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Retirement is an important event in the life of an individual. The decision to retire or exit from full-time employment may be motivated by several factors, including health. This paper explores the effect of both subjective and relatively more objective physical and mental health conditions on the probability of exit from full-time employment. Using longitudinal data on older Americans from ten waves of the Health and Retirement Study (1992–2010), eight health indices are created from a wide range of health measures by principal component analysis. The effect of these health indices on the time until exit from full-time employment is empirically examined in a proportional hazard model. Single and competing risk specifications are estimated that allow for multiple spells of full-time employment and control for unobserved heterogeneity. The main results suggest that better self-reported health decreases the likelihood of exit from full- time employment, while poor physical health (functional limitations factor) increases the likelihood of exit from full-time employment via complete retirement and disability. For mental health, I find that depression increases the likelihood of exit via complete retirement, part-time work and unemployment while cognitive disorders lead to an increase in likelihood of exit via the disability exit route. Hence, physical and mental health problems are both impediments to continued work. These results have implications for public policies targeted towards retaining older workers within the labor market. [ABSTRACT FROM AUTHOR]

Beck's rejection of the relevance of class in Risk Society has had an immense impact on both the fields of class analysis and the sociology of risk. In outlining a novel theory of the systemic importance of risks as side-effects and in making bold claims about how the production and distribution of risks are undermining class inequalities, Beck posed a highly influential challenge to both risk and class studies. Beck's impact on class analysis however has not been mainly due to widespread acceptance of his original claims about risk and class; rather, it has been research building upon Beck's work so as to critically depart from his conclusions through which Beck has made his contributions to the study of class. In seeking to identify the impact of Beck's work on the study of risk and class, this paper, firstly, outlines Beck's challenge to class analysis. It then proceeds to identify three key areas of research whose development was motivated by their critical engagement with Beck's work: the literature on risk and the continuity of class; the critical theory of the individualization of class inequality and the political economy of risk-class. This paper then concludes by critically evaluating Beck's more recent, partial acknowledgement of risk inequalities by arguing that there are significant limitations in his account of class, but that his work continues to offer a valuable opportunity to inspire future work on class and inequality. [ABSTRACT FROM AUTHOR]

In semi-competing risks one considers a terminal event, such as death of a person, and a non-terminal event, such as disease recurrence. We present a model where the time to the terminal event is the first passage time to a fixed level c in a stochastic process, while the time to the non-terminal event is represented by the first passage time of the same process to a stochastic threshold S, assumed to be independent of the stochastic process. In order to be explicit, we let the stochastic process be a gamma process, but other processes with independent increments may alternatively be used. For semi-competing risks this appears to be a new modeling approach, being an alternative to traditional approaches based on illness-death models and copula models. In this paper we consider a fully parametric approach. The likelihood function is derived and statistical inference in the model is illustrated on both simulated and real data. [ABSTRACT FROM AUTHOR]

In this paper, statistical inference for a competing risks model is discussed when latent failure times belong to a general family of inverted exponentiated distributions. Based on a generalized progressive hybrid censored data with partially observed failure causes, estimations for unknown parameters are presented under nonrestricted and restricted parameter cases from classic and Bayesian perspectives, respectively. The existence and uniqueness of maximum likelihood estimators of the unknown parameters are established, and the associated approximate confidence intervals are also constructed via Fisher information matrix. In sequel, the Bayes estimators and credible intervals of the parameters are also obtained as well. Finally, the performance of different estimators are evaluated using Monte Carlo simulations and a real data set is also analyzed for illustration. [ABSTRACT FROM AUTHOR]

In this paper, we describe an R package named JMcmprsk, for joint modelling of longitudinal and survival data with competing risks. The package in its current version implements two joint models of longitudinal and survival data proposed to handle competing risks survival data together with continuous and ordinal longitudinal outcomes respectively (Elashoff et al., 2008; Li et al., 2010). The corresponding R implementations are further illustrated with real examples. The package also provides simulation functions to simulate datasets for joint modelling with continuous or ordinal outcomes under the competing risks scenario, which provide useful tools to validate and evaluate new joint modelling methods. [ABSTRACT FROM AUTHOR]

Models with the bathtub-shaped hazard rate function are widely used in lifetime analysis and reliability engineering. In this paper, we adopted the reduced new modified Weibull (RNMW) distribution with a bathtub-shaped hazard rate function. Under consideration that the population units are failing with two independent causes of failure and the failure time is distributed with RNMW distribution, we formulate the model which is known as competing risks model. The model parameters under the type-II censoring scheme are estimated with the maximum likelihood method with the corresponding asymptotic confidence intervals. Also, the Bayes point and credible intervals with the help of MCMC methods are constructed. The real and simulated datasets are analyzed for illustrative purposes. Finally, the estimators are compared with the Monte Carlo simulation study. [ABSTRACT FROM AUTHOR]

Kundu and Gupta [Analysis of hybrid life-tests in presence of competing risks. Metrica. 2007;65:159–170] provided the analysis of Type-I hybrid censored competing risks data, when the lifetime distributions of the competing cause of failures follows exponential distribution. In this paper, we consider the analysis of Type-II hybrid censored competing risks data. It is assumed that latent lifetime distributions of the competing causes of failures follow independent exponential distributions with different scale parameters. It is observed that the maximum likelihood estimators of the unknown parameters do not always exist. We propose the modified estimators of the scale parameters, which coincide with the corresponding maximum likelihood estimators when they exist, and asymptotically they are equivalent. We obtain the exact distribution of the proposed estimators. Using the exact distributions of the proposed estimators, associated confidence intervals are obtained. The asymptotic and bootstrap confidence intervals of the unknown parameters are also provided. Further, Bayesian inference of some unknown parametric functions under a very flexible Beta-Gamma prior is considered. Bayes estimators and associated credible intervals of the unknown parameters are obtained using the Monte Carlo method. Extensive Monte Carlo simulations are performed to see the effectiveness of the proposed estimators and one real data set has been analysed for the illustrative purposes. It is observed that the proposed model and the method work quite well for this data set. [ABSTRACT FROM AUTHOR]

In this paper we consider an informative model of competing risks. We offer a new power estimate for the distribution function and prove its asymptotic equivalence to the previously known estimates and its efficiency compared to the well-known multiplicative Kaplan-Meier estimate. [ABSTRACT FROM AUTHOR]

In this paper, we consider some problems of estimation and reconstruction based on middle censored competing risks data. It is assumed that the lifetime distributions of the latent failure times are independent and exponential distributed with different parameters and also that the censoring mechanism is independent. The maximum likelihood estimators (MLEs) of the unknown parameters are obtained. We then use the asymptotic distribution of the MLEs to construct approximate confidence intervals. Based on gamma priors, Lindley's approximation method is applied to obtain the Bayesian estimates of the unknown parameters under squared error loss function. Since it is not possible to construct the credible intervals, we propose and implement the Gibbs sampling technique to construct the credible intervals. Several point reconstructors for failure time of censored units are provided. Finally, a simulation study is given by Monte-Carlo simulations to evaluate the performances of the different methods and a data set is analysed to illustrate the proposed procedures. [ABSTRACT FROM PUBLISHER]

Effective measurement of system resilience provides a comprehensive understanding of the system's characteristics. However, little research has been devoted to the resilience of a technical system that is affected by both the degradation process of the system and the external shocks. In addition, existing studies have mainly evaluated the resilience of systems without considering competing risks, and rarely investigated the transient resilience evaluation subjected to the interaction of shocks and maintenance. In this paper, a new resilience model is proposed for the systems under competing risks. The paper first introduces a competing risk model to depict the failure modes of the single-component system, and then uses semi-Markov processes to describe the state transition process when the system suffers the attacks of multiple shocks. Then, according to the multi-state division of the system, the resistibility index, absorbability index and recoverability index are proposed and the overall resilience is then introduced. Considering that the system needs to meet the reliability requirement, constrained by limit budget for maintenance, a reliability and cost-based resilience model is proposed. Finally, the case of a radar system subjected to shocks of one type and multiple types of shocks is given to illustrate the concept developed in this paper. [ABSTRACT FROM AUTHOR]

We propose a stochastic model for the failure times of items subject to two external random shocks occurring as events in an underlying bivariate counting process. This is a special formulation of the competing risks model, which is of interest in reliability theory and survival analysis. Specifically, we assume that a system, or an item, fails when the sum of the two types of shock reaches a critical random threshold. In detail, the two kinds of shock occur according to a bivariate space-fractional Poisson process, which is a two-dimensional vector of independent homogeneous Poisson processes time-changed by an independent stable subordinator. Various results are given, such as analytic hazard rates, failure densities, the probability that the failure occurs due to a specific type of shock, and the survival function. Some special cases and ageing notions related to the NBU characterization are also considered. In this way we generalize certain results in the literature, which can be recovered when the underlying process reduces to the homogeneous Poisson process. [ABSTRACT FROM AUTHOR]

System reliability depends on the reliability of the system's components and the structure of the system. For example, in a competing risks model, the system fails when the weakest component fails. The reliability function and the quantile function of a complicated system are two important metrics for characterizing the system's reliability. When there are data available at the component level, the system reliability can be estimated by using the component level information. Confidence intervals (CIs) are needed to quantify the statistical uncertainty in the estimation. Obtaining system reliability CI procedures with good properties is not straightforward, especially when the system structure is complicated. In this paper, we develop a general procedure for constructing a CI for the system failure-time quantile function by using the implicit delta method. We also develop general procedures for constructing a CI for the cumulative distribution function (cdf) of the system. We show that the recommended procedures are asymptotically valid and have good statistical properties. We conduct simulations to study the finite-sample coverage properties of the proposed procedures and compare them with existing procedures. We apply the proposed procedures to three applications; two applications in competing risks models and an application with a $$k\text{-out-of-}s$$ system. The paper concludes with some discussion and an outline of areas for future research. [ABSTRACT FROM AUTHOR]

In this paper, a competing risks model based on the generalized progressive hybrid censored two‐parameter Rayleigh distributions is studied under the assumption that the lifetime distributions of failure causes are identically distributed with same location and different scale parameters. We obtain maximum likelihood estimates of unknown parameters with associated existence uniqueness. The approximate confidence intervals are constructed using the asymptotic distribution of maximum likelihood estimates via the observed information matrix. Further, Bayes point estimates and the highest probability density credible intervals of unknown parameters are presented, and the Gibbs sampling technique is used to approximate corresponding estimates. A Monte Carlo simulation study is conducted to compare the accuracy of proposed estimates. Finally, a real‐life example is presented for illustration purpose. [ABSTRACT FROM AUTHOR]

Background: Missing data can complicate the interpretability of a clinical trial, especially if the proportion is substantial and if there are different, potentially outcome-dependent causes. Methods: We aimed to obtain unbiased estimates, in the presence of a high level of missing data, for the intervention effects in a prodromal Alzheimer's disease trial: the LipiDiDiet study. We used a competing risk joint model that can simultaneously model each patient's longitudinal outcome trajectory in combination with the timing and type of missingness. Results: Using the competing risk joint model, we were able to provide unbiased estimates of the intervention effects in the presence of the different types of missingness. For the LipiDiDiet study, the intervention effects remained statistically significant after this correction for the timing and type of missingness. Conclusion: Missing data is a common problem in (Alzheimer) clinical trials. It is important to realize that statistical techniques make specific assumptions about the missing data mechanisms. When there are different missing data sources, a competing risk joint model is a powerful method because it can explicitly model the association between the longitudinal data and each type of missingness. Trial registration: Dutch Trial Register, NTR1705. Registered on 9 March 2009 [ABSTRACT FROM AUTHOR]

This paper considers the statistical inference for the competing risks model from generalized Rayleigh distribution based on progressive Type-II censoring when the parameters of the latent lifetime distributions are different or common. Maximum likelihood estimates are obtained, where the existence of the point estimators are proved, and the confidence intervals are established via the observed Fisher information matrix as well. Bayesian estimates of unknown parameters and reliability characteristics are derived under symmetric and asymmetric loss functions, and Monte Carlo Markov Chain sampling method is used to compute the Bayesian point estimates and the highest posterior density credible intervals. In addition, Bootstrap methods are also considered to obtain bias-corrected point estimates and approximate confidence intervals. Then we carry out hypothesis test using likelihood ratio test statistics. Monte Carlo simulation and a set of real data are presented to assess the performance of our proposed methods. Finally, the optimal censoring scheme issue is studied. [ABSTRACT FROM AUTHOR]

In this paper, we first propose a dependent Dirichlet process (DDP) model using a mixture of Weibull models with each mixture component resembling a Cox model for survival data. We then build a Dirichlet process mixture model for competing risks data without regression covariates. Next we extend this model to a DDP model for competing risks regression data by using a multiplicative covariate effect on subdistribution hazards in the mixture components. Though built on proportional hazards (or subdistribution hazards) models, the proposed nonparametric Bayesian regression models do not require the assumption of constant hazard (or subdistribution hazard) ratio. An external time-dependent covariate is also considered in the survival model. After describing the model, we discuss how both cause-specific and subdistribution hazard ratios can be estimated from the same nonparametric Bayesian model for competing risks regression. For use with the regression models proposed, we introduce an omnibus prior that is suitable when little external information is available about covariate effects. Finally we compare the models' performance with existing methods through simulations. We also illustrate the proposed competing risks regression model with data from a breast cancer study. An R package "DPWeibull" implementing all of the proposed methods is available at CRAN. [ABSTRACT FROM AUTHOR]

Semi‐competing risks data include the time to a nonterminating event and the time to a terminating event, while competing risks data include the time to more than one terminating event. Our work is motivated by a prostate cancer study, which has one nonterminating event and two terminating events with both semi‐competing risks and competing risks present as well as two censoring times. In this paper, we propose a new multi‐risks survival (MRS) model for this type of data. In addition, the proposed MRS model can accommodate noninformative right‐censoring times for nonterminating and terminating events. Properties of the proposed MRS model are examined in detail. Theoretical and empirical results show that the estimates of the cumulative incidence function for a nonterminating event may be biased if the information on a terminating event is ignored. A Markov chain Monte Carlo sampling algorithm is also developed. Our methodology is further assessed using simulations and also an analysis of the real data from a prostate cancer study. As a result, a prostate‐specific antigen velocity greater than 2.0 ng/mL per year and higher biopsy Gleason scores are positively associated with a shorter time to death due to prostate cancer. [ABSTRACT FROM AUTHOR]

Recently, the study of the lifetime of systems in reliability and survival analysis in the presence of several causes of failure (competing risks) has attracted attention in the literature. In this paper, series and parallel systems with exponential lifetime for each item of the system are considered. Several causes of failure independently affect lifetime distributions and observations of failure times of the systems are considered under progressive Type-II censored scheme. For series systems, the maximum likelihood estimates of parameters are computed and confidence intervals for parameters of the model are obtained using Fisher information matrix. For parallel systems, the generalized EM algorithm which uses the Newton-Raphson algorithm inside the EM algorithm is used to compute the maximum likelihood estimates of parameters. Also, the standard errors of the maximum likelihood estimates are computed by using the supplemented EM algorithm. The simulation study confirms the good performance of the introduced approach. [ABSTRACT FROM AUTHOR]

In this paper, two bivariate models based on the proposed methods of Marshall and Olkin are introduced. In the first model, the new bivariate distribution is presented based on the proposed method of Marshall and Olkin (1967) which has natural interpretations, and it can be applied in fatal shock models or in competing risks models. In the second model, the proposed method of Marshall and Olkin (1997) is generalized to bivariate case and a new bivariate distribution is introduced. We call these new distributions as the bivariate Gompertz (BGP) distribution and bivariate Gompertz-geometric (BGPG) distribution, respectively. Moreover, the BGP model can be obtained as a special case of the BGPG model. Then, we present various properties of the new bivariate models. In this regard, the joint and conditional density functions, the joint cumulative distribution function can be obtained in compact forms. Also, the aging properties and the bivariate hazard gradient are discussed. This model has five unknown parameters and the maximum likelihood estimators cannot be obtained in explicit form. We propose to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters, and it is computationally quite tractable. Also, Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm. Finally, we analyze three real data sets for illustrative purposes. [ABSTRACT FROM AUTHOR]

Reliability analysis of multicomponent repairable systems with dependent component failures is challenging for two reasons. First, the failure mechanism of one component may depend on other components when considering component failure dependence. Second, imperfect repair actions can have accumulated effects on the repaired components and these accumulated effects are difficult to measure. In this paper, we propose a parametric statistical model to capture the failure dependence information with general component repair actions. We apply the maximum likelihood method to estimate the model parameters by utilizing the historical failure data. Statistical hypothesis tests are developed to determine the dependence structure of the component failures based on the proposed reliability model. The proposed methodology is demonstrated by a simulation study and case studies of a car body assembly process and a forklift vehicle system. [ABSTRACT FROM PUBLISHER]

This paper explores the relationship between local unemployment rates and the length of time people who have lost their job spend unemployed, using a competing risks model. High local unemployment is found to reduce the probability of re-employment for someone who was employed prior to a period of unemployment. However, individual factors such as age, education and experience are more important predictors of re-employment. This suggests there could be benefits from a policy response that focuses more on the individuals, and building skills that are resilient to structural change, than on job creation in local areas. [ABSTRACT FROM AUTHOR]

In this paper, a new survival cure rate model is introduced considering the Yule–Simon distribution [12] to model the number of concurrent causes. We study some properties of this distribution and the model arising when the distribution of the competing causes is the Weibull model. We call this distribution the Weibull–Yule–Simon distribution. Maximum likelihood estimation is conducted for model parameters. A small scale simulation study is conducted indicating satisfactory parameter recovery by the estimation approach. Results are applied to a real data set (melanoma) illustrating the fact that the model proposed can outperform traditional alternative models in terms of model fitting. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to examine the impact of the moral failure of a scandalized foreign brand afflicted with a product-harm crisis on competing brands (i.e. within the same product category) while taking into account the country of origin (COO) of the brands.Design/methodology/approach This paper presents the results of two studies. The first study uses an experimental design, while the second uses a survey to examine a real-life product-harm crisis.Findings The results indicate that the moral failure of a scandalized foreign brand has an indirect negative effect on the intention to purchase competing foreign brands from the COO of the scandalized foreign brand. This effect is, however, reversed for domestic brands, where moral failure has an indirect positive effect on the intention to purchase competing domestic brands.Research limitations/implications The results of this research were based on an examination of how US consumers responded to the moral failure of Japanese and German brands. Future studies should examine brands from different COOs in different countries.Practical implications These results suggest that competing foreign brands from the COO of the scandalized brand should collaborate to quickly handle a product-harm crisis to prevent a spillover and that domestic competitors should capitalize on the opportunity to attract new customers.Originality/value This study represents a first attempt to examine the effect of a foreign brand’s moral failure in handling product-harm crisis on competing brands, both foreign and domestic. [ABSTRACT FROM AUTHOR]

Competing risks consider time to first event and type of first event. This subdiscipline of survival analysis is challenging in that multiple hazards determine the outcome probabilities. The paper demonstrates that Nightingale and Farr were aware of these connections in their co-operative work in hospital epidemiology. At the fourth International Statistical Congress (in London, 1860), they suggested forms for reporting hospital mortality that were conceptually more complete than many reported competing risks analyses today. [ABSTRACT FROM AUTHOR]

Background: Competing risks are a common occurrence in survival analysis. They arise when a patient is at risk of more than one mutually exclusive event, such as death from different causes, and the occurrence of one of these may prevent any other event from ever happening. Methods: There are two main approaches to modelling competing risks: the first is to model the cause-specific hazards and transform these to the cumulative incidence function; the second is to model directly on a transformation of the cumulative incidence function. We focus on the first approach in this paper. This paper advocates the use of the flexible parametric survival model in this competing risk framework. Results: An illustrative example on the survival of breast cancer patients has shown that the flexible parametric proportional hazards model has almost perfect agreement with the Cox proportional hazards model. However, the large epidemiological data set used here shows clear evidence of non-proportional hazards. The flexible parametric model is able to adequately account for these through the incorporation of time-dependent effects. Conclusion: A key advantage of using this approach is that smooth estimates of both the cause-specific hazard rates and the cumulative incidence functions can be obtained. It is also relatively easy to incorporate time-dependent effects which are commonly seen in epidemiological studies. [ABSTRACT FROM AUTHOR]

There are many situations in reliability or medical studies, where items may fail due to one of several causes. Further, censoring is unavoidable in any life testing. In this paper attempts to estimate problem for the competing risks model where the data are adaptive type-II progressive hybrid censored scheme and follow the inverse Weibull distribution. In this regards, we obtain the maximum likelihood estimation of the parameters and the asymptotic confidence intervals for the unknown parameters. Further, Bayes estimates of the parameters which obtained based on squared error and LINEX loss functions under the assumptions of independent gamma priors. For Bayesian estimation, we take advantage of Markov Chain Monte Carlo techniques by applying the Metropolis-Hasting algorithm under the square error and LINEX loss function to derive Bayesian estimators. Finally, two data sets with a Monte Carlo simulation study and a real data set of the electronic applications are analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

The reliability analysis is usually concerned with failures in the time domain which show the difference between the quality control and reliability engineering. Also, It is very common in engineering or biological science units are falling under different causes of failure, which is known by competing risks model. In this paper, we have adopted the competing risks model when the lifetime of units distributed with generalized half-logistic (GHL) distribution. This model is formulated under consideration the failure done with two independent causes of failure. Also, to balance in statistical inference between the minimum number of failure and ideal test time, we are using, the type-I generalized hybrid censoring scheme (GHCS). The model parameters are estimated by maximum likelihood (ML) and Bayes approaches. The approximate confidence intervals, bootstrap confidence intervals and credible intervals are constructed. The developed results are discussed and assessed through Monte Carlo simulation study. A real data set is used and analyzed to report and illustrate the developed results. [ABSTRACT FROM AUTHOR]

The article reports on the pricing of preferred stocks and discusses the paper, "On the Pricing of Preferred Stock" by Eric H. Sorensen and Clark A. Hawkins. Sorensen and Hawkins look at the preferred stock prices before and after the National Association of Insurance Commissioners instituted the law to enable insurance companies to hold sinking fund preferred issues at book value instead of market value in 1979. This changed the value of the sinking fund in preferred stock. The sinking fund of a preferred stock is important because the stock legally represents the equity instead of the debt of a firm.

The relative failure frequency among different failure modes of a production system is referred to as failure profile in this paper. Identification of failure profile based on failure-time data collected in the production phase of a system can help pinpoint the bottleneck problems, and provide valuable information for system design evaluation and maintenance management. Major challenges of effective failure profile identification come from time-varying and limited failure-time data. In this paper, the failure profile is estimated by using the maximum likelihood method. In addition, statistical hypothesis testing procedures are proposed to inspect the existence of a dominating failure mode, and possible changes of failure profiles during a production period. The developed methods are illustrated with an automation system of a high throughput screening (HTS) process, and a production process for cylinder heads. [ABSTRACT FROM PUBLISHER]

A popular model for competing risks postulates the existence of a latent unobserved failure time for each risk. Assuming that these underlying failure times are independent is attractive since it allows standard statistical tools for right-censored lifetime data to be used in the analysis. This paper proposes simple independence score tests for the validity of this assumption when the individual risks are modeled using semiparametric proportional hazards regressions. It assumes that covariates are available, making the model identifiable. The score tests are derived for alternatives that specify that copulas are responsible for a possible dependency between the competing risks. The test statistics are constructed by adding to the partial likelihoods for the individual risks an explanatory variable for the dependency between the risks. A variance estimator is derived by writing the score function and the Fisher information matrix for the marginal models as stochastic integrals. Pitman efficiencies are used to compare test statistics. A simulation study and a numerical example illustrate the methodology proposed in this paper. [ABSTRACT FROM AUTHOR]

Case–cohort studies are useful when information on certain risk factors is difficult or costly to ascertain. Particularly, a case–cohort study may be well suited in situations where several case series are of interest, e.g. in studies with competing risks, because the same sub-cohort may serve as a comparison group for all case series. Previous analyses of this kind of sampled cohort data most often involved estimation of rate ratios based on a Cox regression model. However, with competing risks this method will not provide parameters that directly describe the association between covariates and cumulative risks. In this paper, we study regression analysis of cause-specific cumulative risks in case–cohort studies using pseudo-observations. We focus mainly on the situation with competing risks. However, as a by-product, we also develop a method by which absolute mortality risks may be analyzed directly from case–cohort survival data. We adjust for the case–cohort sampling by inverse sampling probabilities applied to a generalized estimation equation. The large-sample properties of the proposed estimator are developed and small-sample properties are evaluated in a simulation study. We apply the methodology to study the effect of a specific diet component and a specific gene on the absolute risk of atrial fibrillation. [ABSTRACT FROM AUTHOR]

The cause of failure in cohort studies that involve competing risks is frequently incompletely observed. To address this, several methods have been proposed for the semiparametric proportional cause-specific hazards model under a missing at random assumption. However, these proposals provide inference for the regression coefficients only, and do not consider the infinite dimensional parameters, such as the covariate-specific cumulative incidence function. Nevertheless, the latter quantity is essential for risk prediction in modern medicine. In this paper we propose a unified framework for inference about both the regression coefficients of the proportional cause-specific hazards model and the covariate-specific cumulative incidence functions under missing at random cause of failure. Our approach is based on a novel computationally efficient maximum pseudo-partial-likelihood estimation method for the semiparametric proportional cause-specific hazards model. Using modern empirical process theory we derive the asymptotic properties of the proposed estimators for the regression coefficients and the covariate-specific cumulative incidence functions, and provide methodology for constructing simultaneous confidence bands for the latter. Simulation studies show that our estimators perform well even in the presence of a large fraction of missing cause of failures, and that the regression coefficient estimator can be substantially more efficient compared to the previously proposed augmented inverse probability weighting estimator. The method is applied using data from an HIV cohort study and a bladder cancer clinical trial. [ABSTRACT FROM AUTHOR]

In this paper, we try to supplement the distribution theory literature by introducing a new distribution, called the logarithmic transformed Weibull (LTW) distribution by logarithm transformation method. The proposed distribution exhibits constant, decreasing, increasing, unimodal and unimodal then bathtub‐shaped hazard rates. Although our main focus is on the estimation from the frequentist point of view, in addition, we derive some useful structural and statistical properties of the proposed LTW distribution. The LTW parameters are estimated by eight frequentist methods of estimation. We perform extensive simulation experiments to show the performances of the proposed estimators. Applications of the model are presented by reanalyzing two real data sets, and comparisons are made with the fit attained by some other well‐known distributions for illustrative purposes. As an illustration, one data set is analyzed for competing risks to demonstrate the flexibility of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, the estimation of unknown parameters of Chen distribution is considered under progressive Type-II censoring in the presence of competing failure causes. It is assumed that the latent causes of failures have independent Chen distributions with the common shape parameter, but different scale parameters. From a frequentist perspective, the maximum likelihood estimate of parameters via expectation–maximization (EM) algorithm is obtained. Also, the expected Fisher information matrix based on the missing information principle is computed. By using the obtained expected Fisher information matrix of the MLEs, asymptotic 95% confidence intervals for the parameters are constructed. We also apply the bootstrap methods (Bootstrap-p and Bootstrap-t) to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are computed by applying the Markov chain Monte Carlo (MCMC) procedure, the average length and coverage rate of credible intervals are also carried out. The Bayes inference is based on the squared error, LINEX, and general entropy loss functions. The performance of point estimators and confidence intervals is evaluated by a simulation study. Finally, a real-life example is considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

This paper proposes a mathematical model, the competing risks method, to investigate highway-rail grade crossing (HRGC) crash frequency and crash severity simultaneously over a 30-year period. The proposed competing risks model is a special type of survival analysis to accommodate the competing nature of multiple outcomes from the same event of interest; in this case, the competing multiple outcomes are crash severities, while event of interest is crash occurrence. Knowledge-gain-based benefits to be discovered through the application of this model and 30-year dataset are as follows: (1) a straightforward and integrated one-step estimation process that considers both crash frequency and severity likelihood in the same model, so direct hazard ranking considering both crash frequency and severity likelihood is possible; (2) interpretative effects of identified covariates from both the direction and magnitude perspectives; and (3) the long-term cumulative effect of contributors with the cumulative incidence function. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the estimation problem of the competing risks model when the exact cause of failure for some units may not be completely observed. The failure times of the components are assumed to follow Weibull distributions with different shape and scale parameters according to each competing risk. In the applied competing risks analysis, it is common to have failed units during life testing which do not have a certain cause of failure. Actually, the cause is not completely missed but is only known to belong to a certain subset of all possible causes. This case is known as masking. We propose to analyse these data assuming an underling masking mechanism as apart of data model, to allow the potential dependency of the masking probability on the unknown cause of failure and/or the observed failure time, applying an appropriate Generalized Linear Model. The parameters of the joint competing risks and masking mechanism model are estimated using the maximum likelihood approach. Also, several simulation studies are conducted to access the effect of different masking rates, mechanisms and sample sizes on the parameter estimation of Weibull competing risks data with different sets of shape and scale parameters. Finally, a real data example is analysed to illustrate the application of the proposed methods. [ABSTRACT FROM AUTHOR]

Competing risks arise when an individual is exposed to the several causes of failure. In this case, the recorded data includes two components, the failure times and the cause of failure indicators. Such data may suffer from censoring in the former part and missingness in the latter part. Prior researches have ignored the missing mechanism when analysing such data which might lead to invalid statistical inferences. Since the ignorability assumption is unverifiable from the available data, the sensitivity analysis is recommended. In this paper, the Bayesian index of local sensitivity to non-ignorability (ISNI) is derived to quantify the sensitivity of Bayesian estimators to the ignorability assumption for hybrid censored incomplete competing risks data when the lifetimes follow exponential, Weibull, and generalized exponential distributions. Also, some simulation studies are conducted to evaluate the performance of the proposed Bayesian ISNI in different missing and competing risks scenarios. Finally, a real-world example is analysed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, we discussed the estimation problem for the competing risks model when the data are progressive interval censored and follow Weibull distribution with an unknown common shape parameter. The parameters were estimated using both maximum likelihood and Bayesian methods and the Fisher information matrix was derived. The importance sampling method was employed to obtain the Bayes estimates. In the presence of competing risks, it is possible that the causes of failure for some units are not observed and the problem of missing causes of failure arises. In this situation, discussing the consequences of departures from the ignorability assumption on the Bayes estimates of the model parameters is crucial. Therefore, we studied the impact of missing causes of failure on inference in the proposed competing risks model using the Bayesian "index of local sensitivity to non-ignorability". A simulation study was conducted to compare Bayes estimates under both informative and less informative priors with the corresponding maximum likelihood estimates, and also to assess the sensitivity of the parameter estimation to the non-ignorable missing data in a Bayesian setup. An illustrative example based on the real data is given. [ABSTRACT FROM AUTHOR]

For the analysis of competing risks data, three different types of hazard functions have been considered in the literature, namely the cause-specific hazard, the sub-distribution hazard, and the marginal hazard function. Accordingly, medical researchers can fit three different types of the Cox model to estimate the effect of covariates on each of the hazard function. While the relationship between the cause-specific hazard and the sub-distribution hazard has been extensively studied, the relationship to the marginal hazard function has not yet been analyzed due to the difficulties related to non-identifiability. In this paper, we adopt an assumed copula model to deal with the model identifiability issue, making it possible to establish a relationship between the sub-distribution hazard and the marginal hazard function. We then compare the two methods of fitting the Cox model to competing risks data. We also extend our comparative analysis to clustered competing risks data that are frequently used in medical studies. To facilitate the numerical comparison, we implement the computing algorithm for marginal Cox regression with clustered competing risks data in the R joint.Cox package and check its performance via simulations. For illustration, we analyze two survival datasets from lung cancer and bladder cancer patients. [ABSTRACT FROM AUTHOR]

Background: Under competing risks, the commonly used sub-distribution hazard ratio (SHR) is not easy to interpret clinically and is valid only under the proportional sub-distribution hazard (SDH) assumption. This paper introduces an alternative statistical measure: the restricted mean time lost (RMTL).Methods: First, the definition and estimation methods of the measures are introduced. Second, based on the differences in RMTLs, a basic difference test (Diff) and a supremum difference test (sDiff) are constructed. Then, the corresponding sample size estimation method is proposed. The statistical properties of the methods and the estimated sample size are evaluated using Monte Carlo simulations, and these methods are also applied to two real examples.Results: The simulation results show that sDiff performs well and has relatively high test efficiency in most situations. Regarding sample size calculation, sDiff exhibits good performance in various situations. The methods are illustrated using two examples.Conclusions: RMTL can meaningfully summarize treatment effects for clinical decision making, which can then be reported with the SDH ratio for competing risks data. The proposed sDiff test and the two calculated sample size formulas have wide applicability and can be considered in real data analysis and trial design. [ABSTRACT FROM AUTHOR]

In this paper, joint modeling of longitudinal ordinal measurements and time to some events of interest as competing risks is discussed. For this purpose, a latent variable sub-model under linear mixed-effects assumption is considered for modeling ordinal longitudinal measurements. Also, a Weibull cause-specific sub-model is used to model competing risks data. These two sub-models are simultaneously considered in a unique model by a shared parameter model framework. Some simulation studies are performed for illustration of the proposed approaches; also, the proposed approaches are used for analyzing 15 years of lipid and glucose follow-up study in Tehran. [ABSTRACT FROM AUTHOR]

Medical research frequently involves comparing an event time of interest between treatment groups. Rather than comparing the entire survival or cumulative incidence curves, it is sometimes preferable to evaluate these probabilities at a fixed point in time. Performing a covariate adjusted analysis can improve efficiency, even in randomized clinical trials, but no currently available group sequential test for fixed point analysis provides this adjustment. This paper introduces covariate adjusted group sequential pointwise comparisons of survival and cumulative incidence probabilities. Their test statistics have an asymptotic distribution with independent increments, permitting use of common stopping boundary specification methods. These tests are demonstrated through a redesign of BMT CTN 0402, a clinical trial that evaluated a prophylactic treatment for adverse outcomes following blood and marrow transplantation. A simulation study demonstrates that these tests maintain the type I error rate and power at nominal levels under a variety of settings involving influential covariates. [ABSTRACT FROM AUTHOR]

A competing risks phenomenon arises in industrial life tests, where multiple types of failure determine the working duration of a unit. To model dependence among marginal failure times, copula models and frailty models have been developed for competing risks failure time data. In this paper, we propose a frailty‐copula model, which is a hybrid model including both a frailty term (for heterogeneity among units) and a copula function (for dependence between failure times). We focus on models that are useful to investigate the reliability of marginal failure times that are Weibull distributed. Furthermore, we develop likelihood‐based inference methods based on competing risks data, including accelerated failure time models. We also develop a model‐diagnostic procedure to assess the adequacy of the proposed model to a given dataset. Simulations are conducted to demonstrate the operational performance of the proposed methods, and a real dataset is analyzed for illustration. We make an R package "gammaGumbel" such that users can apply the suggested statistical methods to their data. [ABSTRACT FROM AUTHOR]

Cure rate models have been used in a number of fields. These models are applied to analyze survival data when the population has a proportion of subjects insusceptible to the event of interest. In this paper, we propose a new cure rate survival model formulated under a competing risks setup. The number of competing causes follows the negative binomial distribution, while for the latent times we posit the power piecewise exponential distribution. Samples from the posterior distribution are drawn through MCMC methods. Some properties of the estimators are assessed in a simulation study. A dataset on cutaneous melanoma is analyzed using the proposed model as well as some existing models for the sake of comparison. [ABSTRACT FROM AUTHOR]

In many circumstances, the increase in life expectancy when certain causes of death are eliminated is sought. These calculations are typically based on the assumption that the causes in question are simply omitted, which is equivalent to the causes being taken out of consideration, from the outset, with certainty. In this paper, we propose models whereby probability distributions for the cures of specific causes of death over time can be incorporated so as to more accurately predict the increase in life expectancy that would ensue. The theoretical results are applied to a real data set involving Diabetes and HIV-related deaths from Denver, Colorado, United States of America, between the years 1990 and 2015 inclusive. [ABSTRACT FROM AUTHOR]