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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]

The author discusses the article "Meta-Analysis for Surrogacy: Accelerated Failure Time (AFT) Models and Semi-Competing Risks Modeling," by D. Ghosh et al. He focuses on some issues raised by the methodology for trial-level surrogacy used in the paper. He restricts attention to oncology trials as their illustrative application is in oncology. He also argues on the recommendation by the authors not to use composite time-to-event endpoints in the trial.

Ross Prentice's work has had the most profound impact on the theory and practice of statistics. His research interests range from survival analysis, longitudinal data analysis, epidemiologic designs and analysis, to genomic studies. His contributions are so broad and so deep that it would be impossible to provide a comprehensive review in any limited amount of space. In this commentary, I will attempt to give a brief tour of some of his statistical work, focusing on ten of my favorite papers of his. I will describe the main ideas in those papers and their influence on the directions of statistical research and on the designs and analysis of medical studies. I will mention a few stories along the way. [ABSTRACT FROM AUTHOR]

We use the proportional hazard model (PHM) to study purchase-timing behavior of households in two product categories: laundry detergents and paper towels. The PHM decomposes a household's instantaneous probability of buying the product at a point of time into two components: the baseline hazard that captures the household's intrinsic purchase pattern over time and the covariate function that captures the effects of marketing variables on the household's purchase timing decision. We compare the continuous-time and discrete-time PHMs, where the latter explicitly accounts for households' shopping trips that do not involve purchase of the product. We find that the discrete-time PHM empirically outperforms the continuous-time PHM in terms of explaining the observed purchase outcomes. We compare five different parametric specifications of the baseline hazard, and find that the three-parameter expo-power specification outperforms the exponential, Erlang-2, Weibull, and log-logistic specifications. We use a cause-specific, competing-risks PHM to distinguish between two types of purchase events that differ in terms of whether or not they were preceded by a shopping trip that involved purchase of the product. Such a cause-specific, competing-risks PHM is shown to outperform the traditional discrete-time PHM. We then estimate a nonparametric version of the PHM and find that it does not offer any additional insights compared to the parsimonious parametric PHM. Finally, we accommodate unobserved heterogeneity across households by allowing all of the parameters of the PHM to follow a discrete distribution across households whose locations and supports are nonparametrically estimated from the data. We find evidence for substantial unobserved heterogeneity in the data, both in the parameters of marketing variables and in the baseline hazards. This study will be a useful reference to researchers hoping to use the PHM to study event times. [ABSTRACT FROM AUTHOR]

In this paper, we propose a statistical model to describe the behaviour of failure times associated with groups of repairable systems hierarchically represented, under a competing risks framework, considering the existence of unobserved heterogeneity that acts individually on systems of each group, as well as the possibility of imperfect repairs whose initial failure rate is in the form of the power law. In this context for the unobserved heterogeneity in the groups, we consider the multiplicative frailty. To illustrate the use of the proposed model, we consider a database with the failures of 38 agricultural machines categorized into five different groups. We understand that the tractor fleet corresponds to the farm's agricultural system, therefore the need for intervention in this system occurs with the failure of any unit, individually, in a serial structure, of competing risks.e On the other hand, the understanding of the time in which all the machinery that makes up the fleet will have required some intervention is obtained by analysing the results under a parallel structure. [ABSTRACT FROM AUTHOR]

In this paper, we develop a Bayesian two-stage cure rate model whose biological destructive mechanism (immune system) of the competing risk factors of death is suitable for detecting the impact on the long-term survival function of three sources of variance well-known in accident theory: randomness, liability and proneness. From a survival analysis viewpoint, proneness means individual effect or destructive mechanism and liability corresponds to external effects or covariates. The flexibility of the generalized Waring frailty distribution in capturing these variance components separately enables one to understand the nature of overdispersion of the risk factors involved in studying risk of death after a long-term treatment of the patient. A new cure rate, involving covariate and destructive mechanism, is developed here under a competing cause scenario. A simulation study and an application to colorectal cancer data set are finally presented to demonstrate the usefulness of the proposed model and the inferential results developed here. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

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]

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]

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]

Purpose: This paper analyses the collapse of credit booms into soft landings or systemic banking crises. Design/methodology/approach: A discrete-time competing risks duration model is employed to disentangle the factors behind the length of benign and harmful credit booms. Findings: The results show that economic growth and monetary authorities play the major role in explaining the differences in the length and outcome of credit booms. Moreover, both types of credit expansions display positive duration dependence, i.e. both are more likely to end as they grow older, but hard landing credit booms have proven to be longer than those that land softly. Originality/value: This paper contributes to our understanding of what affects the length of credit booms and why some end up creating havoc and others do not. In particular, it calls the attention to the important role that Central Bank independence plays regarding credit booms length and outcome. [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]

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]

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]

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]

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]

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]

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]

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]

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]

In many practical situations, more than one failure mechanism may contribute to product failure. Many studies assume independence between the different competing risks of failure. Nevertheless, the assumption of independence is not always justified in various practical applications. When the competing risks are assumed dependent, it is important to identify models that describe their dependence structure. Copulas are considered a powerful tool to model such dependence structures. This paper addresses the problem of developing Bayesian life test acceptance criteria through two-sample prediction of future observations based on another independent Weibull progressively Type-II censored sample with binomial random removals. It is assumed that unit failure occurs due to only one of two competing risks. Dependence among the competing risks of failure is modeled using Archimedean copulas with nonconjugate prior distributions. A Metropolis–Hastings Markov chain Monte Carlo algorithm is implemented to derive the prediction intervals that define the proposed acceptance criteria. The derived acceptance criteria enable manufacturers to conform to the required quality specifications and help their clients to properly set their quality expectations. A real data example is provided to illustrate the proposed life test acceptance criteria. [ABSTRACT FROM AUTHOR]

In observational/field studies, competing risks and left-truncation may co-exist, yielding 'left-truncated competing risks' settings. Under the assumption of independent competing risks, parametric estimation methods were developed for left-truncated competing risks data. However, competing risks may be dependent in real applications. In this paper, we propose a Bayesian estimator for both independent competing risks and copula-based dependent competing risks models under left-truncation. The simulations show that the Bayesian estimator for the copula-based dependent risks model yields the desired performance when competing risks are dependent. We also comprehensively explore the choice of the prior distributions (Gamma, Inverse-Gamma, Uniform, half Normal and half Cauchy) and hyperparameters via simulations. Finally, two real datasets are analyzed to demonstrate the proposed estimators. [ABSTRACT FROM AUTHOR]

This paper explores inferences for a competing risk model with dependent causes of failure. When the lifetimes of competing risks are modelled by a Marshall–Olikin bivariate Kies distribution, classical and Bayesian estimations are studied under generalized progressive hybrid censoring. The existence and uniqueness results for maximum likelihood estimators of unknown parameters are established, whereas approximate confidence intervals are constructed using the observed Fisher information matrix. In addition, Bayes estimates are explored based on a flexible Gamma-Dirichlet prior information. Furthermore, when there is a priori order information on competing risk parameters being available, traditional classical likelihood and Bayesian estimates are also established under restricted parameter case. The behavior of the proposed estimators is evaluated through extensive simulation studies, and a real data study is presented for illustrative purposes. [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 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]

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]

A system consisting of interconnected components in series is under consideration. This research focuses on estimating the parameters of this system for incomplete lifetime data within the framework of competing risks, employing an underlying inverse Weibull distribution. While one popular method for parameter estimation involves the Newton–Raphson (NR) technique, its sensitivity to initial value selection poses a significant drawback, often resulting in convergence failures. Therefore, this paper opts for the expectation–maximization (EM) algorithm. In competing risks scenarios, the precise cause of failure is frequently unidentified, and these issues can be further complicated by potential censoring. Thus, incompleteness may arise due to both censoring and masking. In this study, we present the EM‐type parameter estimation and demonstrate its superiority over parameter estimation based on the NR method. Two illustrative examples are provided. The proposed method is compared with the existing Weibull competing risks model, revealing the superiority of our approach. Through Monte Carlo simulations, we also examine the sensitivity of the initial value selection for both the NR‐type method and our proposed method. [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]