Using the so-called martingale difference correlation(MDC), we propose a novel censoredconditional-quantile screening approach for ultrahigh-dimensional survival data with heterogeneity(which is often present in such ...Using the so-called martingale difference correlation(MDC), we propose a novel censoredconditional-quantile screening approach for ultrahigh-dimensional survival data with heterogeneity(which is often present in such data). By incorporating a weighting scheme, this method is a natural extension of MDCbased conditional quantile screening, as considered by Shao and Zhang(2014), to handle ultrahigh-dimensional survival data. The proposed screening procedure has a sure-screening property under certain technical conditions and an excellent capability of detecting the nonlinear relationship between independent and censored dependent variables. Both simulation results and an analysis of real data demonstrate the effectiveness of the new censored conditional quantile-screening procedure.展开更多
The main goal of this research is to assess the impact of race, age at diagnosis, sex, and phenotype on the incidence and survivability of acute lymphocytic leukemia (ALL) among patients in the United States. By takin...The main goal of this research is to assess the impact of race, age at diagnosis, sex, and phenotype on the incidence and survivability of acute lymphocytic leukemia (ALL) among patients in the United States. By taking these factors into account, the study aims to explore how existing cancer registry data can aid in the early detection and effective treatment of ALL in patients. Our hypothesis was that statistically significant correlations exist between race, age at which patients were diagnosed, sex, and phenotype of the ALL patients, and their rate of incidence and survivability data were evaluated using SEER*Stat statistical software from National Cancer Institute. Analysis of the incidence data revealed that a higher prevalence of ALL was among the Caucasian population. The majority of ALL cases (59%) occurred in patients aged between 0 to 19 years at the time of diagnosis, and 56% of the affected individuals were male. The B-cell phenotype was predominantly associated with ALL cases (73%). When analyzing survivability data, it was observed that the 5-year survival rates slightly exceeded the 10-year survival rates for the respective demographics. Survivability rates of African Americans patients were the lowest compared to Caucasian, Asian, Pacific Islanders, Alaskan Native, Native Americans and others. Survivability rates progressively decreased for older patients. Moreover, this study investigated the typical treatment methods applied to ALL patients, mainly comprising chemotherapy, with occasional supplementation of radiation therapy as required. The study demonstrated the considerable efficacy of chemotherapy in enhancing patients’ chances of survival, while those who remained untreated faced a less favorable prognosis from the disease. Although a significant amount of data and information exists, this study can help doctors in the future by diagnosing patients with certain characteristics. It will further assist the health care professionals in screening potential patients and early detection of cases. This could also save the lives of elderly patients who have a higher mortality rate from this disease.展开更多
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 s...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.展开更多
Lung cancer is the most common cancer type worldwide and has the highest and second highest mortality rate for men and women respectively in Germany.Yet,the role of comorbid illnesses in lung cancer patient prognosis ...Lung cancer is the most common cancer type worldwide and has the highest and second highest mortality rate for men and women respectively in Germany.Yet,the role of comorbid illnesses in lung cancer patient prognosis is still debated.We analyzed administrative claims data from one of the largest statutory health insurance(SHI)funds in Germany,covering close to 9 million people(11%of the national population);observation period was from 2005 to 2019.Lung cancer patients and their concomitant diseases were identified by ICD-10-GM codes.Comorbidities were classified according to the Charlson Comorbidity Index(CCI).Incidence,comorbidity prevalence and survival are estimated considering sex,age at diagnosis,and place of residence.Kaplan Meier curves with 95%confidence intervals were built in relation to common comorbidities.We identified 70,698 lung cancer incident cases in the sample.Incidence and survival figures are comparable to official statistics in Germany.Most prevalent comorbidities are chronic obstructive pulmonary disease(COPD)(36.7%),followed by peripheral vascular disease(PVD)(18.7%),diabetes without chronic complications(17.4%),congestive heart failure(CHF)(16.5%)and renal disease(14.7%).Relative to overall survival,lung cancer patients with CHF,cerebrovascular disease(CEVD)and renal disease are associated with largest drops in survival probabilities(9%or higher),while those with PVD and diabetes without chronic complications with moderate drops(7%or lower).The study showed a negative association between survival and most common comorbidities among lung cancer patients,based on a large sample for Germany.Further research needs to explore the individual effect of comorbidities disentangled from that of other patient characteristics such as cancer stage and histology.展开更多
To the Editor:A large international study has been recently published focusing on the combination of morphological aspects and alpha-fetoprotein(AFP)as predictors of survival in patients with hepatocellular cancer(HCC...To the Editor:A large international study has been recently published focusing on the combination of morphological aspects and alpha-fetoprotein(AFP)as predictors of survival in patients with hepatocellular cancer(HCC)treated with liver transplantation(LT)[1].As a matter of fact,morphology and biology represent the two sides of the same展开更多
The object of our present study is to develop a piecewise constant hazard model by using an Artificial Neural Network (ANN) to capture the complex shapes of the hazard functions, which cannot be achieved with conventi...The object of our present study is to develop a piecewise constant hazard model by using an Artificial Neural Network (ANN) to capture the complex shapes of the hazard functions, which cannot be achieved with conventional survival analysis models like Cox proportional hazard. We propose a more convenient approach to the PEANN created by Fornili et al. to handle a large amount of data. In particular, it provides much better prediction accuracies over both the Poisson regression and generalized estimating equations. This has been demonstrated with lung cancer patient data taken from the Surveillance, Epidemiology and End Results (SEER) program. The quality of the proposed model is evaluated by using several error measurement criteria.展开更多
To explore the influencing factors of survival time of patients with heart failure, a total of 1789 patients with heart failure were collected from Shanghai Shuguang Hospital. The Cox proportional hazards model and th...To explore the influencing factors of survival time of patients with heart failure, a total of 1789 patients with heart failure were collected from Shanghai Shuguang Hospital. The Cox proportional hazards model and the mixed effects Cox model were used to analyze the factors on survival time of patients. The results of Cox proportional hazards model showed that age (RR = 1.32), hypertension (RR = 0.67), ARB (RR = 0.55), diuretic (RR = 1.48) and antiplatelet (RR = 0.53) have significant impacts on the survival time of patients. The results of mixed effects Cox model showed that age (RR = 1.16), hypertension (RR = 0.61), lung infection (RR = 1.43), ARB (RR = 0.64), β-blockers (RR = 0.77) and antiplatelet (RR = 0.69) have a significant impact on the survival time of patients. The results are consistent with the covariates age, hypertension, ARB and antiplatelet but inconsistent with the covariates lung infection and β-blockers.展开更多
Background:In the past decade,many researchers focused on to robot-assisted surgery.However,on long-term outcomes for patients with early-stage non-small cell lung cancer(NSCLC),whether the robotic procedure is superi...Background:In the past decade,many researchers focused on to robot-assisted surgery.However,on long-term outcomes for patients with early-stage non-small cell lung cancer(NSCLC),whether the robotic procedure is superior to video-assisted thoracic surgery(VATS) and thoracotomy is unclear.Nonetheless,in the article titled "Long-term survival based on the surgical approach to lobectomy for clinical stage I non-small cell lung cancer:comparison of robotic,video assisted thoracic surgery,and thoracotomy lobectomy" by Yang et al.that was recently published in Annals of Surgery,the authors provided convincing evidence that the robotic procedure results in similar long-term survival as compared with VATS and thoracotomy.Minimally invasive procedures typically result in shorter lengths of hospital stay,and the robotic procedure in particular results in superior lymph node assessment.Main body:Our propensity score-matched study generated high-quality data.Based on our findings,we see promise in expanding patient access to robotic lung resections.In this study,propensity score matching minimized the bias involved between groups.Nevertheless,due to its retrospective nature,bias may still exist.Currently,the concept of rapid rehabilitation is widely accepted,and it is very difficult to set up a randomized controlled trial to compare robotic,VATS,and thoracotomy procedures for the treatment of NSCLC.Therefore,to overcome this limitation and to minimize bias,the best approach is to use a registry and prospectively collected,propensity score-matched data.Conclusions:Robotic lung resections result in similar long-term survival as compared with VATS and thoracotomy.Robot-assisted and VATS procedures are associated with short lengths of hospital stay,and the robotic procedure in particular results in superior lymph node assessment.Considering the alarming increase in the incidence of lung cancer in China,a nationwide database of prospectively collected data available for clinical research would be especially important.展开更多
With the increasing impact of climate change,carbon emissions and removals have become major issues.Forests are major carbon pools,and forest fires are an essential part of the carbon cycle.This study introduces a mod...With the increasing impact of climate change,carbon emissions and removals have become major issues.Forests are major carbon pools,and forest fires are an essential part of the carbon cycle.This study introduces a model for estimating the detailed actual CO_(2)removal in burned forests using burn severity and tree survivability.Actual CO_(2)removal was estimated from empirical yield tables without using the standard carbon removal provided by the national inventory.The primary CO_(2)calculation method followed the guidelines of the International Panel on Climate Change.The burn severity was mapped using Sentinel-2 multispectral instrument data,and the survivability of each forest type was estimated according to burn severity.The survivability was applied to the pre-fire CO_(2)removal of each forest to estimate post-fire CO_(2)removal.In our case study,the burned forest area was 1,034 ha,and the CO_(2)removal before the fire was 8,615.3t/year.After the fire,removal decreased by 81.2%to 1,618.4 t/yr.In particular,the decrease in coniferous forests was high,more than 86%.The lack of survivability data on burned trees was a major limitation of our study.Systematically accumulating field monitoring data of post-fire forests will be necessary for future research and could serve as a reference for devising immediate countermeasures against forest fires.展开更多
Objective: To construct Markov model for clinical follow up data and predict the number of survivals and deaths. Methods: The state of patients was classified into survival. death and censorship. The weighted least sq...Objective: To construct Markov model for clinical follow up data and predict the number of survivals and deaths. Methods: The state of patients was classified into survival. death and censorship. The weighted least squares method was used for estimating parameters. Results: Markov model for survival analysis of follow--up data was presented. By using an example, the transition probability matrices were obtained and the number of survivals and deaths at each observation point was predicted respectively. Conclusion: Markov model constructed in the present study to analyze clinical follow up data could be used as effective supplemention for life table analysis.展开更多
BACKGROUND Lutetium has been shown to be an important potential innovation in pre-treated metastatic castration-resistant prostate cancer.Two clinical trials have evaluated lutetium thus far(therap and vision with 99 ...BACKGROUND Lutetium has been shown to be an important potential innovation in pre-treated metastatic castration-resistant prostate cancer.Two clinical trials have evaluated lutetium thus far(therap and vision with 99 and 385 patients,respectively),but their results are discordant.AIM To synthetize the available evidence on the effectiveness of lutetium in pre-treated metastatic castration-resistant prostate cancer;and to test the application of a new artificial intelligence technique that synthetizes effectiveness based on reconstructed patient-level data.METHODS We employed a new artificial intelligence method(shiny method)to pool the survival data of these two trials and evaluate to what extent the lutetium cohorts differed from one another.The shiny technique employs an original reconstruction of individual patient data from the Kaplan-Meier curves.The progression-free survival graphs of the two lutetium cohorts were analyzed and compared.RESULTS The hazard ratio estimated was in favor of the vision trial;the difference was statistically significant(P<0.001).These results indicate that further studies on lutetium are needed because the survival data of the two trials published thus far are conflicting.CONCLUSION Our study confirms the feasibility of reconstructing patient-level data from survival graphs in order to generate a survival statistics.展开更多
基金supported by the National Statistical Scientific Research Projects(Grant No.2015LZ54)
文摘Using the so-called martingale difference correlation(MDC), we propose a novel censoredconditional-quantile screening approach for ultrahigh-dimensional survival data with heterogeneity(which is often present in such data). By incorporating a weighting scheme, this method is a natural extension of MDCbased conditional quantile screening, as considered by Shao and Zhang(2014), to handle ultrahigh-dimensional survival data. The proposed screening procedure has a sure-screening property under certain technical conditions and an excellent capability of detecting the nonlinear relationship between independent and censored dependent variables. Both simulation results and an analysis of real data demonstrate the effectiveness of the new censored conditional quantile-screening procedure.
文摘The main goal of this research is to assess the impact of race, age at diagnosis, sex, and phenotype on the incidence and survivability of acute lymphocytic leukemia (ALL) among patients in the United States. By taking these factors into account, the study aims to explore how existing cancer registry data can aid in the early detection and effective treatment of ALL in patients. Our hypothesis was that statistically significant correlations exist between race, age at which patients were diagnosed, sex, and phenotype of the ALL patients, and their rate of incidence and survivability data were evaluated using SEER*Stat statistical software from National Cancer Institute. Analysis of the incidence data revealed that a higher prevalence of ALL was among the Caucasian population. The majority of ALL cases (59%) occurred in patients aged between 0 to 19 years at the time of diagnosis, and 56% of the affected individuals were male. The B-cell phenotype was predominantly associated with ALL cases (73%). When analyzing survivability data, it was observed that the 5-year survival rates slightly exceeded the 10-year survival rates for the respective demographics. Survivability rates of African Americans patients were the lowest compared to Caucasian, Asian, Pacific Islanders, Alaskan Native, Native Americans and others. Survivability rates progressively decreased for older patients. Moreover, this study investigated the typical treatment methods applied to ALL patients, mainly comprising chemotherapy, with occasional supplementation of radiation therapy as required. The study demonstrated the considerable efficacy of chemotherapy in enhancing patients’ chances of survival, while those who remained untreated faced a less favorable prognosis from the disease. Although a significant amount of data and information exists, this study can help doctors in the future by diagnosing patients with certain characteristics. It will further assist the health care professionals in screening potential patients and early detection of cases. This could also save the lives of elderly patients who have a higher mortality rate from this disease.
文摘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.
文摘Lung cancer is the most common cancer type worldwide and has the highest and second highest mortality rate for men and women respectively in Germany.Yet,the role of comorbid illnesses in lung cancer patient prognosis is still debated.We analyzed administrative claims data from one of the largest statutory health insurance(SHI)funds in Germany,covering close to 9 million people(11%of the national population);observation period was from 2005 to 2019.Lung cancer patients and their concomitant diseases were identified by ICD-10-GM codes.Comorbidities were classified according to the Charlson Comorbidity Index(CCI).Incidence,comorbidity prevalence and survival are estimated considering sex,age at diagnosis,and place of residence.Kaplan Meier curves with 95%confidence intervals were built in relation to common comorbidities.We identified 70,698 lung cancer incident cases in the sample.Incidence and survival figures are comparable to official statistics in Germany.Most prevalent comorbidities are chronic obstructive pulmonary disease(COPD)(36.7%),followed by peripheral vascular disease(PVD)(18.7%),diabetes without chronic complications(17.4%),congestive heart failure(CHF)(16.5%)and renal disease(14.7%).Relative to overall survival,lung cancer patients with CHF,cerebrovascular disease(CEVD)and renal disease are associated with largest drops in survival probabilities(9%or higher),while those with PVD and diabetes without chronic complications with moderate drops(7%or lower).The study showed a negative association between survival and most common comorbidities among lung cancer patients,based on a large sample for Germany.Further research needs to explore the individual effect of comorbidities disentangled from that of other patient characteristics such as cancer stage and histology.
文摘To the Editor:A large international study has been recently published focusing on the combination of morphological aspects and alpha-fetoprotein(AFP)as predictors of survival in patients with hepatocellular cancer(HCC)treated with liver transplantation(LT)[1].As a matter of fact,morphology and biology represent the two sides of the same
文摘The object of our present study is to develop a piecewise constant hazard model by using an Artificial Neural Network (ANN) to capture the complex shapes of the hazard functions, which cannot be achieved with conventional survival analysis models like Cox proportional hazard. We propose a more convenient approach to the PEANN created by Fornili et al. to handle a large amount of data. In particular, it provides much better prediction accuracies over both the Poisson regression and generalized estimating equations. This has been demonstrated with lung cancer patient data taken from the Surveillance, Epidemiology and End Results (SEER) program. The quality of the proposed model is evaluated by using several error measurement criteria.
文摘To explore the influencing factors of survival time of patients with heart failure, a total of 1789 patients with heart failure were collected from Shanghai Shuguang Hospital. The Cox proportional hazards model and the mixed effects Cox model were used to analyze the factors on survival time of patients. The results of Cox proportional hazards model showed that age (RR = 1.32), hypertension (RR = 0.67), ARB (RR = 0.55), diuretic (RR = 1.48) and antiplatelet (RR = 0.53) have significant impacts on the survival time of patients. The results of mixed effects Cox model showed that age (RR = 1.16), hypertension (RR = 0.61), lung infection (RR = 1.43), ARB (RR = 0.64), β-blockers (RR = 0.77) and antiplatelet (RR = 0.69) have a significant impact on the survival time of patients. The results are consistent with the covariates age, hypertension, ARB and antiplatelet but inconsistent with the covariates lung infection and β-blockers.
文摘Background:In the past decade,many researchers focused on to robot-assisted surgery.However,on long-term outcomes for patients with early-stage non-small cell lung cancer(NSCLC),whether the robotic procedure is superior to video-assisted thoracic surgery(VATS) and thoracotomy is unclear.Nonetheless,in the article titled "Long-term survival based on the surgical approach to lobectomy for clinical stage I non-small cell lung cancer:comparison of robotic,video assisted thoracic surgery,and thoracotomy lobectomy" by Yang et al.that was recently published in Annals of Surgery,the authors provided convincing evidence that the robotic procedure results in similar long-term survival as compared with VATS and thoracotomy.Minimally invasive procedures typically result in shorter lengths of hospital stay,and the robotic procedure in particular results in superior lymph node assessment.Main body:Our propensity score-matched study generated high-quality data.Based on our findings,we see promise in expanding patient access to robotic lung resections.In this study,propensity score matching minimized the bias involved between groups.Nevertheless,due to its retrospective nature,bias may still exist.Currently,the concept of rapid rehabilitation is widely accepted,and it is very difficult to set up a randomized controlled trial to compare robotic,VATS,and thoracotomy procedures for the treatment of NSCLC.Therefore,to overcome this limitation and to minimize bias,the best approach is to use a registry and prospectively collected,propensity score-matched data.Conclusions:Robotic lung resections result in similar long-term survival as compared with VATS and thoracotomy.Robot-assisted and VATS procedures are associated with short lengths of hospital stay,and the robotic procedure in particular results in superior lymph node assessment.Considering the alarming increase in the incidence of lung cancer in China,a nationwide database of prospectively collected data available for clinical research would be especially important.
基金supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(2021R1A6A1A03044326,2017R1D1A1B06036077)。
文摘With the increasing impact of climate change,carbon emissions and removals have become major issues.Forests are major carbon pools,and forest fires are an essential part of the carbon cycle.This study introduces a model for estimating the detailed actual CO_(2)removal in burned forests using burn severity and tree survivability.Actual CO_(2)removal was estimated from empirical yield tables without using the standard carbon removal provided by the national inventory.The primary CO_(2)calculation method followed the guidelines of the International Panel on Climate Change.The burn severity was mapped using Sentinel-2 multispectral instrument data,and the survivability of each forest type was estimated according to burn severity.The survivability was applied to the pre-fire CO_(2)removal of each forest to estimate post-fire CO_(2)removal.In our case study,the burned forest area was 1,034 ha,and the CO_(2)removal before the fire was 8,615.3t/year.After the fire,removal decreased by 81.2%to 1,618.4 t/yr.In particular,the decrease in coniferous forests was high,more than 86%.The lack of survivability data on burned trees was a major limitation of our study.Systematically accumulating field monitoring data of post-fire forests will be necessary for future research and could serve as a reference for devising immediate countermeasures against forest fires.
文摘目的将共享随机效应模型(shared random-effect model,SREM)应用于轻度认知障碍(mild cognitive impairment,MCI)向认知正常(normal cognition,NC)逆转的研究,比较不同纵向认知标志物对MCI逆转的预测性能,并评价影响因素的协变量效应。方法SREM模型包括两个子模型,其中纵向子模型采用线性混合效应模型对纵向认知标志物的变化轨迹建模,生存子模型采用比例风险模型对生存过程建模。基于对数似然函数值和信息准则进行模型拟合优度检验,采用ROC曲线下面积(area under the curve,AUC)评价不同纵向认知标志物(MMSE、CDRSB、FAQ、ADAS11、ADAS13和ADASQ4)对MCI逆转的预测性能;同时进行纵向子模型和生存子模型的影响因素分析。结果843名MCI患者中72名(8.54%)在随访结束后逆转为NC。以spline-PH-GH参数分布为基准风险函数的SREM模型对数似然函数值最大,AIC和BIC最小;以CDRSB为纵向认知标志物建立的SREM模型拟合最好,在不同时间的AUC值均表现良好,范围为0.797~0.852,且预测误差最小,范围为0.0427~0.0429;年龄、性别、受教育程度、婚姻状况和APOEε4基因均会影响MCI患者的认知功能和日常活动功能,六种纵向认知标志物均会影响MCI患者的逆转。结论CDR评分对MCI患者的认知功能和逆转预测性能最佳;认知功能和日常活动功能可作为MCI逆转的动态监测指标。
文摘Objective: To construct Markov model for clinical follow up data and predict the number of survivals and deaths. Methods: The state of patients was classified into survival. death and censorship. The weighted least squares method was used for estimating parameters. Results: Markov model for survival analysis of follow--up data was presented. By using an example, the transition probability matrices were obtained and the number of survivals and deaths at each observation point was predicted respectively. Conclusion: Markov model constructed in the present study to analyze clinical follow up data could be used as effective supplemention for life table analysis.
文摘BACKGROUND Lutetium has been shown to be an important potential innovation in pre-treated metastatic castration-resistant prostate cancer.Two clinical trials have evaluated lutetium thus far(therap and vision with 99 and 385 patients,respectively),but their results are discordant.AIM To synthetize the available evidence on the effectiveness of lutetium in pre-treated metastatic castration-resistant prostate cancer;and to test the application of a new artificial intelligence technique that synthetizes effectiveness based on reconstructed patient-level data.METHODS We employed a new artificial intelligence method(shiny method)to pool the survival data of these two trials and evaluate to what extent the lutetium cohorts differed from one another.The shiny technique employs an original reconstruction of individual patient data from the Kaplan-Meier curves.The progression-free survival graphs of the two lutetium cohorts were analyzed and compared.RESULTS The hazard ratio estimated was in favor of the vision trial;the difference was statistically significant(P<0.001).These results indicate that further studies on lutetium are needed because the survival data of the two trials published thus far are conflicting.CONCLUSION Our study confirms the feasibility of reconstructing patient-level data from survival graphs in order to generate a survival statistics.