and CSS outcomes for patients with cirrhosis aged over 65 years.Age,race,marital status,grade,cirrhosis status,tumor size,and AFP level were selected to construct the XGBoost models based on the training cohort.The areas under the curve(AUCs)for 1,3,and 5 years in the validation cohort were 0.88,0.81,and 0.79,respectively.Calibration plots further demonstrated the consistency between the predicted and actual values in both the training and validation cohorts.Conclusion RFA can improve the survival of patients diagnosed with a solitary HCC lesion≤5 cm.In certain clinical scenarios,RFA achieves survival outcomes comparable to those of hepatectomy.The XGBoost models developed in this study performed admirably in predicting the CSS of patients with solitary HCC tumors smaller than 5 cm following RFA.

Bayesian network-based survival prediction model for patients having undergone post-transjugular intrahepatic portosystemic shunt for portal hypertension

BACKGROUND Portal hypertension(PHT),primarily induced by cirrhosis,manifests severe symptoms impacting patient survival.Although transjugular intrahepatic portosystemic shunt(TIPS)is a critical intervention for managing PHT,it carries risks like hepatic encephalopathy,thus affecting patient survival prognosis.To our knowledge,existing prognostic models for post-TIPS survival in patients with PHT fail to account for the interplay among and collective impact of various prognostic factors on outcomes.Consequently,the development of an innovative modeling approach is essential to address this limitation.AIM To develop and validate a Bayesian network(BN)-based survival prediction model for patients with cirrhosis-induced PHT having undergone TIPS.METHODS The clinical data of 393 patients with cirrhosis-induced PHT who underwent TIPS surgery at the Second Affiliated Hospital of Chongqing Medical University between January 2015 and May 2022 were retrospectively analyzed.Variables were selected using Cox and least absolute shrinkage and selection operator regression methods,and a BN-based model was established and evaluated to predict survival in patients having undergone TIPS surgery for PHT.RESULTS Variable selection revealed the following as key factors impacting survival:age,ascites,hypertension,indications for TIPS,postoperative portal vein pressure(post-PVP),aspartate aminotransferase,alkaline phosphatase,total bilirubin,prealbumin,the Child-Pugh grade,and the model for end-stage liver disease(MELD)score.Based on the above-mentioned variables,a BN-based 2-year survival prognostic prediction model was constructed,which identified the following factors to be directly linked to the survival time:age,ascites,indications for TIPS,concurrent hypertension,post-PVP,the Child-Pugh grade,and the MELD score.The Bayesian information criterion was 3589.04,and 10-fold cross-validation indicated an average log-likelihood loss of 5.55 with a standard deviation of 0.16.The model’s accuracy,precision,recall,and F1 score were 0.90,0.92,0.97,and 0.95 respectively,with the area under the receiver operating characteristic curve being 0.72.CONCLUSION This study successfully developed a BN-based survival prediction model with good predictive capabilities.It offers valuable insights for treatment strategies and prognostic evaluations in patients having undergone TIPS surgery for PHT.

Development of a new Cox model for predicting long-term survival in hepatitis cirrhosis patients underwent transjugular intrahepatic portosystemic shunts

BACKGROUND Transjugular intrahepatic portosystemic shunt(TIPS)placement is a procedure that can effectively treat complications of portal hypertension,such as variceal bleeding and refractory ascites.However,there have been no specific studies on predicting long-term survival after TIPS placement.AIM To establish a model to predict long-term survival in patients with hepatitis cirrhosis after TIPS.METHODS A retrospective analysis was conducted on a cohort of 224 patients who un-derwent TIPS implantation.Through univariate and multivariate Cox regression analyses,various factors were examined for their ability to predict survival at 6 years after TIPS.Consequently,a composite score was formulated,encompassing the indication,shunt reasonability,portal venous pressure gradient(PPG)after TIPS,percentage decrease in portal venous pressure(PVP),indocyanine green retention rate at 15 min(ICGR15)and total bilirubin(Tbil)level.Furthermore,the performance of the newly developed Cox(NDC)model was evaluated in an in-ternal validation cohort and compared with that of a series of existing models.RESULTS The indication(variceal bleeding or ascites),shunt reasonability(reasonable or unreasonable),ICGR15,post-operative PPG,percentage of PVP decrease and Tbil were found to be independent factors affecting long-term survival after TIPS placement.The NDC model incorporated these parameters and successfully identified patients at high risk,exhibiting a notably elevated mortality rate following the TIPS procedure,as observed in both the training and validation cohorts.Additionally,in terms of predicting the long-term survival rate,the performance of the NDC model was significantly better than that of the other four models[Child-Pugh,model for end-stage liver disease(MELD),MELD-sodium and the Freiburg index of post-TIPS survival].CONCLUSION The NDC model can accurately predict long-term survival after the TIPS procedure in patients with hepatitis cirrhosis,help identify high-risk patients and guide follow-up management after TIPS implantation.

Risk factors and survival prediction model establishment for prognosis in patients with radical resection of gallbladder cancer

BACKGROUND Gallbladder cancer(GBC)is the most common malignant tumor of the biliary system,and is often undetected until advanced stages,making curative surgery unfeasible for many patients.Curative surgery remains the only option for long-term survival.Accurate postsurgical prognosis is crucial for effective treatment planning.tumor-node-metastasis staging,which focuses on tumor infiltration,lymph node metastasis,and distant metastasis,limits the accuracy of prognosis.Nomograms offer a more comprehensive and personalized approach by visually analyzing a broader range of prognostic factors,enhancing the precision of treatment planning for patients with GBC.AIM A retrospective study analyzed the clinical and pathological data of 93 patients who underwent radical surgery for GBC at Peking University People's Hospital from January 2015 to December 2020.Kaplan-Meier analysis was used to calculate the 1-,2-and 3-year survival rates.The log-rank test was used to evaluate factors impacting prognosis,with survival curves plotted for significant variables.Single-factor analysis revealed statistically significant differences,and multivariate Cox regression identified independent prognostic factors.A nomogram was developed and validated with receiver operating characteristic curves and calibration curves.Among 93 patients who underwent radical surgery for GBC,30 patients survived,accounting for 32.26%of the sample,with a median survival time of 38 months.The 1-year,2-year,and 3-year survival rates were 83.87%,68.82%,and 53.57%,respectively.Univariate analysis revealed that carbohydrate antigen 19-9 expre-ssion,T stage,lymph node metastasis,histological differentiation,surgical margins,and invasion of the liver,ex-trahepatic bile duct,nerves,and vessels(P≤0.001)significantly impacted patient prognosis after curative surgery.Multivariate Cox regression identified lymph node metastasis(P=0.03),histological differentiation(P<0.05),nerve invasion(P=0.036),and extrahepatic bile duct invasion(P=0.014)as independent risk factors.A nomogram model with a concordance index of 0.838 was developed.Internal validation confirmed the model's consistency in predicting the 1-year,2-year,and 3-year survival rates.CONCLUSION Lymph node metastasis,tumor differentiation,extrahepatic bile duct invasion,and perineural invasion are independent risk factors.A nomogram based on these factors can be used to personalize and improve treatment strategies.

Modelling the Survival of Western Honey Bee Apis mellifera and the African Stingless Bee Meliponula ferruginea Using Semiparametric Marginal Proportional Hazards Mixture Cure Model

Classical survival analysis assumes all subjects will experience the event of interest, but in some cases, a portion of the population may never encounter the event. These survival methods further assume independent survival times, which is not valid for honey bees, which live in nests. The study introduces a semi-parametric marginal proportional hazards mixture cure (PHMC) model with exchangeable correlation structure, using generalized estimating equations for survival data analysis. The model was tested on clustered right-censored bees survival data with a cured fraction, where two bee species were subjected to different entomopathogens to test the effect of the entomopathogens on the survival of the bee species. The Expectation-Solution algorithm is used to estimate the parameters. The study notes a weak positive association between cure statuses (ρ1=0.0007) and survival times for uncured bees (ρ2=0.0890), emphasizing their importance. The odds of being uncured for A. mellifera is higher than the odds for species M. ferruginea. The bee species, A. mellifera are more susceptible to entomopathogens icipe 7, icipe 20, and icipe 69. The Cox-Snell residuals show that the proposed semiparametric PH model generally fits the data well as compared to model that assume independent correlation structure. Thus, the semi parametric marginal proportional hazards mixture cure is parsimonious model for correlated bees survival data.

Development of a model based on the age-adjusted Charlson comorbidity index to predict survival for resected perihilar cholangiocarcinoma

BACKGROUND Perihilar cholangiocarcinoma(pCCA)has a poor prognosis and urgently needs a better predictive method.The predictive value of the age-adjusted Charlson comorbidity index(ACCI)for the long-term prognosis of patients with multiple malignancies was recently reported.However,pCCA is one of the most surgically difficult gastrointestinal tumors with the poorest prognosis,and the value of the ACCI for the prognosis of pCCA patients after curative resection is unclear.AIM To evaluate the prognostic value of the ACCI and to design an online clinical model for pCCA patients.METHODS Consecutive pCCA patients after curative resection between 2010 and 2019 were enrolled from a multicenter database.The patients were randomly assigned 3:1 to training and validation cohorts.In the training and validation cohorts,all patients were divided into low-,moderate-,and high-ACCI groups.Kaplan-Meier curves were used to determine the impact of the ACCI on overall survival(OS)for pCCA patients,and multivariate Cox regression analysis was used to determine the independent risk factors affecting OS.An online clinical model based on the ACCI was developed and validated.The concordance index(C-index),calibration curve,and receiver operating characteristic(ROC)curve were used to evaluate the predictive performance and fit of this model.RESULTS A total of 325 patients were included.There were 244 patients in the training cohort and 81 patients in the validation cohort.In the training cohort,116,91 and 37 patients were classified into the low-,moderate-and high-ACCI groups.The Kaplan-Meier curves showed that patients in the moderate-and high-ACCI groups had worse survival rates than those in the low-ACCI group.Multivariable analysis revealed that moderate and high ACCI scores were independently associated with OS in pCCA patients after curative resection.In addition,an online clinical model was developed that had ideal C-indexes of 0.725 and 0.675 for predicting OS in the training and validation cohorts.The calibration curve and ROC curve indicated that the model had a good fit and prediction performance.CONCLUSION A high ACCI score may predict poor long-term survival in pCCA patients after curative resection.High-risk patients screened by the ACCI-based model should be given more clinical attention in terms of the management of comorbidities and postoperative follow-up.

The impact of genotyping strategies and statistical models on accuracy of genomic prediction for survival in pigs

Background:Survival from birth to slaughter is an important economic trait in commercial pig productions.Increasing survival can improve both economic efficiency and animal welfare.The aim of this study is to explore the impact of genotyping strategies and statistical models on the accuracy of genomic prediction for survival in pigs during the total growing period from birth to slaughter.Results:We simulated pig populations with different direct and maternal heritabilities and used a linear mixed model,a logit model,and a probit model to predict genomic breeding values of pig survival based on data of individual survival records with binary outcomes(0,1).The results show that in the case of only alive animals having genotype data,unbiased genomic predictions can be achieved when using variances estimated from pedigreebased model.Models using genomic information achieved up to 59.2%higher accuracy of estimated breeding value compared to pedigree-based model,dependent on genotyping scenarios.The scenario of genotyping all individuals,both dead and alive individuals,obtained the highest accuracy.When an equal number of individuals(80%)were genotyped,random sample of individuals with genotypes achieved higher accuracy than only alive individuals with genotypes.The linear model,logit model and probit model achieved similar accuracy.Conclusions:Our conclusion is that genomic prediction of pig survival is feasible in the situation that only alive pigs have genotypes,but genomic information of dead individuals can increase accuracy of genomic prediction by 2.06%to 6.04%.

Development of preoperative prognostic models including radiological features for survival of singular nodular HCC patients

Background:Early singular nodular hepatocellular carcinoma(HCC)is an ideal surgical indication in clinical practice.However,almost half of the patients have tumor recurrence,and there is no reliable prognostic prediction tool.Besides,it is unclear whether preoperative neoadjuvant therapy is necessary for patients with early singular nodular HCC and which patient needs it.It is critical to identify the patients with high risk of recurrence and to treat these patients preoperatively with neoadjuvant therapy and thus,to improve the outcomes of these patients.The present study aimed to develop two prognostic models to preoperatively predict the recurrence-free survival(RFS)and overall survival(OS)in patients with singular nodular HCC by integrating the clinical data and radiological features.Methods:We retrospective recruited 211 patients with singular nodular HCC from December 2009 to January 2019 at Eastern Hepatobiliary Surgery Hospital(EHBH).They all met the surgical indications and underwent radical resection.We randomly divided the patients into the training cohort(n=132)and the validation cohort(n=79).We established and validated multivariate Cox proportional hazard models by the preoperative clinicopathologic factors and radiological features for association with RFS and OS.By analyzing the receiver operating characteristic(ROC)curve,the discrimination accuracy of the models was compared with that of the traditional predictive models.Results:Our RFS model was based on HBV-DNA score,cirrhosis,tumor diameter and tumor capsule in imaging.RFS nomogram had fine calibration and discrimination capabilities,with a C-index of 0.74(95%CI:0.68-0.80).The OS nomogram,based on cirrhosis,tumor diameter and tumor capsule in imaging,had fine calibration and discrimination capabilities,with a C-index of 0.81(95%CI:0.74-0.87).The area under the receiver operating characteristic curve(AUC)of our model was larger than that of traditional liver cancer staging system,Korea model and Nomograms in Hepatectomy Patients with Hepatitis B VirusRelated Hepatocellular Carcinoma,indicating better discrimination capability.According to the models,we fitted the linear prediction equations.These results were validated in the validation cohort.Conclusions:Compared with previous radiography model,the new-developed predictive model was concise and applicable to predict the postoperative survival of patients with singular nodular HCC.Our models may preoperatively identify patients with high risk of recurrence.These patients may benefit from neoadjuvant therapy which may improve the patients’outcomes.

A Comparison of Within-Subjects and Between-Subjects Designs in Studies with Discrete-Time Survival Outcomes

Crossover designs are well-known to have major advantages when comparing the effects of various non-curative treatments. We compare efficiencies of several crossover designs along with the Balaam’s design with that of a parallel group design pertaining to longitudinal studies where event time can only be measured in discrete time intervals. With equally sized sequences, the parallel group design results in the greater efficiency if the number of time periods is small. However, the crossover and Balaam’s designs tend to be more efficient as the study duration increases. The degree to which these designs add efficiency depends on the baseline hazard function and effect size. Additionally, we incorporate different cost considerations at the subject level when comparing the designs to determine the most cost-efficient design. Researchers might consider the crossover or Balaam’s design more efficient if the duration of the study is long enough, especially if the costs of applying the baseline treatment are higher.

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.

Survival outcomes of right-lobe living donor liver transplantation for patients with high Model for End-stage Liver Disease scores

BACKGROUND: Controversy exists over whether living donor liver transplantation (LDLT) should be offered to patients with high Model for End-stage Liver Disease (MELD) scores. This study tried to determine whether a high MELD score would result in inferior outcomes of right-lobe LDLT. METHODS: Among 411 consecutive patients who received right-lobe LDLT at our center, 143 were included in this study. The patients were divided into two groups according to their MELD scores: a high-score group (MELD score ≥25; n=75) and a low-score group (MELD score 【25; n=68). Their demographic data and perioperative conditions were compared. Univariable and multivariable analyses were performed to identify risk factors affecting patient survival. RESULTS: In the high-score group, more patients required preoperative intensive care unit admission (49.3% vs 2.9%; P【0.001), mechanical ventilation (21.3% vs 0%; P【0.001), or hemodialysis (13.3% vs 0%; P=0.005); the waiting time before LDLT was shorter (4 vs 66 days; P【0.001); more blood was transfused during operation (7 vs 2 units; P【0.001); patients stayed longer in the intensive care unit (6 vs 3 days; P【0.001) and hospital (21 vs 15 days; P=0.015) after transplantation;more patients developed early postoperative complications (69.3% vs 50.0%; P=0.018); and values of postoperative peak blood parameters were higher. However, the two groups had comparable hospital mortality. Graft survival and patient overall survival at one year (94.7% vs 95.6%; 95.9% vs 96.9%), three years (91.9% vs 92.6%; 93.2% vs 95.3%), and five years (90.2% vs 90.2%; 93.2% vs 95.3%) were also similar between the groups. CONCLUSIONS: Although the high-score group had signifi-cantly more early postoperative complications, the two groups had comparable hospital mortality and similar satisfactory rates of graft survival and patient overall survival. Therefore, a high MELD score should not be a contraindication to right-lobe LDLT if donor risk and recipient benefit are taken into full account.

Nomograms and risk score models for predicting survival in rectal cancer patients with neoadjuvant therapy

BACKGROUND Colorectal cancer is a common digestive cancer worldwide.As a comprehensive treatment for locally advanced rectal cancer(LARC),neoadjuvant therapy(NT)has been increasingly used as the standard treatment for clinical stage II/III rectal cancer.However,few patients achieve a complete pathological response,and most patients require surgical resection and adjuvant therapy.Therefore,identifying risk factors and developing accurate models to predict the prognosis of LARC patients are of great clinical significance.AIM To establish effective prognostic nomograms and risk score prediction models to predict overall survival(OS)and disease-free survival(DFS)for LARC treated with NT.METHODS Nomograms and risk factor score prediction models were based on patients who received NT at the Cancer Hospital from 2015 to 2017.The least absolute shrinkage and selection operator regression model were utilized to screen for prognostic risk factors,which were validated by the Cox regression method.Assessment of the performance of the two prediction models was conducted using receiver operating characteristic curves,and that of the two nomograms was conducted by calculating the concordance index(C-index)and calibration curves.The results were validated in a cohort of 65 patients from 2015 to 2017.RESULTS Seven features were significantly associated with OS and were included in the OS prediction nomogram and prediction model:Vascular_tumors_bolt,cancer nodules,yN,body mass index,matchmouth distance from the edge,nerve aggression and postoperative carcinoembryonic antigen.The nomogram showed good predictive value for OS,with a C-index of 0.91(95%CI:0.85,0.97)and good calibration.In the validation cohort,the C-index was 0.69(95%CI:0.53,0.84).The risk factor prediction model showed good predictive value.The areas under the curve for 3-and 5-year survival were 0.811 and 0.782.The nomogram for predicting DFS included ypTNM and nerve aggression and showed good calibration and a C-index of 0.77(95%CI:0.69,0.85).In the validation cohort,the C-index was 0.71(95%CI:0.61,0.81).The prediction model for DFS also had good predictive value,with an AUC for 3-year survival of 0.784 and an AUC for 5-year survival of 0.754.CONCLUSION We established accurate nomograms and prediction models for predicting OS and DFS in patients with LARC after undergoing NT.

Application of a biochemical and clinical model to predict individual survival in patients with end-stage liver disease

AIM:To investigate the capability of a biochemical and clinical model,BioCliM,in predicting the survival of cirrhotic patients.METHODS:We prospectively evaluated the survival of 172 cirrhotic patients.The model was constructed using clinical(ascites,encephalopathy and variceal bleeding) and biochemical(serum creatinine and serum total bilirubin) variables that were selected from a Cox proportional hazards model.It was applied to estimate 12-,52-and 104-wk survival.The model's calibration using the Hosmer-Lemeshow statistic was computed at 104 wk in a validation dataset.Finally,the model's validity was tested among an independent set of 85 patients who were stratified into 2 risk groups(low risk≤8 and high risk>8).RESULTS:In the validation cohort,all measures of fi t,discrimination and calibration were improved when the biochemical and clinical model was used.The proposed model had better predictive values(c-statistic:0.90,0.91,0.91) than the Model for End-stage Liver Disease(MELD) and Child-Pugh(CP) scores for 12-,52-and 104-wk mortality,respectively.In addition,the Hosmer-Lemeshow(H-L) statistic revealed that the biochemical and clinical model(H-L,4.69) is better calibrated than MELD(H-L,17.06) and CP(H-L,14.23).There were no significant differences between the observed and expected survival curves in the stratified risk groups(low risk,P=0.61;high risk,P=0.77).CONCLUSION:Our data suggest that the proposed model is able to accurately predict survival in cirrhotic patients.

Discrete-time movement model of a group of trains on a rail line with stochastic disturbance

This paper presents a discrete-time model to describe the movements of a group of trains, in which some operational strategies, including traction operation, braking operation and impact of stochastic disturbance, are defined. To show the dynamic characteristics of train traffic flow with stochastic disturbance, some numerical experiments on a railway line are simulated. The computational results show that the discrete-time movement model can well describe the movements of trains on a rail line with the moving-block signalling system. Comparing with the results of no disturbance, it finds that the traffic capacity of the rail line will decrease with the influence of stochastic disturbance. Additionally, the delays incurred by stochastic disturbance can be propagated to the subsequent trains, and then prolong their traversing time on the rail line. It can provide auxiliary information for rescheduling trains When the stochastic disturbance occurs on the railway.

The Survival Probability in Generalized Poisson Risk Model

In this paper we generalize the aggregated premium income process from a constant rate process to a poisson process for the classical compound Poinsson risk model,then for the generalized model and the classical compound poisson risk model ,we respectively get its survival probability in finite time period in case of exponential claim amounts.

Parametric Cure Model versus Proportional Hazards Model in Survival Analysis of Breast Cancer and Other Malignancies

As cancer therapy has progressed dramatically, its goal has shifted toward cure of the disease (curative therapy) rather than prolongation of time to death (life-prolonging therapy). Consequently, the proportion of cured patients (c) has become an important measure of the long-term survival benefit derived from therapy. In 1949, Boag addressed this issue by developing the parametric log-normal cure model, which provides estimates of c and m where m is the mean of log times to death from cancer among uncured patients. Unfortunately, traditional methods based on the proportional hazards model like the Cox regression and log-rank tests cannot provide an estimate of either c or m. Rather, these methods estimate only the differences in hazard between two or more groups. In order to evaluate the long-term validity and usefulness of the parametric cure model compared with the proportional hazards model, we reappraised randomized controlled trials and simulation studies of breast cancer and other malignancies. The results reveal that: 1) the traditional methods fail to distinguish between curative and life-prolonging therapies;2) in certain clinical settings, these methods may favor life-prolonging treatment over curative treatment, giving clinicians a false estimate of the best regimen;3) although the Boag model is less sensitive to differences in failure time when follow-up is limited, it gains power as more failures occur. In conclusion, unless the disease is always fatal, the primary measure of survival benefit should be c rather than m or hazard ratio. Thus, the Boag lognormal cure model provides more accurate and more useful insight into the long-term benefit of cancer treatment than the traditional alternatives.

Establishment and evaluation of a prognostic model for patients with unresectable gastric cancer liver metastases

BACKGROUND Liver metastases(LM)is the primary factor contributing to unfavorable outcomes in patients diagnosed with gastric cancer(GC).The objective of this study is to analyze significant prognostic risk factors for patients with GCLM and develop a reliable nomogram model that can accurately predict individualized prognosis,thereby enhancing the ability to evaluate patient outcomes.AIM To analyze prognostic risk factors for GCLM and develop a reliable nomogram model to accurately predict individualized prognosis,thereby enhancing patient outcome assessment.METHODS Retrospective analysis was conducted on clinical data pertaining to GCLM(type III),admitted to the Department of General Surgery across multiple centers of the Chinese PLA General Hospital from January 2010 to January 2018.The dataset was divided into a development cohort and validation cohort in a ratio of 2:1.In the development cohort,we utilized univariate and multivariate Cox regression analyses to identify independent risk factors associated with overall survival in GCLM patients.Subsequently,we established a prediction model based on these findings and evaluated its performance using receiver operator characteristic curve analysis,calibration curves,and clinical decision curves.A nomogram was created to visually represent the prediction model,which was then externally validated using the validation cohort.RESULTS A total of 372 patients were included in this study,comprising 248 individuals in the development cohort and 124 individuals in the validation cohort.Based on Cox analysis results,our final prediction model incorporated five independent risk factors including albumin levels,primary tumor size,presence of extrahepatic metastases,surgical treatment status,and chemotherapy administration.The 1-,3-,and 5-years Area Under the Curve values in the development cohort are 0.753,0.859,and 0.909,respectively;whereas in the validation cohort,they are observed to be 0.772,0.848,and 0.923.Furthermore,the calibration curves demonstrated excellent consistency between observed values and actual values.Finally,the decision curve analysis curve indicated substantial net clinical benefit.CONCLUSION Our study identified significant prognostic risk factors for GCLM and developed a reliable nomogram model,demonstrating promising predictive accuracy and potential clinical benefit in evaluating patient outcomes.

Robustness Analysis of Discrete-time Indirect Model Reference Adaptive Control with Normalized Adaptive Laws

For a class of discrete-time systems with unmodeled dynamics and bounded disturbance, the design and analysis of robust indirect model reference adaptive control （MRAC） with normalized adaptive law are investigated. The main work includes three parts. Firstly, it is shown that the constructed parameter estimation algorithm not only possesses the same properties as those of traditional estimation algorithms, but also avoids the possibility of division by zero. Secondly, by establishing a relationship between the plant parameter estimate and the controller parameter estimate, some similar properties of the latter are also established. Thirdly, by using the relationship between the normalizing signal and all the signals of the closed-loop system, and some important mathematical tools on discrete-time systems, as in the continuous-time case, a systematic stability and robustness analysis approach to the discrete indirect robust MRAC scheme is developed rigorously.

Probability Prediction in Multistate Survival Models for Patients with Chronic Myeloid Leukaemia

In order to find an appropriate model suitable for a multistate survival experiment, 634 patients with chronic myeloid leukaemia (CML) were selected to illustrate the method of analysis. After transplantation, there were 4 possible situations for a patient: disease free, relapse but still alive, death before relapse, and death after relapse. The last 3 events were considered as treatment failure. The results showed that the risk of death before relapse was higher than that of the relapse, especially in the first year after transplantation with competing-risk method. The result of patients with relapse time less than 12 months was much poor by the Kaplan-Meier method. And the multistate survival models were developed, which were detailed and informative based on the analysis of competing risks and Kaplan-Meier analysis. With the multistate survival models, a further analysis on conditional probability was made for patients who were disease free and still alive at month 12 after transplantation. It was concluded that it was possible for an individual patient to predict the 4 possible probabilities at any time. Also the prognoses for relapse either death or not and death either before or after relapse may be given. Furthermore, the conditional probabilities for patients who were disease free and still alive in a given time after transplantation can be predicted.

Survival probability and ruin probability of a risk model

In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.