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.

Coronary heart disease incidence and competing risks： an important issue

The estimation of lifetime morbid events is not a rare presentation of relatively old and of more recent epidemi- ological investigations, accompanied by evaluating rates, risks and predictors （more in general determinants or risk factors）. However, when the follow-up period is very long and Kaplan-Meier survival curves are adopted, or Kaplan- Meier-based more complex models such as Cox＇s analysis are used, clinical （or epidemiological） reality may well be distorted since by these survival methods risks tend to be overestimated, whereas survival tends to be reduced.

Dependence Rayleigh competing risks model with generalized censored data

The inference for the dependent competing risks model is studied and the dependent structure of failure causes is modeled by a Marshall-Olkin bivariate Rayleigh distribution. Under generalized progressive hybrid censoring(GPHC), maximum likelihood estimates are established and the confidence intervals are constructed based on the asymptotic theory. Bayesian estimates and the highest posterior density credible intervals are obtained by using Gibbs sampling. Simulation and a real life electrical appliances data set are used for practical illustration.

Bayesian Inference on Type-Ⅰ Progressively Hybrid Competing Risks Model

In this paper, we construct a Bayesian framework combining Type-Ⅰ progressively hybrid censoring scheme and competing risks which are independently distributed as exponentiated Weibull distribution with one scale parameter and two shape parameters. Since there exist unknown hyper-parameters in prior density functions of shape parameters, we consider the hierarchical priors to obtain the individual marginal posterior density functions,Bayesian estimates and highest posterior density credible intervals. As explicit expressions of estimates cannot be obtained, the componentwise updating algorithm of Metropolis-Hastings method is employed to compute the numerical results. Finally, it is concluded that Bayesian estimates have a good performance.

Parametric Regression Approach for Gompertz Survival Times with Competing Risks

Regression models play a vital role in the study of data regarding survival of subjects.The Cox proportional hazards model for regression analysis has been frequently used in sur-vival modelling.In survival studies,it is also possible that survival time may occur with multiple occurrences of event or competing risks.The situation of competing risks arises when there are more than one mutually exclusive causes of death(or failure)for the person(or subject).In this paper,we developed a parametric regression model using Gompertz distribution via the Cox proportional hazards model with competing risks.We discussed point and interval estimation of unknown parameters and cumulative cause-specific hazard function with maximum-likelihood method and Bayesian method of estimation.The Bayes estimates are obtained based on non-informative priors and symmetric as well as asym-metric loss functions.To observe the finite sample behaviour of the proposed model under both estimation procedures,we carried out a Monte Carlo simulation analysis.To demon-strate our methodology,we also included real data analysis.

Identifying Factors that Affect the Probability of Being Cured from MDR-TB Disease, KwaZulu-Natal, South Africa: A Competing Risks Analysis

Setting: Four decentralised sites are located in rural areas and one centralised hospital in KwaZulu-Natal province, South Africa. Objective: To analyse risk factors associated with multidrug-resistant tuberculosis (MDR-TB) using competing risks analysis. Understanding factors associated with MDR-TB and obtaining valid parameter estimates could help in designing control and intervention strategies to lower TB mortality. Method: A prospective study was performed using a competing risk analysis in patients receiving treatment for MDR-TB. The study focused on 1542 patients (aged 18 years and older) who were diagnosed of MDR-TB between July 2008 and June 2010. Time to cure MDR-TB was used as the dependent variable and time to death was the competing risk event. Results: The Fine-Gray regression model indicated that baseline weight was highly significant with sub-distribution hazard ration (SHR) = 1.02, 95% CI: 1.01 - 1.02. This means that weight gain in a month increased chances of curing MDR-TB by 2%. Results show that lower chances to cure MDR-TB were among patients between 41 to 50 years compared to those patients who were between 18 to 30 years old (SHR = 0.80, 95% CI: 0.61 - 1.06). The chances of curing MDR-TB in female patients were low compared to male patients (SHR = 0.84, 95% CI = 0.68 - 1.03), however this was not significant. Furthermore, HIV negative patients had higher chances to cure MDR-TB (SHR = 1.07, 95% CI: 0.85 - 1.35) compared to HIV positive patients. Patients who were treated in the decentralised sites had lower chances to be cured of MDR-TB (SHR = 0.19, 95% CI: 0.07 - 0.54) as compared to patients who were treated in the centralised hospital. Conclusion: Identifying key factors associated with TB and specifying strategies to prevent them can reduce mortality of patients due to TB disease, hence positive treatment outcomes leading to the goal of reducing or end TB deaths. Urgent action is required to improve the coverage and quality of diagnosis, treatment and care for people with drug-resistant TB.

Health evaluation method for degrading systems subject to dependent competing risks

This paper proposes a health evaluation method for degrading systems subject to competing risks of dependent soft and hard failures. To characterize the time-varying degradation rate, the degradation process is determined by a non-stationary Gamma process and the soft failure is encountered when it exceeds a predefined critical level. For the hard failure, a Cox’s proportional hazard model is applied to describe the hazard rate of the time to system failure. The dependent relationship is modeled by incorporating the degradation process as a time-varying covariate into the Cox’s proportional hazard model. To facilitate the health characteristics evaluation, a discretization technique is applied both to the degradation process and the monitoring time.All health characteristics can be obtained in the explicit form using the transition probability matrix, which is computationally attractive for practical applications. Finally, a numerical analysis is carried out to show the effectiveness and the performance of the proposed health evaluation method.

Understanding Dependent Competing Risks： A Simulation Study to Illustrate the Relationship Between Cause-Specific Hazard and Marginal Hazard

In the analysis of competing risk data, the observed effect of a covariate can be obtained via a Fine and Gray sub-distribution hazard ratio. Sometimes, it is also desirable to obtain the virtual effect of a covariate as if the competing risks were non-existent. Under the latent failure time scenario, when the event of interest and the competing risk event are independent, the cause-specific hazard ratio obtained from the Cox model where the competing events are censored represents the ratio of the marginal hazards and can be interpreted as the virtual effect of the covariate. However, when the two events are not independent, the cause-specific hazard ratio is not the ratio of the marginal hazards as the ratio depends not only on the marginal hazards but also on the correlation between the competing risk and the event of interest. Using simulation, we investigated the degree to which the cause-specific hazard ratio changes relative to the marginal hazard with this correlation. It was found that the discrepancy between the cause-specific hazard ratio and the theoretical marginal hazard ratio increased as the proportion of competing risk events and the correlation between the events increased （〉0.2）. Depending on the direction of the correlation, the cause-specific hazard ratio can over- or under-estimate the marginal hazard ratio. Using real-life datasets, we show how these results can be used to make inferences on the virtual effects.

Competing Risks Data Analysis with High-dimensional Covariates:An Application in Bladder Cancer

Analysis of microarray data is associated with the methodological problems of high dimension and small sample size. Various methods have been used for variable selection in high- dimension and small sample size cases with a single survival endpoint. However, little effort has been directed toward addressing competing risks where there is more than one failure risks. This study compared three typical variable selection techniques including Lasso, elastic net, and likelihood-based boosting for high-dimensional time-to-event data with competing risks. The per- formance of these methods was evaluated via a simulation study by analyzing a real dataset related to bladder cancer patients using time-dependent receiver operator characteristic （ROC） curve and bootstrap .632 ＋ prediction error curves. The elastic net penalization method was shown to outper- form Lasso and boosting. Based on the elastic net, 33 genes out of 1381 genes related to bladder cancer were selected. By fitting to the Fine and Gray model, eight genes were highly significant（P 〈 0.001）. Among them, expression of RTN4, SON, IGF1R, SNRPE, PTGR1, PLEK, and ETFDHwas associated with a decrease in survival time, whereas SMARCAD1 expression was asso- ciated with an increase in survival time. This study indicates that the elastic net has a higher capacity than the Lasso and boosting ＇for the prediction of survival time in bladder cancer patients. Moreover, genes selected by all methods improved the predictive power of the model based on only clinical variables, indicating the value of information contained in the mieroarray features.

An Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks Data

This paper proposes a flexible additive-multiplicative Cox-Aalen hazard model which allows time-varying covariate effects for the subdistribution in a competing risks study.Weigh ted estimating equation approaches under an covariates-dependent adjusted weight by fitting the Cox proportional hazard model for the censoring distribution are established for inference on the model parametric and nonparametric components.In addition,large number properties are presented and the finite sample behavior of the proposed estimators is evaluated through simulation studies,estimators from the proposed method perform satisfactorily on reduction of the bias.The authors apply our model to a competing risks data set from a tamoxifen trail for breast cancer study.

Statistical analysis of dependent competing risks model in constant stress accelerated life testing with progressive censoring based on copula function

In this paper, we consider the statistical analysis for the dependent competing risks model in theconstant stress accelerated life testing (CSALT) with Type-II progressive censoring. It is focusedon two competing risks from Lomax distribution. The maximum likelihood estimators of theunknown parameters, the acceleration coefficients and the reliability of unit are obtained by usingthe Bivariate Pareto Copula function and the measure of dependence known as Kendall’s tau.In addition, the 95% confidence intervals as well as the coverage percentages are obtained byusing Bootstrap-p and Bootstrap-t method. Then, a simulation study is carried out by the MonteCarlo method for different measures of Kendall’s tau and different testing schemes. Finally, a realcompeting risks data is analysed for illustrative purposes. The results indicate that using copulafunction to deal with the dependent competing risks problems is effective and feasible.

Stenting as a bridge to surgery in obstructing colon cancer:Longterm recurrence pattern and competing risk of mortality

BACKGROUND Stenting as a bridge to curative surgery(SBTS)for obstructing colon cancer(OCC)has been associated with possibly worse oncological outcomes.AIM To evaluate the recurrence patterns,survival outcomes,and colorectal cancer(CRC)-specific death in patients undergoing SBTS for OCC.METHODS Data from 62 patients undergoing SBTS at a single tertiary centre over ten years between 2007 and 2016 were retrospectively examined.Primary outcomes were recurrence patterns,overall survival(OS),cancer-specific survival(CSS),and CRC-specific death.OS and CSS were estimated using the Kaplan-Meier curves.Competing risk analysis with cumulative incidence function(CIF)was used to estimate CRC-specific mortality with other cause-specific death as a competing event.Fine-Gray regressions were performed to determine prognostic factors of CRC-specific death.Univariate and multivariate subdistribution hazard ratios and their corresponding Wald test P values were calculated.RESULTS 28 patients(45.2%)developed metastases after a median period of 16 mo.Among the 18 patients with single-site metastases:Four had lung-only metastases(14.3%),four had liver-only metastases(14.3%),and 10 had peritoneum-only metastases(35.7%),while 10 patients had two or more sites of metastatic disease(35.7%).The peritoneum was the most prevalent(60.7%)site of metastatic involvement(17/28).The median follow-up duration was 46 mo.26(41.9%)of the 62 patients died,of which 16(61.5%)were CRC-specific deaths and 10(38.5%)were deaths owing to other causes. The 1-, 3-, and 5-year OS probabilities were 88%, 74%, and 59%;1-, 3-, and5-year CSS probabilities were 97%, 83%, and 67%. The highest CIF for CRC-specific death at 60 mowas liver-only recurrence (0.69). Liver-only recurrence, peritoneum-only recurrence, and two ormore recurrence sites were predictive of CRC-specific death.CONCLUSIONThe peritoneum was the most common metastatic site among patients undergoing SBTS. Liveronlyrecurrence, peritoneum-only recurrence, and two or more recurrence sites were predictors ofCRC-specific death.

Multiple myeloma survival in New South Wales, Australia, by treatment era to 2020

Objective: Australia has relatively high multiple myeloma(MM) incidence and mortality rates. Advancements in MM treatment over recent decades have driven improvements in MM survival in high-income countries;however, reporting in Australia is limited. We investigated temporal trends in population-wide MM survival across 3 periods of treatment advancements in New South Wales(NSW), Australia.Methods: Individuals with an MM diagnosis in the NSW Cancer Registry between 1985 and 2015 with vital follow-up to 2020, were categorized into 3 previously defined treatment eras according to their diagnosis date(1985±1995, chemotherapy only;1996±2007, autologous stem cell transplantation;and 2008±2015, novel agents including proteasome inhibitors and immunomodulatory drugs). Both relative survival and cause-specific survival according to Fine and Gray's competing risks cumulative incidence function were calculated by treatment era and age at diagnosis.Results: Overall, 11,591 individuals were included in the study, with a median age of 70 years at diagnosis. Five-year relative survival improved over the 36-year(1985±2020) study period(31.0% in 1985±1995;41.9% in 1996±2007;and 56.1% in 2008±2015). For individuals diagnosed before 70 years of age, the 5-year relative survival nearly doubled, from 36.5% in 1985±1995 to 68.5% in 2008±2015. Improvements for those > 70 years of age were less pronounced between 1985±1995 and 1996±2007;however, significant improvements were observed for those diagnosed in 2008±2015. Similar overall and age-specific patterns were observed for causespecific survival. After adjustment for gender and age at diagnosis, treatment era was strongly associated with both relative and cause-specific survival(P < 0.0001).Conclusions: Survival of individuals with MM is improving in Australia with treatment advances. However, older age groups continue to experience poor survival outcomes with only modest improvements over time. Given the increasing prevalence of MM in Australia, the effects of MM treatment on quality of life, particularly in older age, warrant further attention.

Likelihood Inference under Generalized Hybrid Censoring Scheme with Comp eting Risks

Statistical inference is developed for the analysis of generalized type-Ⅱ hybrid censoring data under exponential competing risks model. In order to solve the problem that approximate methods make unsatisfactory performances in the case of small sample size,we establish the exact conditional distributions of estimators for parameters by conditional moment generating function(CMGF). Furthermore, confidence intervals(CIs) are constructed by exact distributions, approximate distributions as well as bootstrap method respectively,and their performances are evaluated by Monte Carlo simulations. And finally, a real data set is analyzed to illustrate all the methods developed here.

Factors Predicting Progression to Severe COVID-19: A Competing Risk Survival Analysis of 1753 Patients in Community Isolation in Wuhan, China

Most studies of coronavirus disease 2019(COVID-19)progression have focused on the transfer of patients within secondary or tertiary care hospitals from regular wards to intensive care units.Little is known about the risk factors predicting the progression to severe COVID-19 among patients in community iso-lation,who are either asymptomatic or suffer from only mild to moderate symptoms.Using a multivari-able competing risk survival analysis,we identify several important predictors of progression to severe COVID-19—rather than to recovery—among patients in the largest community isolation center in Wuhan,China from 6 February 2020(when the center opened)to 9 March 2020(when it closed).All patients in community isolation in Wuhan were either asymptomatic or suffered from mild to moderate COVID-19 symptoms.We performed competing risk survival analysis on time-to-event data from a cohort study of all COVID-19 patients(n=1753)in the isolation center.The potential predictors we inves-tigated were the routine patient data collected upon admission to the isolation center:age,sex,respira-tory symptoms,gastrointestinal symptoms,general symptoms,and computed tomography(CT)scan signs.The main outcomes were time to severe COVID-19 or recovery.The factors predicting progression to severe COVID-19 were:male sex(hazard ratio(HR)=1.29,95%confidence interval(CI)1.04–1.58,p=0.018),young and old age,dyspnea(HR=1.58,95%CI 1.24–2.01,p<0.001),and CT signs of ground-glass opacity(HR=1.39,95%CI 1.04–1.86,p=0.024)and infiltrating shadows(HR=1.84,95%CI 1.22–2.78,p=0.004).The risk of progression was found to be lower among patients with nausea or vomiting(HR=0.53,95%CI 0.30–0.96,p=0.036)and headaches(HR=0.54,95%CI 0.29–0.99,p=0.046).Our results suggest that several factors that can be easily measured even in resource-poor set-tings(dyspnea,sex,and age)can be used to identify mild COVID-19 patients who are at increased risk of disease progression.Looking for CT signs of ground-glass opacity and infiltrating shadows may be an affordable option to support triage decisions in resource-rich settings.Common and unspecific symptoms(headaches,nausea,and vomiting)are likely to have led to the identification and subsequent community isolation of COVID-19 patients who were relatively unlikely to deteriorate.Future public health and clinical guidelines should build on this evidence to improve the screening,triage,and monitoring of COVID-19 patients who are asymtomatic or suffer from mild to moderate symptoms.

Competing risk analysis on outcome after hepatic resection of hepatocellular carcinoma in cirrhotic patients

To investigate death for liver failure and for tumor recurrence as competing events after hepatectomy of hepatocellular carcinoma.METHODSData from 864 cirrhotic Child-Pugh class A consecutive patients, submitted to curative hepatectomy (1997-2013) at two tertiary referral hospitals, were used for competing-risk analysis through the Fine and Gray method, aimed at assessing in which circumstances the oncological benefit from tumour removal is greater than the risk of dying from hepatic decompensation. To accomplish this task, the average risk of these two competing events, over 5 years of follow-up, was calculated through the integral of each cumulative incidence function, and represented the main comparison parameter.RESULTSWithin a median follow-up of 5.6 years, death was attributable to tumor recurrence in 63.5%, and to liver failure in 21.2% of cases. In the first 16 mo, the risk of dying due to liver failure exceeded that of dying due to tumor relapse. Tumor stage only affects death from recurrence; whereas hepatitis C infection, Model for End-stage Liver Disease score, extent of hepatectomy and portal hypertension influence death from liver failure (P < 0.05 in all cases). The combination of these clinical and tumoral features identifies those patients in whom the risk of dying from liver failure did not exceed the tumour-related mortality, representing optimal surgical candidates. It also identifies those clinical circumstances where the oncological benefit would be borderline or even where the surgery would be harmful.CONCLUSIONHaving knowledge of these competing events can be used to weigh the risks and benefits of hepatic resection in each clinical circumstance, separating optimal from non-optimal surgical candidates.

Heterogeneous length-of-stay modeling of post-acute care residents in the nursing home with competing discharge dispositions

Post-acute care(PAC)residents in nursing homes(NHs)are recently hospitalized patients with medically complex diagnoses,ranging from severe orthopedic injuries to cardiovascular diseases.A major role of NHs is to maximize restoration of PAC residents during their NH stays with desirable discharge outcomes,such as higher community discharge likelihood and lower re/hospitalization risk.Accurate prediction of the PAC residents’length-of-stay(LOS)with multiple discharge dispositions(e.g.,community discharge and re/hospitalization)will allow NH management groups to stratify NH residents based on their individualized risk in realizing personalized and resident-centered NH care delivery.Due to the highly heterogeneous health conditions of PAC residents and their multiple types of correlated discharge dispositions,developing an accurate prediction model becomes challenging.Existing predictive analytics methods,such as distribution-/regression-based methods and machine learning methods,either fail to incorporate varied individual characteristics comprehensively or ignore multiple discharge dispositions.In this work,a data-driven predictive analytics approach is considered to jointly predict the individualized re/hospitalization risk and community discharge likelihood over time in the presence of varied residents’characteristics.A sampling algorithm is further developed to generate accurate predictive samples for a heterogeneous population of PAC residents in an NH and facilitate facility-level performance evaluation.A real case study using large-scale NH data is provided to demonstrate the superior prediction performance of the proposed work at individual and facility levels through comprehensive comparison with a large number of existing prediction methods as benchmarks.The developed analytics tools will allow NH management groups to identify the most at-risk residents by providing them with more proactive and focused care to improve resident outcomes.

Risk factors for hepatocellular carcinoma in cirrhosis:A comprehensive analysis from a decade-long study

BACKGROUND Cirrhosis is a significant risk factor for the development of hepatocellular carcinoma(HCC).Variability in HCC risk among patients with cirrhosis is notable,particularly when considering the diverse etiologies of cirrhosis.AIM To identify specific risk factors contributing to HCC development in patients with cirrhosis.METHODS This retrospective study analyzed data from cirrhotic patients at Beijing Youan Hospital from January 1,2012 to September 30,2022 with at least 6 mo of followup.Patient demographics,medical histories,etiologies,and clinical characteristics were examined.Cox regression analysis was used to analyze correlations of the above parameters with hepatocarcinogenesis,while competing risk regression was used to estimate their adjusted hazard ratios accounting for death.The cumulative incidence was plotted over time.RESULTS Overall,5417 patients with cirrhosis(median age:54 years;65.8%males)were analyzed.Hepatitis B virus(HBV)was the most common etiology(23.3%),with 25%(n=1352)developing HCC over a 2.9-year follow-up period.Patients with multiple etiologies had the HCC highest incidence(30.3%),followed by those with HBV-related cirrhosis(29.5%).Significant risk factors included male sex,advanced age,hepatitis C virus(HCV)infection,elevated blood ammonia,and low platelet count.Men had a higher 5-year HCC risk than women(37.0%vs 31.5%).HBV,HCV,and HBV/HCV co-infected patients had 5-year risks of HCC of 45.8%,42.9%,and 48.1%,respectively,compared to 29.5%in nonviral hepatitis cases,highlighting the significant HCC risk from viral hepatitis,especially HBV,and underscores the importance of monitoring these high-risk groups.CONCLUSION In conclusion,HBV-related cirrhosis strongly correlates with HCC,with male sex,older age,viral hepatitis,elevated blood ammonia,and lower albumin and platelet levels increasing the risk of HCC.

Semiparametric estimation for accelerated failure time mixture cure model allowing non-curable competing risk

The mixture cure model is the most popular model used to analyse the major event with a potential cure fraction.But in the real world there may exist a potential risk from other non-curable competing events.In this paper,we study the accelerated failure time model with mixture cure model via kernel-based nonparametric maximum likelihood estimation allowing non-curable competing risk.An EM algorithm is developed to calculate the estimates for both the regression parameters and the unknown error densities,in which a kernel-smoothed conditional profile likelihood is maximised in the M-step,and the resulting estimates are consistent.Its performance is demonstrated through comprehensive simulation studies.Finally,the proposed method is applied to the colorectal clinical trial data.

Nonparametrie Quantile Inference for Cause-specific Residual Life Function Under Length-biased Sampling

This paper considers a competing risks model for right-censored and length-biased survival data from prevalent sampling.We propose a nonparametric quantile inference procedure for cause-specific residual life distribution with competing risks data.We also derive the asymptotic properties of the proposed estimators of this quantile function.Simulation studies and the unemployment data demonstrate the practical utility of the methodology.