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The advances in science and technology have led to vast amounts of complex and heterogeneous data from multiple sources of random sample length. This paper aims to investigate the extreme behavior of competing risks with random sample sizes. Two accelerated mixed types of stable distributions are obtained as the extreme limit laws of random sampling competing risks under linear and power normalizations, respectively. The theoretical findings are well illustrated by typical examples and numerical studies. The developed methodology and models provide new insights into modeling complex data across numerous fields. [ABSTRACT FROM AUTHOR]

In this paper Chen-Burr XII distribution is constructed and graphical description of the probability density function, hazard rate and reversed hazard rate functions of the proposed model is obtained. Also, some statistical characteristics of the Chen-Burr XII distribution are discussed and some new models as sub-models from the Chen-Burr XII distribution are introduced. Moreover, maximum likelihood estimation of the parameters, reliability, hazard rate and reversed hazard rate functions of the Chen-Burr XII distribution are considered. Also, the asymptotic confidence intervals of the distribution parameters, reliability, hazard rate and reversed hazard rate functions are presented. Finally, three real life data sets are applied to prove how the Chen-Burr XII distribution can be applied in real life and to confirm its superiority over some existing distributions. [ABSTRACT FROM AUTHOR]

In this paper, studies of competing risks model are considered when the observations are left-truncated and right-censored data. When the failure times of the competing risks are distributed by a generalized inverted exponential model with same scale but different shape parameters with partially observed failure causes, statistical inference for the unknown model parameters is discussed from classical and Bayesian approaches, respectively. Maximum likelihood estimators of the unknown parameters, along with associated existence and uniqueness, are established, and the asymptotic likelihood theory is also used to construct the confidence interval via the observed Fisher information matrix. Moreover, Bayesian estimates and the corresponding highest posterior density credible intervals are also obtained based a flexible Gamma-Beta prior, and a Gibbs sampling technique is constructed to compute associated estimates. Further, under a general practical assumption with order-restriction parameter case, classical and Bayesian estimations are also established under order restriction situations, respectively. Extensive Monte-Carlo simulations are carried out to investigate the performances of our results and two real-life examples are analyzed to show the applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

Competing risks data arise when occurrence of an event hinders observation of other types of events, and they are encountered in various research areas including biomedical research. These data have been usually analyzed using the hazard-based models, not survival times themselves. In this paper, we propose a joint accelerated failure time (AFT) modeling approach to model clustered competing risks data. Times to competing events are assumed to be log-linear with normal errors and correlated through a scaled random effect that follows a zero-mean normal distribution. Inference on the model parameters is based on the h-likelihood. Performance of the proposed method is evaluated through extensive simulation studies. The simulation results show that the estimated regression parameters are robust against the violation of the assumed parametric distributions. The proposed method is illustrated with three real competing risks data sets. [ABSTRACT FROM AUTHOR]

Competing risks models, also known as weakest-link models, are utilized to analyze diverse strength distributions exhibiting multi-modality, often attributed to various types of defects within the material. The weakest-link theory posits that a material's fracture is dictated by its most severe defect. However, multimodal problems can become intricate due to potential censoring, a common constraint stemming from time and cost limitations during experiments. Additionally, determining the mode of failure can be challenging due to factors like the absence of suitable diagnostic tools, costly autopsy procedures, and other obstacles, collectively referred to as the masking problem. In this paper, we investigate the distribution of strength for multimodal failures with censored data. We consider both full and partial maskings and present an EM-type parameter estimate for the Birnbaum-Saunders distribution under competing risks. We compare the results with those obtained from other distributions, such as lognormal, Weibull, and Wald (inverse-Gaussian) distributions. The effectiveness of the proposed method is demonstrated through two illustrative examples, as well as an analysis of the sensitivity of parameter estimates to variations in starting values. [ABSTRACT FROM AUTHOR]

This paper introduces a new four-parameter additive model, named xgamma-Burr XII distribution, by considering two competing risks: the former has the xgamma distribution and the latter has the Burr XII distribution. A graphical description of the xgamma-Burr XII distribution is presented, including plots of the probability density function, hazard rate and reversed hazard rate functions. The xgamma-Burr XII density has different shapes such as decreasing, unimodal, approximately symmetric and decreasing-unimodal. The main statistical properties of the proposed model are studied. The unknown model parameters, reliability, hazard rate and reversed hazard rate functions are estimated via the maximum likelihood method. The asymptotic confidence intervals of the parameters, reliability function, hazard rate function and reversed hazard rate function are also obtained. A simulation study is carried out to evaluate the performance of the maximum likelihood estimates. In addition, three real data are applied to show the superiority of the xgamma-Burr XII distribution over some known distributions in real-life applications. [ABSTRACT FROM AUTHOR]

Many non-fatal events can be considered recurrent in that they can occur repeatedly over time, and some researchers may be interested in the trajectory and relative risk of non-fatal events. With the competing risk of death, the treatment effect on the mean number of recurrent events is non-identifiable since the observed mean is a function of both the recurrent event and terminal event processes. In this paper, we assume independence between the non-fatal and the terminal event process, conditional on the shared frailty, to fit a parametric model that recovers the trajectory of, and identifies the effect of treatment on, the non-fatal event process in the presence of the competing risk of death. Simulation studies are conducted to verify the reliability of our estimators. We illustrate the method and perform model diagnostics using the Carvedilol Prospective Randomized Cumulative Survival trial which involves heart-failure events. [ABSTRACT FROM AUTHOR]

Competing risks data frequently appear in real-world operations like quality inspections, survival analysis, reliability tests, and clinical trials. From the quality point of view, relative risk rate can be considered an interesting quality indicator in analyzing the competing risks data for statistical process monitoring purposes. The relative risk rate measures the proportion of failures caused by the primary risk among a set of competing risks. This paper introduces two Shewhart-type control charts for monitoring the relative risk rate when the lifetimes of competing risks are independent Weibull random variables. The former chart is constructed based on the maximum likelihood estimation method, while the latter is developed based on the Bayesian approach. The proposed control charts can be applied in Phase II. The calculation of the Bayesian control charts and the evaluation of both process monitoring techniques have been done based on Monte Carlo simulations. The performance of the proposed control charts has been examined based on the average run length metric. The illustrative example is also discussed in detail to demonstrate the applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

A phase‐type distribution is the distribution of time to absorption for an absorbing continuous‐time finite state Markov chain. The paper first reviews the extension of the phase‐type setting to modeling of competing risks by introducing multiple absorbing states. The main study of the paper is the further extension to introducing instantaneous transitions at certain stages of the original models. The motivation is from applications to repair and maintenance, bringing failed systems into working ones by instantaneous repair actions. Two slightly different approaches are studied. The first one is based on restarting the original Markov chain upon absorption, leading to the consideration of a Markov renewal process. The second approach involves periodically inspected systems, where maintenance actions are modeled by instantaneous transitions made at regular inspection times. For both approaches are suggested measures of reliability and maintenance based on long run properties. [ABSTRACT FROM AUTHOR]

Recently, an improved adaptive Type-II progressive censoring scheme is proposed to ensure that the experimental time will not pass a pre-fixed time and ends the test after recording a pre-fixed number of failures. This paper studies the inference of the competing risks model from Weibull distribution under the improved adaptive progressive Type-II censoring. For this goal, we used the latent failure time model with Weibull lifetime distributions with common shape parameters. The point and interval estimation problems of parameters, reliability and hazard rate functions using the maximum likelihood and Bayesian estimation methods are considered. Moreover, making use of the asymptotic normality of classical estimators and delta method, approximate intervals are constructed via the observed Fisher information matrix. Following the assumption of independent gamma priors, the Bayes estimates of the scale parameters have closed expressions, but when the common shape parameter is unknown, the Bayes estimates cannot be formed explicitly. To solve this difficulty, we recommend using Markov chain Monte Carlo routine to compute the Bayes estimates and to construct credible intervals. A comprehensive Monte Carlo simulation is conducted to judge the behavior of the offered methods. Ultimately, analysis of electrodes data from the life-test of high-stress voltage endurance is provided to illustrate all proposed inferential procedures. [ABSTRACT FROM AUTHOR]

In this paper, we have considered the classical and Bayesian inference of the unknown parameters of the lifetime distribution based on the observations obtained from a simple step‐stress life‐testing (SSLT) experiment and when more than one cause of failures are observed. We have used the Tampered Random Variable (TRV) approach. The main advantage of the TRV approach is that it can be easily extended to a multiple step‐stress model as well as for different lifetime distributions. In this paper, it is assumed that the lifetime of the experimental units at each stress level follows Weibull distribution with the same shape parameter and different scale parameters. Further, we have introduced different tempering co‐efficient for different causes of failures. The maximum likelihood estimators and the associated asymptotic confidence intervals are obtained based on Type‐II censored observations. Further, we have considered the Bayesian inference of the unknown model parameters based on a fairly general class prior distributions. An extensive simulation study is performed to examine the performances of the proposed method, and the analysis of a real data set has been provided to show how the method can be used in practice. We have compared the TRV model with some of the other existing models, and the TRV model provides a better fit in terms of information theoretic criteria. We have also provided some optimality criteria, to determine the optimal stress change time and some sensitivity analyses have been performed. Most of the methods can be extended for other lifetime distributions also. [ABSTRACT FROM AUTHOR]

A retention strategy based on an enlightened lapse model is a powerful profitability lever for a life insurer. Some machine learning models are excellent at predicting lapse, but from the insurer's perspective, predicting which policyholder is likely to lapse is not enough to design a retention strategy. In our paper, we define a lapse management framework with an appropriate validation metric based on Customer Lifetime Value and profitability. We include the risk of death in the study through competing risks considerations in parametric and tree-based models and show that further individualization of the existing approaches leads to increased performance. We show that survival tree-based models outperform parametric approaches and that the actuarial literature can significantly benefit from them. Then, we compare, on real data, how this framework leads to increased predicted gains for a life insurer and discuss the benefits of our model in terms of commercial and strategic decision-making. [ABSTRACT FROM AUTHOR]

Background: Hemodialysis tunneled catheters are prone to failure due to infection or thrombosis. Prediction of catheter dysfunction chance and finding the predisposing risk factors might help clinicians to prolong proper catheter function. The multidimensional mechanism of failures following infection or thrombosis needs a multivariable and comprehensive analytic approach.Methods: A longitudinal cross-sectional study was implemented on 1048 patients admitted for the first hemodialysis tunneled catheterization attempt between 2013 and 2019 in Shahid Hasheminejdad hospital, Tehran, Iran. Patients' information was extracted from digital and also paper records. Based on their criteria, single and multiple variable analyses were done separately in patients with catheter dysfunction due to thrombosis and infection. T-test and Chi-square test were performed in quantitative and categorical variables, respectively. Competing risk regression was performed under the assumption of proportionality for infection and thrombosis, and the sub-distributional hazard ratios (SHR) were calculated. All statistical inferences were made with a significance level of 0.05.Results: Four hundred sixty-six patients were enrolled in the analysis based on study criteria. Samples' mean (SD) age was 54(15.54), and 322 (69.1%) patients were female. Three hundred sixty-five catheter dysfunction cases were observed due to thrombosis 123(26.4%) and infection 242(52%). The Median (range) time to catheter dysfunction event was 243(36-1131) days. Single variable analysis showed a statistically significant higher proportion of thrombosis in females (OR = 2.66, 95% CI: 1.77-4.00) and younger patients, respectively. Multivariate competing risk regression showed a statistically significant higher risk of thrombosis in females (Sub-distributional hazard (SHR) = 1.81), hypertensive (SHR = 1.82), and more obese patients (BMI SHR = 1.037). A higher risk of infection was calculated in younger (Age SHR = 0.98) and diabetic (SHR = 1.63) patients using the same method.Conclusion: Female and hypertensive patients are considerably at higher risk of catheter thrombosis, whereas diabetes is the most critical risk factor for infectious catheter dysfunction. Competing risk regression analysis showed a comprehensive result in the assessment of risk factors of catheter dysfunction. [ABSTRACT FROM AUTHOR]

Identifying and distinguishing risk factors for heterogeneous disease subtypes has been of great interest. However, missingness in disease subtypes is a common problem in those data analyses. Several methods have been proposed to deal with the missing data, including complete-case analysis, inverse-probability weighting, and multiple imputation. Although extant literature has compared these methods in missing problems, none has focused on the competing risk setting. In this paper, we discuss the assumptions required when complete-case analysis, inverse-probability weighting, and multiple imputation are used to deal with the missing failure subtype problem, focusing on how to implement these methods under various realistic scenarios in competing risk settings. Besides, we compare these three methods regarding their biases, efficiency, and robustness to model misspecifications using simulation studies. Our results show that complete-case analysis can be seriously biased when the missing completely at random assumption does not hold. Inverse-probability weighting and multiple imputation estimators are valid when we correctly specify the corresponding models for missingness and for imputation, and multiple imputation typically shows higher efficiency than inverse-probability weighting. However, in real-world studies, building imputation models for the missing subtypes can be more challenging than building missingness models. In that case, inverse-probability weighting could be preferred for its easy usage. We also propose two automated model selection procedures and demonstrate their usage in a study of the association between smoking and colorectal cancer subtypes in the Nurses' Health Study and Health Professional Follow-Up Study. [ABSTRACT FROM AUTHOR]

In this paper, we derive the copula‐graphic estimator (Zheng and Klein) for marginal survival functions using Archimedean copula models based on competing risks data subject to univariate right censoring and prove its uniform consistency and asymptotic properties. We then propose a novel parameter estimation method based on the semi‐competing risks data using Archimedean copula models. Based on our estimation strategy, we propose a new model selection procedure. We also describe an easy way to accommodate possible covariates in data analysis using our strategies. Simulation studies have shown that our parameter estimate outperforms the estimator proposed by Lakhal, Rivest and Abdous for the Hougaard model and the model selection procedure works quite well. We fit a leukemia dataset using our model and end our paper with some discussion. [ABSTRACT FROM AUTHOR]

Decisions regarding competing risks are usually based on a continuous-valued marker toward predicting a cause-specific outcome. The classification power of a marker can be summarized using the time-dependent receiver operating characteristic curve and the corresponding area under the curve (AUC). This paper proposes a Gaussian copula-based model to represent the joint distribution of the continuous-valued marker, the overall survival time, and the cause-specific outcome. Then, it is used to characterize the time-varying ROC curve in the context of competing risks. Covariate effects are incorporated by linking linear components to the skewed normal distribution for the margin of the marker, a parametric proportional hazards model for the survival time, and a logit model for the cause of failure. Estimation is carried out using maximum likelihood, and a bootstrap technique is implemented to obtain confidence intervals for the AUC. Information-criteria strategies are employed to find a parsimonious model. The performance of the proposed model is evaluated in simulation studies, considering different sample sizes and censoring distributions. The methods are illustrated with the reanalysis of a prostate cancer clinical trial. The joint regression strategy produces a straightforward and flexible model of the time-dependent ROC curve in the presence of competing risks, enhancing the understanding of how covariates may affect the discrimination of a marker. [ABSTRACT FROM AUTHOR]

Targeted maximum likelihood estimation (TMLE) provides a general methodology for estimation of causal parameters in presence of high-dimensional nuisance parameters. Generally, TMLE consists of a two-step procedure that combines data-adaptive nuisance parameter estimation with semiparametric efficiency and rigorous statistical inference obtained via a targeted update step. In this paper, we demonstrate the practical applicability of TMLE based causal inference in survival and competing risks settings where event times are not confined to take place on a discrete and finite grid. We focus on estimation of causal effects of time-fixed treatment decisions on survival and absolute risk probabilities, considering different univariate and multidimensional parameters. Besides providing a general guidance to using TMLE for survival and competing risks analysis, we further describe how the previous work can be extended with the use of loss-based cross-validated estimation, also known as super learning, of the conditional hazards. We illustrate the usage of the considered methods using publicly available data from a trial on adjuvant chemotherapy for colon cancer. R software code to implement all considered algorithms and to reproduce all analyses is available in an accompanying online appendix on Github. [ABSTRACT FROM AUTHOR]

Considering the influence of performance degradation on a product's traumatic failure, under the condition that only degradation data are observed and no traumatic failure data are observed, this paper proposes a subdistribution competing risk model to achieve a motorized spindle life assessment. This paper assumes that the failure rate ratio of the tested products does not change with time under different stress levels. Basic reliability with zero traumatic failure data is modeled by a unilateral confidence limit method under a two-parameter Weibull distribution. Performance degradation data are taken as covariates. The regression coefficients of the covariates are calculated by SPSS software. Then, a subdistribution competing risk model is constructed, which reflects the dependency relationship between reliability and performance degradation, and the product's reliability life can be evaluated accordingly. The correctness and advantages of the model built in this paper are verified by a case analysis combined with the performance degradation information of a motorized spindle. [ABSTRACT FROM AUTHOR]

Ranked set sampling (RSS) has been proved to be an efficient sampling design for parametric and nonparametric inference. This paper explores inference for a maximum RSS procedure with unequal samples (MRSSU) with multiple dependent failure causes. When the lifetimes of units are characterized by a proposed complementary competing risks model, classical likelihood and Bayesian approaches are discussed for parameters and reliability estimation. Maximum likelihood estimators of model parameters and associated existence and uniqueness are established, and approximate confidence intervals are constructed using asymptotic theory and delta methods. With respect to general flexible priors, Bayesian estimates of interested quantities are also performed and a Monte Carlo sampling algorithm is proposed for complex posterior computation. Additionally, when extra historical information between the competing risks parameters is available, likelihood and Bayesian estimation are also studied under an order restriction case. Different methods are compared based on extensive simulation studies, and another real data example is demonstrated for application propose. [ABSTRACT FROM AUTHOR]

Clustered bivariate survival data arise in various fields, such as biology and medicine, when individuals in a dataset are clustered and exhibit two survival outcomes. Recently, the joint frailty-copula model was proposed to analyze clustered bivariate survival outcomes by accommodating the between-cluster heterogeneity via a shared frailty term. In this model, researchers fitted the baseline hazard functions via the nonparametric model, the spline model, or the Weibull model. However, when a population has extremely large survival time, the baseline hazard functions are better modeled by a heavy-tailed distribution. In this paper, we adopt the Pareto type I distribution for the joint frailty-copula model, which is one of the most popular heavy-tailed distributions. We show that the moments of the Pareto type I joint frailty copula model diverge to infinity owing to the heavy right-tail. We develop statistical inference methods based on three types of censoring schemes: (i) bivariate random censoring, (ii) semi-competing risks, and (iii) competing risks. We develop maximum likelihood estimation procedures, and make our computational tools available for users. Simulations are performed to check the accuracy of the proposed method. We finally analyze a real dataset for illustration. [ABSTRACT FROM AUTHOR]

This paper describes estimation of the regression parameters and prediction of the cumulative incidence functions under the cause-specific proportional hazards model when some of covariates are not fully observed. Assuming that missingness mechanism is missing at random, we propose the augmented inverse probability weighted method for estimation and inference procedures. A nonparametric regression approach is adapted for estimating selection probabilities and conditional expectations of missing covariates in the augmented estimating function. We establish the asymptotic properties of the predicted cumulative incidence functions under the cause-specific proportional hazards model with missing covariates and derive consistent variance estimators of the predicted cumulative incidence functions. Simulation studies show that the procedures perform well. The proposed methods are illustrated with stage IV breast cancer data obtained from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute. [ABSTRACT FROM AUTHOR]

Competing risks survival analysis is used to answer questions about the time to occurrence of events with the extension of multiple causes of failure. Studies that investigate how clinical features and risk factors of COVID-19 are associated with the survival of patients in the presence of competing risks (CRs) are limited. The main objective of this paper is, under a CRs setting, to estimate the Cumulative Incidence Function (CIF) of COVID-19 death, the CIF of other-causes death, and the probability of being cured in subjects with COVID-19, who have been under observation from the date of symptoms to the date of death or exit from the study because they are cured. In particular, we compared the non-parametric estimator of the CIF based on the naive technique of Kaplan–Meier (K–M) with the Aalen–Johansen estimator based on the cause-specific approach. Moreover, we compared two of the most popular regression approaches for CRs data: the cause-specific hazard (CSH) and the sub-distribution hazard (SDH) approaches. A clear overestimation of the CIF function over time was observed under the K–M estimation technique. Moreover, exposure to asthma, diabetes, obesity, older age, male sex, black and indigenous races, absence of flu vaccine, admission to the ICU, and the presence of other risk factors, such as immunosuppression and chronic kidney, neurological, liver, and lung diseases, significantly increased the probability of COVID-19 death. The highest hazard ratio of 2.03 was observed for subjects with an age greater than 70 years compared with subjects aged 50–60 years. The SDH approach showed slightly higher survival probabilities compared with the CSH approach. An important foundation for producing precise individualized predictions was provided by the competing risks regression models discussed in this paper. This foundation allowed us, in general, to more realistically model complex data, such as the COVID-19 data, and can be used, for instance, by many modern statistical learning and personalized medicine techniques to obtain more accurate conclusions. [ABSTRACT FROM AUTHOR]

Competing risks data are commonly encountered in randomized clinical trials and observational studies. This paper considers the situation where the ending statuses of competing events have different clinical interpretations and/or are of simultaneous interest. In clinical trials, often more than one competing event has meaningful clinical interpretations even though the trial effects of different events could be different or even opposite to each other. In this paper, we develop estimation procedures and inferential properties for the joint use of multiple cumulative incidence functions (CIFs). Additionally, by incorporating longitudinal marker information, we develop estimation and inference procedures for weighted CIFs and related metrics. The proposed methods are applied to a COVID‐19 in‐patient treatment clinical trial, where the outcomes of COVID‐19 hospitalization are either death or discharge from the hospital, two competing events with completely different clinical implications. [ABSTRACT FROM AUTHOR]

This paper considers a competing risk model defined on the basis of minimum of two dependent failures where the two failures are assumed to jointly follow Marshall–Olkin bivariate Weibull distribution. This paper explores some important features of corresponding likelihood functions and performs a full Bayesian analysis of the model for data resulting from normal as well as accelerated life tests. The accelerated model is described by regressing the scale parameters of the model through inverse power-law relationship. Posterior-based inferences are drawn using the Gibbs sampler algorithm after specifying proper but vague priors for the model parameters. The numerical illustration is provided using real datasets. The performance of the model is assured by Bayesian tools of model compatibility and then the entertained model is compared with the competing risk model based on Marshall–Olkin bivariate exponential assumption. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the shock model with two kinds of shocks from competing risks outlook. A component or system having two failure modes is considered. The two crude probabilities of failures are modelled and assessed. For assessment of the crude probabilities, Type I (time) censoring life test is considered. Monte-Carlo simulation experiments are used to validate the results derived. [ABSTRACT FROM AUTHOR]

In the present paper, we have considered prostate cancer data to study the competing risks. We considered various covariates, their impact on survival for different causes and also the impact of covariates on causes in absence and presence of competing risks. We conclude that for a cause cancer, except for weight index (Wt), history of cardiovascular disease (hx) and serum haemoglobin (HG), all the covariates are statistically significant both in absence and presence of competing risks. In case of Cardio Vascular Disease (CVD), except for history of cardiovascular disease (hx), all are statistically insignificant. Further, we have considered subjects having failure time greater than or equal to 11 months and observed significant changes in the covariates for different causes. [ABSTRACT FROM AUTHOR]

This paper discusses nonparametric identification and estimation of the causal effect of a treatment in the presence of confounding, competing risks and random right-censoring. Our identification strategy is based on an instrumental variable. We show that the competing risks model generates a nonparametric quantile instrumental regression problem. Quantile treatment effects on the subdistribution function can be recovered from the regression function. A distinguishing feature of the model is that censoring and competing risks prevent identification at some quantiles. We characterize the set of quantiles for which exact identification is possible and give partial identification results for other quantiles. We outline an estimation procedure and discuss its properties. The finite sample performance of the estimator is evaluated through simulations. We apply the proposed method to the Health Insurance Plan of Greater New York experiment. [ABSTRACT FROM AUTHOR]

Background: Comprehensive investigations of the prognosis factors and treatment strategies with adjustment of competing causes of death for patients with malignant meningioma (MM) is still lacking. Patient and method: The surveillance, Epidemiology, and End Results (SEER) database were used to include adult patients with this rare disease between 2004 and 2018. The probability of MM-caused mortality (MMCM) and non-MM-caused mortality (non-MMCM) were presented by cumulative incidence function curves. Then, the association between variates with non-MMCM was evaluated by the cox proportional hazard model, and the prognostic factors of MMCM were identified by Fine-Gray competing risk regression model. Furthermore, a nomogram was developed to predict the 1-year, 2-year, and 5-year MMCM and the performance was tested by a time-dependent area under the receiver operating characteristic (ROC) curve and calibration. Result: 577 patients were included, with a median age of 62 (18–100) years old and a median overall survival time of 36 (0–176) months. The percentage of non-MMCM was 15.4% (n = 89) in the entire population and 21.7% (n = 54) in elderly patients. The multivariable Cox proportional hazard regression model revealed that older age and other tumor(s) before or after MM had an independently significant association with higher non-MMCM. After adjustment of competing causes of death, the multivariable Fine-gray regression model identified age group ≥ 65 year, tumor size > 5.3 cm, recurrent MM, and histologic type 9530/3 (Meningioma, malignant) had an independently significant association with higher MMCM. Compared with gross total (GTR) of tumor, subtotal resection of tumor (HR 1.66, 95%CI 1.08–2.56, P = 0.02), partial resection of lobe (HR 2.26, 95%CI 1.32–3.87, P = 0.003), and gross total resection of lobe (HR 1.69, 95%CI 1.12–2.51, P = 0.01) had an independently significant association with higher MMCM. Conclusion: The competing risk nomogram including age group, tumor size, initial status, histologic type, and extent of resection is discriminative and clinically useful. This study emphasized the importance of the GTR of tumor in the treatment of MM patients, which had a significantly lower incidence of MMCM compared with biopsy, STR of tumor, partial resection of lobe, and GTR of lobe. [ABSTRACT FROM AUTHOR]

Background: Retaining clients on antiretroviral therapy (ART) is challenging, especially during the first year on ART. Mobile health (mHealth) interventions show promise to close retention gaps. We aimed to assess reach (who received the intervention?) and effectiveness (did it work?) of a hybrid two-way texting (2wT) intervention to improve ART retention at a large public clinic in Lilongwe, Malawi. Methods: Between August 2021—June 2023, in a quasi-experimental study, outcomes were compared between two cohorts of new ART clients: 1) those opting into 2wT who received automated, weekly motivation short messaging service (SMS) messages and response-requested appointment reminders; and 2) a matched historical cohort receiving standard of care (SoC). Reach was defined as "the proportion clients ≤6 months of ART initiation eligible for 2wT". 2wT effectiveness was assessed in time-to-event analysis. Retention was presented in a Kaplan-Meier plot and compared between 2wT and SoC using a log-rank test. The effect of 2wT on ART dropout (lost to follow-up or stopped ART) was estimated using Fine-Gray competing risk regression models, adjusting for sex, age and WHO HIV stage at ART initiation. Results: Of 1,146 clients screened, 501 were eligible for 2wT, a reach of 44%. Lack of phone (393/645; 61%) and illiteracy (149/645; 23%) were the most common ineligibility reasons. Among 468 participants exposed to 2wT, 12-month probability of ART retention was 91% (95% CI: 88% - 94%) compared to 76% (95% CI: 72% - 80%) among 468 SoC participants (p<0.001). Compared to SoC, 2wT participants had a 65% lower hazard of ART dropout at any timepoint (sub-distribution hazard ratio 0.35, 95% CI: 0.24–0.51; p<0.001). Conclusions: 2wT did not reach all clients. For those who opted-in, 2wT significantly increased 12-month ART retention. Expansion of 2wT as a complement to other retention interventions should be considered in other low-resource, routine ART settings. [ABSTRACT FROM AUTHOR]

Background: According to long-term follow-up data of malignant tumor patients, assessing treatment effects requires careful consideration of competing risks. The commonly used cause-specific hazard ratio (CHR) and sub-distribution hazard ratio (SHR) are relative indicators and may present challenges in terms of proportional hazards assumption and clinical interpretation. Recently, the restricted mean time lost (RMTL) has been recommended as a supplementary measure for better clinical interpretation. Moreover, for observational study data in epidemiological and clinical settings, due to the influence of confounding factors, covariate adjustment is crucial for determining the causal effect of treatment. Methods: We construct an RMTL estimator after adjusting for covariates based on the inverse probability weighting method, and derive the variance to construct interval estimates based on the large sample properties. We use simulation studies to study the statistical performance of this estimator in various scenarios. In addition, we further consider the changes in treatment effects over time, constructing a dynamic RMTL difference curve and corresponding confidence bands for the curve. Results: The simulation results demonstrate that the adjusted RMTL estimator exhibits smaller biases compared with unadjusted RMTL and provides robust interval estimates in all scenarios. This method was applied to a real-world cervical cancer patient data, revealing improvements in the prognosis of patients with small cell carcinoma of the cervix. The results showed that the protective effect of surgery was significant only in the first 20 months, but the long-term effect was not obvious. Radiotherapy significantly improved patient outcomes during the follow-up period from 17 to 57 months, while radiotherapy combined with chemotherapy significantly improved patient outcomes throughout the entire period. Conclusions: We propose the approach that is easy to interpret and implement for assessing treatment effects in observational competing risk data. [ABSTRACT FROM AUTHOR]

Low-Density Lipoprotein (LDL) cholesterol is one of the main target for cardiovascular (CV) prevention and therapy. In the last years, Proprotein Convertase Subtilisin–Kexin type 9 inhibitors (PCSK9-i) has emerged as a key therapeutic target to lower LDL and were introduced for prevention of CV events. Recently (June 2022) the Italian Medicines Agency (AIFA) modified the eligibility criteria for the use of PCSK9-i. We designed an observational study to estimate the prevalence of eligible subjects and evaluate the effectiveness of PCSK9-i applying a Target Trial Emulation (TTE) approach based on Electronic Health Records (EHR). Subjects meeting the eligibility criteria were identified from July 2017 (when PCSK9-i became available) to December 2020. Outcomes were all-cause death and the first hospitalization. Among eligible subjects, we identified those treated at date of the first prescription. Inverse Probability of Treatment Weights (IPTW) were estimated including demographic and clinical covariates, history of treatment with statins and the month/year eligibility date. Competing risk models on weighted cohorts were used to derive the Average Treatment Effect (ATE) and the Conditional Average Treatment Effect (CATE) in subgroups of interest. Out of 1976 eligible subjects, 161 (8%) received treatment with PCSK9-i. Treated individuals were slightly younger, predominantly male, had more severe CV conditions, and were more often treated with statin compared to the untreated subjects. The latter exhibited a higher prevalence of non-CV comorbidities. A significant absolute and relative risk reduction of death and a lower relative risk for the first hospitalization was observed. The risk reduction for death was confirmed in CATE analysis. PCSk9-i were prescribed to a minority of eligible subjects. Within the TTE framework, the analysis confirmed the association between PCSK9-i and lower risk of events, aligning with findings from randomized clinical trials (RCTs). In our study, PCSK9-i provided protection specifically against all-cause death, expanding upon the evidence from RCTs that had primarily focused on composite CV outcomes. [ABSTRACT FROM AUTHOR]

We examine how older Americans' poverty entry and exit patterns are associated with survey sample attrition using a longitudinal data set for 2002-2018 from the Health and Retirement Study. We consider how sample attrition affects estimates of variables associated with poverty entry and exit, and we find that attrition bias is less apparent in models estimating poverty entry than in models of poverty exit. The effect of aging on poverty exit is smaller in competing risks models than in proportional risk models, and cross-model differences in race and ethnicity effects are not statistically significant. This indicates that long-term respondents were more likely to exit poverty than were those who attrited from the sample, implying a change in sample representativeness over time. Our research confirms the importance of understanding panel data attrition biases when examining older Americans' poverty vulnerability. [ABSTRACT FROM AUTHOR]

This study explores the impact of densely-ionizing radiation on non-cancer and cancer diseases, focusing on dose, fractionation, age, and sex effects. Using historical mortality data from approximately 21,000 mice exposed to fission neutrons, we employed random survival forest (RSF), a powerful machine learning algorithm accommodating nonlinear dependencies and interactions, treating cancer and non-cancer outcomes as competing risks. Unlike traditional parametric models, RSF avoids strict assumptions and captures complex data relationships through decision tree ensembles. SHAP (SHapley Additive exPlanations) values and variable importance scores were employed for interpretation. The findings revealed clear dose–response trends, with cancer being the predominant cause of mortality. SHAP value dose–response shapes differed, showing saturation for cancer hazard at high doses (> 2 Gy) and a more linear pattern at lower doses. Non-cancer responses remained more linear throughout the entire dose range. There was a potential inverse dose rate effect for cancer, while the evidence for non-cancer was less conclusive. Sex and age effects were less pronounced. This investigation, utilizing machine learning, enhances our understanding of the patterns of non-cancer and cancer mortality induced by densely-ionizing radiations, emphasizing the importance of such approaches in radiation research, including space travel and radioprotection. [ABSTRACT FROM AUTHOR]

Background: Patients with early-stage breast cancer may have a higher risk of dying from other diseases, making a competing risks model more appropriate. Considering subdistribution hazard ratio, which is used often, limited to model assumptions and clinical interpretation, we aimed to quantify the effects of prognostic factors by an absolute indicator, the difference in restricted mean time lost (RMTL), which is more intuitive. Additionally, prognostic factors of breast cancer may have dynamic effects (time-varying effects) in long-term follow-up. However, existing competing risks regression models only provide a static view of covariate effects, leading to a distorted assessment of the prognostic factor. Methods: To address this issue, we proposed a dynamic effect RMTL regression that can explore the between-group cumulative difference in mean life lost over a period of time and obtain the real-time effect by the speed of accumulation, as well as personalized predictions on a time scale. Results: A simulation validated the accuracy of the coefficient estimates in the proposed regression. Applying this model to an older early-stage breast cancer cohort, it was found that 1) the protective effects of positive estrogen receptor and chemotherapy decreased over time; 2) the protective effect of breastconserving surgery increased over time; and 3) the deleterious effects of stage T2, stage N2, and histologic grade II cancer increased over time. Moreover, from the view of prediction, the mean C-index in external validation reached 0.78. Conclusion: Dynamic effect RMTL regression can analyze both dynamic cumulative effects and real-time effects of covariates, providing a more comprehensive prognosis and better prediction when competing risks exist. [ABSTRACT FROM AUTHOR]

This paper considers the one-step targeted maximum likelihood estimation methodology for multi-dimensional causal parameters in general survival and competing risk settings where event times take place on the positive real line and are subject to right censoring. We focus on effects of baseline treatment decisions possibly confounded by pretreatment covariates, but remark that our work generalizes to settings with time-varying treatment regimes and time-dependent confounding. We point out two overall contributions of our work. First, our methods can be used to obtain simultaneous inference for treatment effects on multiple absolute risks in competing risk settings. Second, our methods can be used to achieve inference for the full survival curve, or a full absolute risk curve, across time. The one-step targeted maximum likelihood procedure is based on a one-dimensional universal least favourable submodel for each cause-specific hazard that we implement in recursive steps along a corresponding nonuniversal multivariate least favourable submodel. Our empirical study demonstrates the practical use of the methods. [ABSTRACT FROM AUTHOR]

In this paper a new bivariate lifetime distribution is introduced. Its marginal distribution functions follow two-parameter Chen distribution, which has a bathtub shaped or increasing hazard rate functions. The proposed distribution, which we call a bivariate Chen distribution (BCD), is of Marshall-Olkin type and it is a singular distribution. Several properties of this proposed distribution are discussed. The BCD distribution has four unknown parameters. The maximum likelihood (ML) method and the Bayes techniques are used to estimate the unknown parameters. The maximum likelihood estimators or the Bayes estimators cannot be obtained in closed form. Numerical methods have been used in both cases. A real data set is analyzed using the proposed distribution for illustrative and comparison purposes. An application to dependent competing risks data is discussed, and finally we have extended the BCD to the multivariate case. [ABSTRACT FROM AUTHOR]

Gompertz distribution is a significant and practical continuous lifetime distribution, which plays an important role in reliability engineering. A Gompertz distribution competing risks model is discussed and studied under general progressive censoring in this paper. When the lifetime model fails for different latent reasons, the maximum likelihood estimates are given for the unknown parameters. The approximate confidence intervals through Fisher information matrix and bootstrap confidence intervals are established, containing bootstrap-p and bootstrap-t techniques. In addition, the Bayes estimation of unknown parameters is investigated under the condition of squared error loss. Moreover, the Bayes credible interval is derived. Finally, a numerical simulation is conducted to evaluate the performances of the proposed methods and real-life data is analyzed by applying the proposed inference methods. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the inference for the competing risks model when the failure times follow Chen distribution. With assumption of two causes of failures, which are partially observed, are considered as independent. The existence and uniqueness of maximum likelihood estimates for model parameters are obtained under generalized progressive hybrid censoring. Also, we discussed the classical and Bayesian inferences of the model parameters under the assumption of restricted and nonrestricted parameters. Performance of classical point and interval estimators are compared with Bayesian point and interval estimators by conducting extensive simulation study. In addition to that, for illustration purpose, a real life example is discussed. Finally, some concluding remarks, regarding the presented model, are made. [ABSTRACT FROM AUTHOR]

Fatal Shock, competing risks and stress models are utilized in reliability and survival analysis to characterize various application types. In this context, this paper aimed to introduce a new class of bivariate distribution based on the Marshall–Olkin type. The proposed distribution termed as the Bivariate Extended Chen (BEC) distribution so that the marginals have Extended Chen distribution. Some properties of this distribution are derived and explained. The BEC distribution parameters are estimated using the maximum likelihood method. Finally, two applications to real life applications highlight the significance and adaptability of the Bivariate Extended Chen (BEC) distribution. The BEC distribution offers a superior fit than different competing bivariate distributions, illustrating its flexibility and applicability in modelling. [ABSTRACT FROM AUTHOR]

The common used goodeness-of-fit tests are based on the empirical distributions functions (EDF) where distances between empirical and theoretical hypothesized distributions are compared to critical values. The aim of this paper is to provide for different sample sizes, tables of goodness-of-fit critical values of modified Kolmogorov-Smirnov statistic D n , Anderson-Darling statistic A2, Cramer-Von Mises statistic W 2 , Liao and Shimokawa statistic Ln, and Watson statistic U2 for the competing risks model of Bertholon which is used to describe the reliability of real systems where failure times can have different risks and in medical studies to characterize the survival time of patients who can have risks of death from different causes. The power of these statistics is studied using some alternatives such as the exponential, the inverse Weibull, the exponentiated Weibull and the exponentiated exponential distributions. All the computation are carried out by using matlab software and Monte Carlo method. [ABSTRACT FROM AUTHOR]

The analysis of left truncated and right censored data is very common in survival and reliability analysis. In lifetime studies patients are often subject to left truncation in addition to right censoring. For example, in bone marrow transplant studies based on International Bone Marrow Transplant Registry (IBMTR), the patients who die while waiting for the transplants will not be reported to the IBMTR. In this paper, we develop novel U-statistics under left truncation and right censoring. We prove the n -consistency of the proposed U-statistics. We derive the asymptotic distribution of the U-statistics using the counting process technique. As an application of the U-statistics, we develop a simple non-parametric test for testing the independence between time to failure and cause of failure in competing risks when the observations are subject to left truncation and right censoring. The finite sample performance of the proposed test is evaluated through a Monte Carlo simulation study. Finally, we illustrate our test procedure using the lifetime data of transformers. [ABSTRACT FROM AUTHOR]

A new model is presented to analyze reliability for systems subjected to competing risks of a typical degradation process and external random shocks. The external random shocks may cause hard failure and instantaneous increases in the degradation process. Random shocks are classified into three types in the new model according to their sizes. Different types will lead to different instantaneous increases in the degradation process. Besides system reliability, the competing failure probabilities are also studied. Competing failure probability indicates the probability that one risk mode fails while the other risk mode does not fail. Competing failure probabilities are helpful in determining which risk mode is more likely to occur during a system's lifetime. It is impractical if both risk modes fail together for systems under competing failure modes, while the system reliability and failure probabilities, which are simply calculated by expression, do not resolve this impractical situation. The modified values of system reliability and competing failure probability are calculated in this paper with the impractical situation excluded. The effectiveness of the presented model is demonstrated by the reliability analysis of the micro-electromechanical system (MEMS), which proved that the probabilities calculated using this method are more practical. In addition, sensitivity analysis is performed for specific parameters. [ABSTRACT FROM AUTHOR]

The additive hazard regression model plays an important role when the excess risk is the quantity of interest compared to the relative risks, where the proportional hazard model is better. This paper discusses parametric regression analysis of survival data using the additive hazards model with competing risks in the presence of independent right censoring. In this paper, the baseline hazard function is parameterized using a modified Weibull distribution as a lifetime model. The model parameters are estimated using maximum likelihood and Bayesian estimation methods. We also derive the asymptotic confidence interval and the Bayes credible interval of the unknown parameters. The finite sample behaviour of the proposed estimators is investigated through a Monte Carlo simulation study. The proposed model is applied to liver transplant data. [ABSTRACT FROM AUTHOR]

The motivation of this paper came from two bivariate diabetic retinopathy data sets. The main aim is to test whether the laser treatment delays the onset of blindness compared to the traditional treatment. The first data set is of 197 patients and it provides the onset of blindness of the two eyes. The observed data are heavily censored on both the variables. The second data set is of 91 patients, and it indicates the minimum time of the onset of blindness between the two eyes. In both the cases there is a significant proportion where the onset of blindness has occured on both the eyes simultaneously, i.e. there is a significant proportion where both the variables are equal. Hence, the two variables cannot be treated as independent. We have used a Marshall-Olkin bivariate exponential or Weibull type a bivariate semi-parametric model, where the base line distribution is more flexible than any parametric distribution. The base line distribution is assumed to have a piecewise constant hazard function and that makes the Bayes line hazard function to be very flexible. Marshall-Olkin bivariate exponential distribution becomes a special case of the model. The maximum likelihood estimators may not always exist, and we have considered the Bayesian inference of the unknown parameters. We have used importance sampling technique to compute Bayes estimators and the associated credible intervals. We have addressed some testing of hypothesis problem also based on Bayes factors. Finally, both the data sets have been analyzed, and it is observed for one data set the laser treatment has a significantly different effect than the traditional treatment, where as for the other data set no significantly different effect has been observed. [ABSTRACT FROM AUTHOR]

In some clinical studies patient survival beyond a specific point in time, t0$$ {t}_0 $$, say, may be of special interest as it may for instance indicate patient cure. To analyze the t0$$ {t}_0 $$‐year risk for such patients may be accomplished using logistic regression with appropriate weights (IPWCC) that may further be augmented (AIPWCC) to improve efficiency. In this paper, we derive the most efficient estimator for this problem, which is different from the AIPWCC based on the full data efficient influence function. We first give the result for a survival endpoint and then generalize to the competing risk setting. The proposed estimators superior behavior is illustrated using simulations as well as applying it to some real data concerning the survival of blood and marrow transplanted patients. [ABSTRACT FROM AUTHOR]

In survival data analysis, a competing risk is an event whose occurrence precludes or alters the chance of the occurrence of the primary event of interest. In large cohort studies with long‐term follow‐up, there are often competing risks. Further, if the event of interest is rare in such large studies, the case‐cohort study design is widely used to reduce the cost and achieve the same efficiency as a cohort study. The conventional additive hazards modeling for competing risks data in case‐cohort studies involves the cause‐specific hazard function, under which direct assessment of covariate effects on the cumulative incidence function, or the subdistribution, is not possible. In this paper, we consider an additive hazard model for the subdistribution of a competing risk in case‐cohort studies. We propose estimating equations based on inverse probability weighting methods for the estimation of the model parameters. Consistency and asymptotic normality of the proposed estimators are established. The performance of the proposed methods in finite samples is examined through simulation studies and the proposed approach is applied to a case‐cohort dataset from the Sister Study. [ABSTRACT FROM AUTHOR]

In this paper, reliability estimation for a competing risks model is discussed under a block progressive censoring scheme, which improves experimental efficiency through testing items under different testing facilities. When the lifetime of units follows an inverted exponentiated exponential distribution (IEED) and taking difference in testing facilities into account, various approaches are established for estimating unknown parameters, reliability performances and the differences in different testing facilities. Maximum likelihood estimators of IEED competing risks parameters together with existence and uniqueness are established, and the reliability performances and the difference in different testing facilities are also obtained in consequence. In addition, a hierarchical Bayes approach is proposed and the Metropolis‐Hastings sampling algorithm is constructed for complex posterior computation. Finally, extensive simulation studies and a real data analysis are carried out to elaborate the performance of the methods, and the numerical results show that the proposed hierarchical Bayes model outperforms than classical likelihood method under block progressive censoring. [ABSTRACT FROM AUTHOR]

In many reliability studies, the experimental units may fail due to one of several causes of failure. It is usually assumed that the competing risks of failure are independent. In many practical situations, however, the interpretation of the failure modes makes the assumption of independence unreasonable. Copulas are considered an effective tool for modeling the dependence structure among the multiple competing risks. This paper presents Bayesian analysis of progressively Type-II censored dependent competing risks data using copulas. The analysis is performed under the assumption of binomial progressive random removals and Weibull failure times, where unit failure occurs due to only one of the competing risks. Bayesian point and interval estimates of the unknown parameters are derived using different Archimedean copulas with non-conjugate prior distributions. A simulation study is carried out to assess the performance of the proposed techniques under different dependence structures. A real data set is analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

Background: The influence of center volume on kidney transplant outcomes is a topic of ongoing debate. In this study, we employed competing risk analyses to accurately estimate the marginal probability of graft failure in the presence of competing events, such as mortality from other causes with long-term outcomes. The incorporation of immunosuppression protocols and extended follow-up offers additional insights. Our emphasis on long-term follow-up aligns with biological considerations where competing risks play a significant role. Methods: We examined data from 219,878 adult kidney-only transplantations across 256 U.S. transplant centers (January 2001-December 2015) sourced from the Organ Procurement and Transplantation Network registry. Centers were classified into quartiles by annual volume: low (Q1 = 28), medium (Q2 = 75), medium-high (Q3 = 121), and high (Q4 = 195). Our study investigated the relationship between center volume and 5-year outcomes, focusing on graft failure and mortality. Sub-population analyses included deceased donors, living donors, diabetic recipients, those with kidney donor profile index >85%, and re-transplants from deceased donors. Results: Adjusted cause-specific hazard ratios (aCHR) for Five-Year Graft Failure and Patient Death were examined by center volume, with low-volume centers as the reference standard (aCHR: 1.0). In deceased donors, medium-high and high-volume centers showed significantly lower cause-specific hazard ratios for graft failure (medium-high aCHR = 0.892, p<0.001; high aCHR = 0.953, p = 0.149) and patient death (medium-high aCHR = 0.828, p<0.001; high aCHR = 0.898, p = 0.003). Among living donors, no significant differences were found for graft failure, while a trend towards lower cause-specific hazard ratios for patient death was observed in medium-high (aCHR = 0.895, p = 0.107) and high-volume centers (aCHR = 0.88, p = 0.061). Conclusion: Higher center volume is associated with significantly lower cause-specific hazard ratios for graft failure and patient death in deceased donors, while a trend towards reduced cause-specific hazard ratios for patient death is observed in living donors. [ABSTRACT FROM AUTHOR]

Background: Intrahepatic cholangiocarcinoma (ICC) correlates with poor outcomes, necessitating the identification of prognostic factors from an inflammation-nutritional perspective in locally advanced ICC patients after R0 resection. Methods: We retrospectively reviewed the medical records of 159 locally advanced ICC patients from Sun Yat-sen University Cancer Center. Univariate and multivariate Cox regression analysis, as well as competing risk analysis, were conducted to explore prognostic variables for locally advanced ICC following surgery. To validate the robustness of our findings, we performed propensity score matching (PSM) analyses to evaluate survival differences based on inflammation-nutritional indexes. Results: Considering non-cancer-specific death as competing risk factors, both systemic immune-inflammation index (SII, HR: 1.934) and prognostic nutrition index (PNI, HR: 0.604) emerged as significant prognostic variables for locally advanced ICC after R0 resection (P < 0.05). After PSM, the survival benefit between the low and high PNI sets remained clear (median survival time: 15.7 months vs 35.1 months, P = 0.002). Although the 5-year overall survival (OS) rate of the low SII group was higher than that of the high SII group, the difference was not statistically significant (17.5% VS 27.4%, P = 0.112). Other influencing factors included tumor number, tumor diameter, preoperative carcinoembryonic antigen (CEA)and carbohydrate antigen 19– 9 (CA19-9) levels, and postoperative adjuvant therapy. Conclusion: Individual inflammatory and nutritional status significantly impact the prognosis of locally advanced ICC undergoing R0 hapectomy. Oncologists should consider incorporating inflammation-nutritional conditions into the decision-making process for this subset of advanced ICC. [ABSTRACT FROM AUTHOR]