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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]

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]

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]

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 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]

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]

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]

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]

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

In reliability and survival analysis, the time-to-failure data play an important role in the development of the reliability and life characteristics of the products. In some cases, these kinds of data are modeled using a competing risks model. The problem of conducting comparative life testing under a competing risks model when the units come from different lines of production has recently been addressed. In this paper, we address this problem when the life of the unit is distributed using the Gompertz distribution, noting that the units come from two lines of production and two independent causes of failure are activated. The data are collected under a joint generalized type-II hybrid censoring scheme. Maximum likelihood estimators of the unknown parameters are derived, along with the corresponding asymptotic confidence intervals. We also adopt two bootstrap confidence intervals. Using independent gamma priors, the Bayes estimators relative to squared error loss function are obtained with credible intervals. The properties and quality of estimators are measured by performing a Monte Carlo simulation study. Finally, a real-life data set is analyzed to discuss the applicability of the proposed methods to real phenomena. The optimal plan with respect to comments on the numerical results is discussed in the conclusion. [ABSTRACT FROM AUTHOR]

The ranked set sampling (RSS) is an efficient and flexible sampling method. Based on a modified RSS named minimum ranked set sampling samples (MinRSSU), inference of a dependent competing risks model is proposed in this paper. Then, Marshall–Olkin bivariate distribution model is used to describe the dependence of competing risks. When the competing risks data follow the proportional hazard rate distribution, a dependent competing risks model based on MinRSSU sampling is constructed. In addition, the model parameters and reliability indices were estimated by the classical and Bayesian method. Maximum likelihood estimators and corresponding asymptotic confidence intervals are constructed by using asymptotic theory. In addition, the Bayesian estimator and highest posterior density credible intervals are established under the general prior. Furthermore, according to E-Bayesian theory, the point and interval estimators of model parameters and reliability indices are obtained by a sampling algorithm. Finally, extensive simulation studies and a real-life example are presented for illustrations. [ABSTRACT FROM AUTHOR]

The proportional subdistribution hazards (PSH) model is popularly used to deal with competing risks data. Censored quantile regression provides an important supplement as well as variable selection methods due to large numbers of irrelevant covariates in practice. In this paper, we study variable selection procedures based on penalized weighted quantile regression for competing risks models, which is conveniently applied by researchers. Asymptotic properties of the proposed estimators, including consistency and asymptotic normality of non-penalized estimator and consistency of variable selection, are established. Monte Carlo simulation studies are conducted, showing that the proposed methods are considerably stable and efficient. Real data about bone marrow transplant (BMT) are also analyzed to illustrate the application of the proposed procedure. [ABSTRACT FROM AUTHOR]

In this paper, monitoring the Weibull shape parameter arising from progressively censored competing risks data is investigated. The competing risks are assumed to be independent and not identically distributed from the Weibull distributions with different shape and scale parameters. Both the shape parameters can be monitored separately by the proposed control charts using censored and predicted observations. We also introduced a control chart for monitoring both shape parameters simultaneously to detect possible shifts in both opposite and the same directions. In addition, the problem of mask data is discussed and an efficient prediction method is proposed. The behavior of the average run length with and without mask data is investigated through extensive simulations. Furthermore, the effects of sample size, number of failures due to each risk, and censoring scheme on the charts' performance are also studied. Finally, an illustrative example is presented to demonstrate the application of the proposed control charts by investigating a real data set of the failure times of two-component ARC-1 VHF communication transmitter receivers of a single commercial airline. Although this data set has been widely investigated in reliability analysis studies, this is the first time it has been analyzed in a statistical process monitoring setting. [ABSTRACT FROM AUTHOR]

In this paper, we propose a hierarchical statistical model for a single repairable system subject to several failure modes (competing risks). The paper describes how complex engineered systems may be modelled hierarchically by use of Bayesian methods. It is also assumed that repairs are minimal and each failure mode has a power-law intensity. Our proposed model generalizes another one already presented in the literature and continues the study initiated by us in another published paper. Some properties of the new model are discussed. We conduct statistical inference under an objective Bayesian framework. A simulation study is carried out to investigate the efficiency of the proposed methods. Finally, our methodology is illustrated by two practical situations currently addressed in a project under development arising from a partnership between Petrobras and six research institutes. [ABSTRACT FROM AUTHOR]

In this paper, a competing risks model with dependent causes of failure is considered under left-truncated and right-censoring scenario. When the dependent failure causes follow a Marshall–Olkin bivariate exponential distribution, estimation of model parameters and reliability indices are proposed from classic and Bayesian approaches, respectively. Maximum likelihood estimators and approximate confidence intervals are constructed, and conventional Bayesian point and interval estimations are discussed as well. In addition, E-Bayesian estimators are proposed and their asymptotic behaviors have been investigated. Further, another objective-Bayesian analysis is also proposed when a noninformative probability matching prior is used. Finally, extensive simulation studies are carried out to investigate the performance of different methods. Two real data examples are presented to illustrate the applicability. [ABSTRACT FROM AUTHOR]

In clinical and epidemiological studies, when the time-to-event(s) and the longitudinal outcomes are associated, modelling them separately may give biased estimates. A joint modelling approach is required to obtain unbiased results and to evaluate their association. In the joint model, a subject may be exposed to more than one type of failure event (competing risks). Considering the competing event as an independent censoring of the time-to-event process may underestimate the true survival probability and give biased results. Within the joint model, longitudinal outcomes may have nonlinear (irregular) trajectories over time and exhibit skewness with heavy tails. Accordingly, fully parametric mixed-effect models may not be flexible enough to model this type of complex longitudinal data. In addition, assuming a Gaussian distribution for model errors may be too restrictive to adequately represent within-individual variations and may lack robustness against deviation from distributional assumptions. To simultaneously overcome these issues, in this paper, we presented semiparametric joint models for competing risks failure time and skewed-longitudinal data by using a smoothing spline approach and a multivariate skew-t distribution. We also considered different parameterization approaches in the formulation of joint models and used a Bayesian approach to make the statistical inference. We illustrated the proposed methods by analyzing real data on a chronic kidney disease. To evaluate the performance of the methods, we also carried out simulation studies. The results of both the application and simulation studies revealed that the joint modelling approach proposed in this study performed well when the semiparametric, random-effects parameterization, and skew-t distribution specifications were taken into account. [ABSTRACT FROM AUTHOR]

In this paper, the dependent competing risks' model is considered in the constant-stress accelerated life test under the adaptive type-II progressive hybrid-censored scheme. The dependency between failure causes is modeled by Marshall–Olkin bivariate Gompertz distribution. The scale and shape parameters in the model both change with the stress levels, and the failure causes of some test units are unknown. Then, the maximum likelihood estimations and approximation confidence intervals of the unknown parameters are considered. And, the necessary and sufficient condition is established for the existence and uniqueness of the maximum likelihood estimations for unknown parameters. The Bayes approach is also employed to estimate the unknown parameters under suitable prior distributions. The Bayes estimations and highest posterior credible intervals of the unknown parameters are obtained. Finally, a simulation experiment has been performed to illustrate the methods proposed in this paper. [ABSTRACT FROM AUTHOR]

Aim: To develop a new comorbidity index for adults with cerebral palsy (CP), the Whitney Comorbidity Index (WCI), which includes relevant comorbidities for this population and better predicts mortality than the Charlson Comorbidity Index (CCI) and Elixhauser Comorbidity Index (ECI). Method: Data from the Optum Clinformatics Data Mart was used for this retrospective cohort study. Diagnosis codes were used to identify adults aged 18 years or older with CP (n=1511 females, n=1511 males; mean [SD; range] age=48y [19y 2mo; 18–89y]) and all comorbidities in the year 2014. The WCI was developed based on the comorbidities of the CCI and ECI and other relevant comorbidities associated with 2‐year mortality using Cox regression and competing risk analysis. The WCI was examined as unweighted (WCIunw) and weighted (WCIw). The model fit and discrimination (C‐statistic) of each index was assessed using Cox regression. Results: Twenty‐seven comorbidities were included in the WCI; seven new comorbidities that were not part of the CCI or ECI were added. The WCIunw and WCIw showed a better model fit and discrimination for 1‐ and 2‐year mortality compared to the CCI and ECI. The WCIunw and WCIw were strong predictors for 1‐ and 2‐year mortality (C‐statistic [95% confidence interval] ranging from 0.81 [0.76–0.85] to 0.88 [0.82–0.94]). Interpretation: The new WCI, designed to include clinically relevant comorbidities, provides a better model fit and discrimination of mortality for adults with CP. What this paper adds: Common comorbidity indices exclude relevant comorbidities for adults with cerebral palsy (CP).A new comorbidity index for adults with CP was created by harmonizing clinical theory and data‐driven methods.The Whitney Comorbidity Index better predicted 1‐ and 2‐year mortality than other commonly used comorbidity indices. What this paper adds: Common comorbidity indices exclude relevant comorbidities for adults with cerebral palsy (CP).A new comorbidity index for adults with CP was created by harmonizing clinical theory and data‐driven methods.The Whitney Comorbidity Index better predicted 1‐ and 2‐year mortality than other commonly used comorbidity indices. This article is commented on by Streiner on page 246 of this issue. [ABSTRACT FROM AUTHOR]

The competing risks model plays an important role in the statistical analysis of engineering, econometric, biological and other fields. A tested product may fail from different causes. Therefore, these failure causes as if competing with each other to bring about the failure of tested products (an experimental unit). Hence, in the statistical literature, this is known as the competing risk problem and it has been studied quite extensively by several researchers when the lifetime of the product is the latent failure time of the first failure cause among all the possible failure causes. In this paper, a competing risks model based on a generalized progressive hybrid type-I (GPH type-I) censoring is considered when the latent lifetime distributions of failure causes are inverse Weibull (IW) distributed and partially observed. We established various estimation methods including Maximum likelihood estimates (MLEs) and Bayes estimates (BEs). MLEs with the corresponding asymptotic confidence intervals are obtained. Bayes estimates of the parameters are obtained based on squared error loss (SEL) function under the assumption of independent gamma priors. Furthermore, we applied Markov Chain Monte Carlo (MCMC) techniques to compute BEs and to calculate the credible intervals. Finally, simulation studies and real data set are used for illustrative purpose. [ABSTRACT FROM AUTHOR]

Competing risk ( C o R ) models are frequently disregarded in failure rate analysis, and traditional statistical approaches are used to study the event of interest. In this paper, we proposed a new lifetime distribution by generalizing the length biased exponential (LBE) distribution using the transmuted Topp-Leone-G ( T T L -G) family of distributions. The new three parameter model is called the transmuted Topp-Leone length biased exponential ( T T L L B E ) distribution. A comprehensive account of various mathematical features of the T T L L B E model are derived. The unknown parameters of the proposed distribution are estimated by six classical approaches: the maximum likelihood (ML) approach, maximum product spacing (MPS) approach, least square (LS) approach, Weighted LS (WLS) approach, Cramér-Von Mises (CVN) approach, Anderson–Darling (AD) approach, and Bayesian approach. The stability of the model parameters is examined through the simulation study. The applications of our proposed distribution are explained through real data and its performance is illustrated through its comparison with the competent existing distributions. The T T L L B E model depend on the C o R model has been obtained and estimated parameter of this model by ML and Bayesian estimation approaches. In electrical appliances, we found two main causes of failure, and the data of electrical appliances are fitted to our model. Therefore, we analyzed the T T L L B E model depend on the C o R model to obtain the strong cause of failure. [ABSTRACT FROM AUTHOR]

In this paper, a dependent competing risks model is considered and investigated by utilizing the copula approach which flexibly constructs dependent relationships between marginal distributions of several competing risk factors, and the closeness of the dependency can be determined by the copula parameters. Samples are collected from the step-stress accelerated life test combined with generalized progressive hybrid censoring, where the test duration is controlled within acceptable limits and a sufficient number of samples are guaranteed. From a classical frequency perspective, the maximum likelihood estimates are derived, then the relevant confidence intervals are provided based on the Fisher information matrix. Furthermore, the bias-corrected accelerated bootstrap method is employed to obtain the interval estimation of parameters. Under the Bayesian framework, Bayesian point estimates and the corresponding credible intervals are also explored, and their results are achieved by Markov Chain Monte Carlo technique. Finally, numerical simulation experiments and real data analysis are developed to more intuitively present the constructed model and the performance of the above-mentioned methods. [ABSTRACT FROM AUTHOR]

In clinical studies of time-to-event data, a quantity of interest to the clinician is their patient's risk of an event. However, methods relying on time matching or risk-set sampling (including Cox regression) eliminate the baseline hazard from the estimating function. As a consequence, the focus has been on reporting hazard ratios instead of survival or cumulative incidence curves. Indeed, reporting patient risk or cumulative incidence requires a separate estimation of the baseline hazard. Using case-base sampling, Hanley & Miettinen (2009) explained how parametric hazard functions can be estimated in continuous-time using logistic regression. Their approach naturally leads to estimates of the survival or risk function that are smooth-in-time. In this paper, we present the casebase R package, a comprehensive and flexible toolkit for parametric survival analysis. We describe how the case-base framework can also be used in more complex settings: non-linear functions of time and non-proportional hazards, competing risks, and variable selection. Our package also includes an extensive array of visualization tools to complement the analysis. We illustrate all these features through three different case studies. * SRB and MT contributed equally to this work. [ABSTRACT FROM AUTHOR]

Masked issues can emerge when dealing with competing risk data. Such issues are exemplified by the cause of a particular failure not being directly exhibited for all units to observe but only proven to be a subset of possible causes of failure. For assessing the impact of explanatory variables (covariates) on the cumulative incidence function (CIF), a process of Bayesian analysis is discussed in this paper. The symmetry assumption is not imposed on the masking probabilities and independent Dirichlet priors assigned to them. The Markov Chain Monte Carlo (MCMC) technique is utilized to implement the Bayesian analysis. The effectiveness of the developed model is tested via numerical studies, including simulated and real data sets. [ABSTRACT FROM AUTHOR]

Background: COVID-19 has rapidly emerged as a global public health threat with infections recorded in nearly every country. Responses to COVID-19 have varied in intensity and breadth, but generally have included domestic and international travel limitations, closure of non-essential businesses, and repurposing of health services. While these interventions have focused on testing, treatment, and mitigation of COVID-19, there have been reports of interruptions to diagnostic, prevention, and treatment services for other public health threats. Objectives: We conducted a scoping review to characterize the early impact of COVID-19 on HIV, tuberculosis, malaria, sexual and reproductive health, and malnutrition. Methods: A scoping literature review was completed using searches of PubMed and preprint servers (medRxiv/bioRxiv) from November 1st, 2019 to October 31st, 2020, using Medical Subject Headings (MeSH) terms related to SARS-CoV-2 or COVID-19 and HIV, tuberculosis, malaria, sexual and reproductive health, and malnutrition. Empiric studies reporting original data collection or mathematical models were included, and available data synthesized by region. Studies were excluded if they were not written in English. Results: A total of 1604 published papers and 205 preprints were retrieved in the search. Overall, 8.0% (129/1604) of published studies and 10.2% (21/205) of preprints met the inclusion criteria and were included in this review: 7.3% (68/931) on HIV, 7.1% (24/339) on tuberculosis, 11.6% (26/224) on malaria, 7.8% (19/183) on sexual and reproductive health, and 9.8% (13/132) on malnutrition. Thematic results were similar across competing health risks, with substantial indirect effects of the COVID-19 pandemic and response on diagnostic, prevention, and treatment services for HIV, tuberculosis, malaria, sexual and reproductive health, and malnutrition. Discussion: COVID-19 emerged in the context of existing public health threats that result in millions of deaths every year. Thus, effectively responding to COVID-19 while minimizing the negative impacts of COVID-19 necessitates innovation and integration of existing programs that are often siloed across health systems. Inequities have been a consistent driver of existing health threats; COVID-19 has worsened disparities, reinforcing the need for programs that address structural risks. The data reviewed here suggest that effective strengthening of health systems should include investment and planning focused on ensuring the continuity of care for both rapidly emergent and existing public health threats. [ABSTRACT FROM AUTHOR]

Geyser eruption is one of the most popular signature attractions at the Yellowstone National Park. The interdependence of geyser eruptions and impacts of covariates are of interest to researchers in geyser studies. In this paper, we propose a parametric covariate-adjusted recurrent event model for estimating the eruption gap time. We describe a general bivariate recurrent event process, where a bivariate lognormal distribution and a Gumbel copula with different marginal distributions are used to model an interdependent dual-type event system. The maximum likelihood approach is used to estimate model parameters. The proposed method is applied to analyzing the Yellowstone geyser eruption data for a bivariate geyser system and offers a deeper understanding of the event occurrence mechanism of individual events as well as the system as a whole. A comprehensive simulation study is conducted to evaluate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

In reliability analysis and life testing studies, the experimenter is frequently interested in studying a specific risk factor in the presence of other factors. In this paper, the estimation of the unknown parameters, reliability and hazard functions of alpha power exponential distribution is considered based on progressively Type-II censored competing risks data. We assume that the latent cause of failures has independent alpha power exponential distributions with different scale and shape parameters. The maximum likelihood method is considered to estimate the model parameters as well as the reliability and hazard rate functions. The approximate and two parametric bootstrap confidence intervals of the different estimators are constructed. Moreover, the Bayesian estimation method of the unknown parameters, reliability and hazard rate functions are obtained based on the squared error loss function using independent gamma priors. To get the Bayesian estimates as well as the highest posterior credible intervals, the Markov Chain Monte Carlo procedure is implemented. A comprehensive simulation experiment is conducted to compare the performance of the proposed procedures. Finally, a real dataset for the relapse of multiple myeloma with transplant-related mortality is analyzed. [ABSTRACT FROM AUTHOR]

Here in this paper, we consider the progressive Type-II censoring Gompertz data under competing risks model with binomial removals. The maximum likelihood estimators of the model parameters involved are obtained by applying numerical methods and the asymptotic variance-covariance matrix of the estimates is also derived. Bayesian estimates based on importance sampling procedure are developed under squared error, LINEX and general entropy loss functions. The confidence intervals using the asymptotic normality and Bayesian approaches are also developed. Finally, a Monte Carlo simulation is conducted to evaluate the performance of the so proposed estimators under all these different estimation methods. [ABSTRACT FROM AUTHOR]

In this paper, inference for a competing risks model is studied when latent failure times follow Kumaraswamy distribution and causes of failure are partially observed. Under generalized progressive hybrid censoring, existence and uniqueness of maximum likelihood estimators of model parameters are established. The confidence intervals are obtained by using asymptotic distribution theory. We further compute Bayes estimators along with credible intervals. In addition, inference is also discussed when there is order restricted shape parameters. The performance of all estimates is investigated using Monte-Carlo simulations. Finally, analysis of a real data set is presented for illustration purposes. [ABSTRACT FROM AUTHOR]

In some applications, the clustered survival data are arranged spatially such as clinical centers or geographical regions. Incorporating spatial variation in these data not only can improve the accuracy and efficiency of the parameter estimation, but it also investigates the spatial patterns of survivorship for identifying high-risk areas. Competing risks in survival data concern a situation where there is more than one cause of failure, but only the occurrence of the first one is observable. In this paper, we considered Bayesian subdistribution hazard regression models with spatial random effects for the clustered HIV/AIDS data. An intrinsic conditional autoregressive (ICAR) distribution was employed to model the areal spatial random effects. Comparison among competing models was performed by the deviance information criterion. We illustrated the gains of our model through application to the HIV/AIDS data and the simulation studies. [ABSTRACT FROM AUTHOR]

Time to failure under normal stress conditions may take a long period of time and statistical inferences under this condition is more serious. Then, the experiment is loaded under stress higher than normal one which is defined as accelerated life tests. This problem in this paper is discussed in the form of partially step-stress accelerated life test model when the lifetime of the product has Gompertz lifetime distribution and unites are fails under the two independent risks. The maximum likelihood method under type-II censoring scheme is used to formulate the point and asymptotic confidence interval estimators of model parameters. The two bootstrap methods are also used to formulate the point and approximate interval estimators. The numerical results are adopted in the form of Monte Carlo studying to illustrate, assess and compare all of the theoretical results. Finally, results are discussed in points to clarify results validity. [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]

In reliability engineering or medical studies, failure of units or individuals may occurring due to several failure modes which is known by competing risks model. In this paper, we have adopted a competing risks model under consideration that, the failure time has generalized inverted exponential distribution (GIED) and the failure modes are independent and partially observed. Under type-II progressive censoring scheme (type-II PCS), the experiment is designed as a quite popular scheme for collecting data specially, for a highly reliable product. The point estimates of the model parameters are formulated under classical approach (maximum likelihood and bootstrap) and Bayesian approach with respect to the symmetric squared error loss function. Also, the approximate confidence intervals under a large sample theory, bootstrap technique's and Markov chain Monte Carlo method (MCMC) are constructed. The estimators are assessed and compared with building the simulation study. Analysis a set of type-II PCS competing risks mortality data for illustration purpose. [ABSTRACT FROM AUTHOR]

The bivariate or multivariate distribution can be used to account for the dependence structure between different failure modes. This paper considers two dependent competing failure modes from Gompertz distribution, and the dependence structure of these two failure modes is handled by the Marshall–Olkin bivariate distribution. We obtain the maximum likelihood estimates (MLEs) based on classical likelihood theory and the associated bootstrap confidence intervals (CIs). The posterior density function based on the conjugate prior and noninformative (Jeffreys and Reference) priors are studied; we obtain the Bayesian estimates in explicit forms and construct the associated highest posterior density (HPD) CIs. The performance of the proposed methods is assessed by numerical illustration. [ABSTRACT FROM AUTHOR]

Hoping to find genomic clues linked to COVID-19 and end the pandemic has driven scientists' tremendous efforts to try all kinds of research. Signs of progress have been achieved but are still limited. This paper intends to prove the existence of at least three genomic signature patterns and at least seven subtypes of COVID-19 driven by five critical genes (the smallest subset of genes) using three blood-sampled datasets. These signatures and subtypes provide crucial genomic information in COVID-19 diagnosis (including ICU patients), research focuses, and treatment methods. Unlike existing approaches focused on gene fold-changes and pathways, gene-gene nonlinear and competing interactions are the driving forces in finding the signature patterns and subtypes. Furthermore, the method leads to high accuracy with hospitalized patients, showing biological and mathematical equivalences between COVID-19 status and the signature patterns and a methodological advantage over other methods that cannot lead to high accuracy. As a result, as new biomarkers, the new findings and genomic clues can be much more informative than other findings for interpreting biological mechanisms, developing the second (third) generation of vaccines, antiviral drugs, and treatment methods, and eventually bringing new hopes of an end to the pandemic. [ABSTRACT FROM AUTHOR]

In this paper, we develop statistical inference of competing risks samples which are collected under a joint Type-II censoring scheme of products with Weibull lifetime distributions. These inferences are drawn from two independent fatal risks and come from two different lines of production with the same facility. The model parameters and the parameters of life (reliability and hazard rate functions) are estimated using maximum likelihood (ML), bootstrap and Bayes methods. Additionally, we constructed asymptotic ML confidence intervals, bootstrap confidence intervals and Bayes credible intervals. Furthermore, the theoretical results are assessed and compared through Monte Carlo simulations. Finally, one real data set is analyzed under the proposed model for illustrative purpose. [ABSTRACT FROM AUTHOR]

This paper has investigated the estimation problem for the competing risks model where the data are adaptive progressively type-II censored and follow the Rayleigh distribution. Maximum likelihood and Bayesian methods are used to estimate the unknown parameters. To generate the interval estimates of the model parameters, approximate confidence intervals and two bootstrap confidence intervals are also considered based on the classical setup. Bayes estimates are obtained using independent gamma priors based on various loss functions including squared error, LINEX, general entropy, weighted SE, and precautionary loss functions. Moreover, Bayes credible intervals and the highest posterior density intervals of the model parameters are obtained. A numerical investigation has been carried out to assess the performance of the classical and Bayes estimates as well as the associated confidence and credible intervals. Finally, one simulated and two real data sets, one for breaking strengths of wire connections and the other for times to failure of small electrical appliances, have been analyzed for illustrative purposes. The results showed that the Bayes estimates using the LINEX loss function provide more reasonable estimates than the classical and Bayes estimates using squared error, general entropy, and precautionary loss functions. [ABSTRACT FROM AUTHOR]

Background: Chronic kidney disease (CKD) is a progressive and usually irreversible disease. Different types of outcomes are of interest in the course of CKD such as time-to-dialysis, transplantation or decline of the glomerular filtration rate (GFR). Statistical analyses aiming at investigating the association between these outcomes and risk factors raise a number of methodological issues. The objective of this study was to give an overview of these issues and to highlight some statistical methods that can address these topics. Methods: A literature review of statistical methods published between 2002 and 2012 to investigate risk factors of CKD outcomes was conducted within the Scopus database. The results of the review were used to identify important methodological issues as well as to discuss solutions for each type of CKD outcome. Results: Three hundred and four papers were selected. Time-to-event outcomes were more often investigated than quantitative outcome variables measuring kidney function over time. The most frequently investigated events in survival analyses were all-cause death, initiation of kidney replacement therapy, and progression to a specific value of GFR. While competing risks were commonly accounted for, interval censoring was rarely acknowledged when appropriate despite existing methods. When the outcome of interest was the quantitative decline of kidney function over time, standard linear models focussing on the slope of GFR over time were almost as often used as linear mixed models which allow various numbers of repeated measurements of kidney function per patient. Informative dropout was accounted for in some of these longitudinal analyses. Conclusions: This study provides a broad overview of the statistical methods used in the last ten years for investigating risk factors of CKD progression, as well as a discussion of their limitations. Some existing potential alternatives that have been proposed in the context of CKD or in other contexts are also highlighted. [ABSTRACT FROM AUTHOR]

Background: Ensuring fair comparisons of cancer survival statistics across population groups requires careful consideration of differential competing mortality due to other causes, and adjusting for imbalances over groups in other prognostic covariates (e.g. age). This has typically been achieved using comparisons of age-standardised net survival, with age standardisation addressing covariate imbalance, and the net estimates removing differences in competing mortality from other causes. However, these estimates lack ease of interpretability. In this paper, we motivate an alternative non-parametric approach that uses a common rate of other cause mortality across groups to give reference-adjusted estimates of the all-cause and cause-specific crude probability of death in contrast to solely reporting net survival estimates.Methods: We develop the methodology for a non-parametric equivalent of standardised and reference adjusted crude probabilities of death, building on the estimation of non-parametric crude probabilities of death. We illustrate the approach using regional comparisons of survival following a diagnosis of rectal cancer for men in England. We standardise to the covariate distribution and other cause mortality of England as a whole to offer comparability, but with close approximation to the observed all-cause region-specific mortality.Results: The approach gives comparable estimates to observed crude probabilities of death, but allows direct comparison across population groups with different covariate profiles and competing mortality patterns. In our illustrative example, we show that regional variations in survival following a diagnosis of rectal cancer persist even after accounting for the variation in deprivation, age at diagnosis and other cause mortality.Conclusions: The methodological approach of using standardised and reference adjusted metrics offers an appealing approach for future cancer survival comparison studies and routinely published cancer statistics. Our non-parametric estimation approach through the use of weighting offers the ability to estimate comparable survival estimates without the need for statistical modelling. [ABSTRACT FROM AUTHOR]

A standard competing risks set-up requires both time to event and cause of failure to be fully observable for all subjects. However, in application, the cause of failure may not always be observable, thus impeding the risk assessment. In some extreme cases, none of the causes of failure is observable. In the case of a recurrent episode of Plasmodium vivax malaria following treatment, the patient may have suffered a relapse from a previous infection or acquired a new infection from a mosquito bite. In this case, the time to relapse cannot be modeled when a competing risk, a new infection, is present. The efficacy of a treatment for preventing relapse from a previous infection may be underestimated when the true cause of infection cannot be classified. In this paper, we developed a novel method for classifying the latent cause of failure under a competing risks set-up, which uses not only time to event information but also transition likelihoods between covariates at the baseline and at the time of event occurrence. Our classifier shows superior performance under various scenarios in simulation experiments. The method was applied to Plasmodium vivax infection data to classify recurrent infections of malaria. [ABSTRACT FROM AUTHOR]

In survival and reliability studies, panel count data arise when we investigate a recurrent event process and each study subject is observed only at discrete time points. If recurrent events of several types are possible, we obtain panel count data with competing risks. Such data arise frequently from transversal studies on recurrent events in demography, epidemiology and reliability experiments where the individuals cannot be observed continuously. In the present paper, we propose an isotonic regression estimator for the cause specific mean function of the underlying recurrent event process of a competing risks panel count data. Further, a nonparametric test is proposed to compare the cause specific mean functions of the panel count competing risks data. Asymptotic properties of the proposed estimator and test statistic are studied. A simulation study is conducted to assess the finite sample behaviour of the proposed estimator and test statistic. Finally, the procedures developed are applied to a real data arising from skin cancer chemo prevention trial. [ABSTRACT FROM AUTHOR]