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The average lifespan of particles, a crucial parameter in nuclear physics, is essential for identification purposes. Modern particle detectors excel at recognizing individual radioactive nuclei arrivals and their subsequent decay events. However, challenges arise when matching arrivals with departures, especially when departures are only partially observed. One inefficient approach involves conducting experiments with very low arrival rates to facilitate matching. The kiloelectron-volt E(keV) emission is obtained during this radio active process. This study focuses on the meticulous surveillance of the average keV emission from partially observed events within the domain of nuclear physics. To accomplish this, the methodology employs the statistical approach known as Distance Weighted Mean (DWM), integrated with the application of censored control charts. The utilization of censored control charts allows for the effective management of incomplete data, enabling researchers to make informed decisions despite potential limitations in observation. We propose a DWM based exponentially weighted moving average-cumulative sum (DWM-EC) control chart for monitoring kiloelectron-volt E(keV) data. The proposed charts is developed for Weibull lifetimes under type-I censoring. For the construction of an efficient control charting structure, we employed the conditional median (CM) methods. The goal is to find changes in the mean of Weibull lifetimes with censored data with known and estimated parameter conditions. The performance of the proposed DWM-EC chart is evaluated by the average run length (ARL). Besides a simulation study, a real-life data set on E(keV) related to the alpha decays of 177 Lutetium isotope is also discussed. [ABSTRACT FROM AUTHOR]

Subsampling designs are useful for reducing computational load and storage cost for large-scale data analysis. For massive survival data with right censoring, we propose a class of optimal subsampling designs under the widely-used Cox model. The proposed designs utilize information from both the outcome and the covariates. Different forms of the design can be derived adaptively to meet various targets, such as optimizing the overall estimation accuracy or minimizing the variation of specific linear combination of the estimators. Given the subsampled data, the inverse probability weighting approach is employed to estimate the model parameters. The resultant estimators are shown to be consistent and asymptotically normally distributed. Simulation results indicate that the proposed subsampling design yields more efficient estimators than the uniform subsampling by using subsampled data of comparable sample sizes. Additionally, the subsampling estimation significantly reduces the computational load and storage cost relative to the full data estimation. An analysis of a real data example is provided for illustration. [ABSTRACT FROM AUTHOR]

In this work, we present classical and Bayesian inferential methods based on samples in the presence of progressive type-II censoring under the Very Flexible Weibull (VFW) distribution. The considered distribution is relevant because it is an alternative to traditional non-flexible distributions and also to some flexible distributions already known in the literature, keeping the low amount of two parameters. In addition, studying it in a context of progressive censoring allows attesting to its applicability in data modeling from various areas of industry and technology that can use this censoring methodology. We obtain the maximum likelihood estimators of the model parameters, as well as their asymptotic variation measures. We propose the use of Markov chain Monte Carlo methods for the computation of Bayes estimates. A simulation study is carried out to evaluate the performance of the proposed estimators under different sample sizes and progressive type-II censoring schemes. Finally, the methodology is illustrated through three real data sets. [ABSTRACT FROM AUTHOR]

In this article, based on progressive type-II censored competing risks data with binomial removals, a constant-stress accelerated life testing is discussed when the lifetime of experiment units follows the Pareto distribution. Under the assumption that the failure time of each cause is statistically independent, the estimation of unknown parameters is obtained by maximum likelihood estimation and Bayesian estimators under symmetric and asymmetric loss functions. The corresponding confidence and credible intervals are constructed with approximation theory, bootstrap method, and MCMC technique respectively. Additionally, the log-linear model is established for the life test and two goodness-of-fit test statistics are constructed. Finally, a simulation study is carried out for the power analysis of different censoring ratio schemes and the numerical results verify the feasibility of the constructed test statistics for the censored data with competing risks. [ABSTRACT FROM AUTHOR]

The document outlines the winners of the 2023 Technometrics Prizes, with Ying Jin, Shan Ba, Kungang Zhang, Anh Bui, and Daniel Apley receiving awards for their respective articles. The prizes include a certificate and a cash award. Additionally, the document provides a historical list of past winners of the Technometrics Prizes from 1969 to 2022, showcasing a diverse range of research topics and authors. [Extracted from the article]

Recent literature has found conditional transition rates to be a useful tool for avoiding Markov assumptions in multi-state models. While the estimation of univariate conditional transition rates has been extensively studied, the intertemporal dependencies captured in the bivariate conditional transition rates still require a consistent estimator. We provide an estimator that is suitable for censored data and emphasiz e the connection to the rich theory of the estimation of bivariate survival functions. Bivariate conditional transition rates are necessary for various applications in the survival context but especially in the calculation of moments in life insurance mathematics. [ABSTRACT FROM AUTHOR]

AbstractModel checking evaluates the appropriateness of a statistical model based on the observed data, and it is essential to make valid statistical analyses. In this paper, a new procedure for model checking type II censored data is proposed. This procedure combines the Kullback-Leibler divergence, the Dirichlet process, and the relative belief ratio. The method is implemented via a computational algorithm and is explained through several examples. [ABSTRACT FROM AUTHOR]

Survival analysis in medical research has witnessed a growing interest in applying deep learning techniques to model complex, high-dimensional, heterogeneous, incomplete, and censored data. Current methods make assumptions about the relations between data that may not be valid in practice. Therefore, we introduce SAVAE (Survival Analysis Variational Autoencoder). SAVAE, based on Variational Autoencoders, contributes significantly to the field by introducing a tailored Evidence Lower BOund formulation, supporting various parametric distributions for covariates and survival time (if the log-likelihood is differentiable). It offers a general method that demonstrates robustness and stability through different experiments. Our proposal effectively estimates time-to-event, accounting for censoring, covariate interactions, and time-varying risk associations. We validate our model in diverse datasets, including genomic, clinical, and demographic tabular data, with varying levels of censoring. This approach demonstrates competitive performance compared to state-of-the-art techniques, as assessed by the Concordance Index and the Integrated Brier Score. SAVAE also offers an interpretable model that parametrically models covariates and time. Moreover, its generative architecture facilitates further applications such as clustering, data imputation, and synthetic patient data generation through latent space inference from survival data. This approach fosters data sharing and collaboration, improving medical research and personalized patient care. [ABSTRACT FROM AUTHOR]

AbstractWe evaluated the co-occurrence of arsenic (As), cadmium (Cd), and lead (Pb) in 10 categories of processed foods intended for infants and young children (<2 years old) and adapted methodology to characterise and evaluate the impact of correlations on toxic element (TE) concentrations in these foods. Co-occurrence was assessed by calculating the frequency of samples having concentrations above the limit of detection (LOD) among TE sets (i.e. As-Cd, As-Pb, Cd-Pb, and As-Cd-Pb). Pairwise correlations were evaluated using two statistical approaches adapted to censored data: (i) non-parametric Kendall’s tau and (ii) parametric Bayesian modelling. Nonparametric and parametric correlation analyses showed similar results. We found positive correlations among one or more pairs of the TEs (As, Pb, and Cd) in 9 of the 10 categories of foods intended for infants and young children and a negative correlation for one TE pair for a single food category. Where positive correlations are observed, removing samples with high concentrations of a given TE reduces the mean of the other TEs in that food. We also explored the impact of correlations among TEs on the fraction of the supply below maximum levels. Positive correlations among TEs have the potential to reduce the impact on the supply when setting multiple maximum levels. [ABSTRACT FROM AUTHOR]

The lifetime performance index (LPI) is an important metric for evaluating product quality, and research on the statistical inference of the LPI is of great significance. This paper discusses both the classical and Bayesian estimations of the LPI under an adaptive progressive type-II censored lifetime test, assuming that the product's lifetime follows a generalized inverse Lindley distribution. At first, the maximum likelihood estimator of the LPI is derived, and the Newton–Raphson iterative method is adopted to solve the numerical solution due to the log-likelihood equations having no analytical solutions. If the exact distribution of the LPI is not available, then the asymptotic confidence interval and bootstrap confidence interval of the LPI are constructed. For the Bayesian estimation, the Bayesian estimators of the LPI are derived under three different loss functions. Due to the complex multiple integrals involved in these estimators, the MCMC method is used to draw samples and further construct the HPD credible interval of the LPI. Finally, Monte Carlo simulations are used to observe the performance of these estimators in terms of the average bias and mean squared error, and two practical examples are used to illustrate the application of the proposed estimation method. [ABSTRACT FROM AUTHOR]

Analysis of jointly censoring schemes has received considerable attention in the last few years. In this paper, maximum likelihood and Bayes methods of estimation are used to estimate the unknown parameters of two Gompertz populations under a joint progressive Type-II censoring scheme. Bayesian estimations of the unknown parameters are obtained based on squared error loss functions under the assumption of independent gamma priors. We propose to apply the Markov Chain Monte Carlo technique to carry out a Bayes estimation procedure. The approximate, bootstrap, and credible confidence intervals for the unknown parameters are also obtained. Also, reliability and hazard rate function of the two Gompertz populations under joint progressive Type-II censoring scheme is obtained and the corresponding approximate confidence intervals. Finally, all the theoretical results obtained are assessed and compared using two real-world data sets and Monte Carlo simulation studies. [ABSTRACT FROM AUTHOR]

The proportional hazard regression models are widely used statistical tools for analyzing survival data and estimating the effects of covariates on survival times. It is assumed that the effects of the covariates are constant across the time. In this paper, we propose a novel extension of the proportional hazard model by incorporating an exponentiated-Weibull distribution to model the baseline line hazard function. The proposed model offers more flexibility in capturing various shapes of failure rates and accommodates both monotonic and non-monotonic hazard shapes. The performance evaluation of the proposed model and comparison with other commonly used survival models including the generalized log–logistic, Weibull, Gompertz, and exponentiated exponential PH regression models are explored using simulation results. The results demonstrate the ability of the introduced model to capture the baseline hazard shapes and to estimate the effect of covariates on the hazard function accurately. Furthermore, two real survival medical data sets are analyzed to illustrate the practical importance of the proposed model to provide accurate predictions of survival outcomes for individual patients. Finally, the survival data analysis reveal that the model is a powerful tool for analyzing complex survival data. [ABSTRACT FROM AUTHOR]

In studies with time-to-event outcomes, multiple, inter-correlated, and time-varying covariates are commonly observed. It is of great interest to model their joint effects by allowing a flexible functional form and to delineate their relative contributions to survival risk. A class of semiparametric transformation (ST) models offers flexible specifications of the intensity function and can be a general framework to accommodate nonlinear covariate effects. In this paper, we propose a partial-linear single-index (PLSI) transformation model that reduces the dimensionality of multiple covariates into a single index and provides interpretable estimates of the covariate effects. We develop an iterative algorithm using the regression spline technique to model the nonparametric single-index function for possibly nonlinear joint effects, followed by nonparametric maximum likelihood estimation. We also propose a nonparametric testing procedure to formally examine the linearity of covariate effects. We conduct Monte Carlo simulation studies to compare the PLSI transformation model with the standard ST model and apply it to NYU Langone Health de-identified electronic health record data on COVID-19 hospitalized patients' mortality and a Veteran's Administration lung cancer trial. [ABSTRACT FROM AUTHOR]

This article explores the estimation of Shannon entropy and Rényi entropy based on the generalized inverse exponential distribution under the condition of stepwise Type II truncated samples. Firstly, we analyze the maximum likelihood estimation and interval estimation of Shannon entropy and Rényi entropy for the generalized inverse exponential distribution. In this process, we use the bootstrap method to construct confidence intervals for Shannon entropy and Rényi entropy. Next, we select the gamma distribution as the prior distribution and apply the Lindley approximation algorithm to calculate 'estimates of Shannon entropy and Rényi entropy under different loss functions including Linex loss function, entropy loss function, and DeGroot loss function respectively. Afterwards, simulation is used to calculate estimates and corresponding mean square errors of Shannon entropy and Rényi entropy in GIED model. The research results show that under DeGroot loss function, estimation accuracy of Shannon entropy and Rényi entropy for generalized inverse exponential distribution is relatively high, overall Bayesian estimation performs better than maximum likelihood estimation. Finally, we demonstrate effectiveness of our estimation method in practical applications using a set of real data. [ABSTRACT FROM AUTHOR]

ABSTRACT As a favorable alternative to the censored quantile regression, censored expectile regression has been popular in survival analysis due to its flexibility in modeling the heterogeneous effect of covariates. The existing weighted expectile regression (WER) method assumes that the censoring variable and covariates are independent, and that the covariates effects has a global linear structure. However, these two assumptions are too restrictive to capture the complex and nonlinear pattern of the underlying covariates effects. In this article, we developed a novel weighted expectile regression neural networks (WERNN) method by incorporating the deep neural network structure into the censored expectile regression framework. To handle the random censoring, we employ the inverse probability of censoring weighting (IPCW) technique in the expectile loss function. The proposed WERNN method is flexible enough to fit nonlinear patterns and therefore achieves more accurate prediction performance than the existing WER method for right censored data. Our findings are supported by extensive Monte Carlo simulation studies and a real data application. [ABSTRACT FROM AUTHOR]

AbstractIn this study, we consider 2- and 3-step estimators for censored quantile regression models with fixed effects. In the first step of these estimators, the informative subset is determined through the estimation of censoring probability. While previous studies often employ symmetric link functions for estimating the censoring probability, these may not accurately identify the best subset when the distribution of the censoring probability is skewed. Given the prevalence of asymmetrically censored data in empirical analyses, we propose using an asymmetric link function for more accurate subset determination. We conduct Monte Carlo simulations and empirical analysis to assess our proposed methods. Our Monte Carlo simulations and empirical analysis confirm that an asymmetric link function offers a better fit for asymmetrically censored data. For symmetrically censored data, the symmetric link function performs better in moderate and large samples, while the asymmetric link function performs slightly better in small samples. These findings underscore the importance of considering both the censoring probability distribution and sample size in panel quantile regression. [ABSTRACT FROM AUTHOR]

AbstractWith the rapid development of data acquisition and storage space, massive datasets exhibited with large sample size emerge increasingly and make more advanced statistical tools urgently need. To accommodate such big volume in the analysis, a variety of methods have been proposed in the circumstances of complete or right censored survival data. However, existing development of big data methodology has not attended to interval-censored outcomes, which are ubiquitous in cross-sectional or periodical follow-up studies. In this work, we propose an easily implemented divide-and-combine approach for analyzing massive interval-censored survival data under the additive hazards model. We establish the asymptotic properties of the proposed estimator, including the consistency and asymptotic normality. In addition, the divide-and-combine estimator is shown to be asymptotically equivalent to the full-data-based estimator obtained from analyzing all data together. Simulation studies suggest that, relative to the full-data-based approach, the proposed divide-and-combine approach has desirable advantage in terms of computation time, making it more applicable to large-scale data analysis. An application to a set of interval-censored data also demonstrates the practical utility of the proposed method. [ABSTRACT FROM AUTHOR]

We propose a non-parametric approach to reduce the overestimation of the Kaplan-Meier (KM) estimator when the event and censoring times are independent. We adjust the KM estimator based on the interval-specific censoring set, a collection of intervals where censored data are observed between two adjacent event times. The proposed interval-specific censoring set adjusted KM estimator reduces to the KM estimator if there are no censored observations or the sample size tends to infinity and the proposed estimator is consistent, as is the case for the KM estimator. We prove theoretically that the proposed estimator reduces the overestimation compared to the KM estimator and provide a mathematical formula to estimate the variance of the proposed estimator based on Greenwood's approach. We also provide a modified log-rank test based on the proposed estimator. We perform four simulation studies to compare the proposed estimator with the KM estimator when the failure rate is constant, decreasing, increasing, and based on the flexible hazard method. The bias reduction in median survival time and survival rate using the proposed estimator is considerably large, especially when the censoring rate is high. The standard deviations are comparable between the two estimators. We implement the proposed and KM estimator for the Nonalcoholic Fatty Liver Disease patients from a population study. The results show the proposed estimator substantially reduce the overestimation in the presence of high observed censoring rate. [ABSTRACT FROM AUTHOR]

Interval-censored failure time data are commonly encountered in many fields and some methods and models have been proposed for them in the literature. In the real situations, interval censoring is informative. For this problem, we propose a new frailty-based generalized estimating equation (GEE) method of the proportional hazards (PH) model with the informatively case K interval-censored failure time data. In this article, a frailty-based generalized estimating equation is developed that can yield an unbiased estimator of the cumulative hazards function. The observation process of the proposed method does not need a non homogeneous Poisson process used in many existing literatures. The asymptotic properties of the proposed method are established, and an extensive simulation study is conducted to assess the performance of the proposed procedure. In addition, an application to an AIDS clinical trial data set is presented. [ABSTRACT FROM AUTHOR]

In this paper, Bayesian estimates are derived for the location and scale parameters of the Laplace distribution based on complete, Type-I, and Type-II censored samples under different prior settings. Subsequently, Bayesian point and interval estimates, as well as the associated statistical inference, are discussed in detail. The developed methods are then applied to two real data sets for illustrative purposes. Moreover, a detailed Monte Carlo simulation study is carried out for evaluating the performance of the inferential methods developed here. Finally, we provide a brief discussion of the established results to demonstrate their practical utility and present some associated problems of further interest. Overall, this study fills an existing gap in the development of Bayesian inferential techniques for the parameters of the two-parameter Laplace distribution, making this research innovative and offering more investigative implications. It showcases the potential for broader methodological applications of Bayesian inference for complex real-world data sets, especially in scenarios involving different forms of censoring. This research provides a critical tool for statistical analysis in different fields such as engineering and finance, where the Laplace distribution is frequently adopted as a fundamental model. [ABSTRACT FROM AUTHOR]

In this article, we draw inferences on stress–strength reliability in a multicomponent system with non-identical strength components based on the progressively censored data from the Kumaraswamy distribution (KuD). When one shape parameter of KuD is known, the uniformly minimum variance unbiased estimator is produced. To evaluate the reliability of such systems when all the parameters are unknown, the maximum likelihood and Bayes estimators are developed. Along with coverage probabilities, the asymptotic confidence and highest posterior credible (HPD) intervals are also obtained. Tierney–Kadane's approximation and Markov chain Monte Carlo methods are used for Bayesian computations. To compare the performance of estimators, a Monte Carlo simulation study is performed. Also, one real-life example is analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

Censored data are nearly ubiquitous in survival analysis. If the proportional hazard assumption is invalid, traditional test methods, such as the log-rank tests, rapidly lose power. In this article, a new slope strategy is presented to improve the power of the test. The aim of this study is to establish effective tests that are familiar in biomedical research and medical practice for censored data. Four tests based on slope are proposed in this article, and Monte Carlo simulations with different survival curves, sample sizes, and censoring rate scenarios are performed to evaluate the test power. Four common tests, the log-rank test, Gehan–Wilcoxon test, and Fleming–Harrington with different parameters, are compared with four new slope tests. The slope tests are more effective when the censoring rate is greater than or equal to 30%, especially for scenarios involving early hazard function differences. Two clinical cases also indicate that the proposed slope methods can detect differences for real data. Slope tests may supplement computing methods of survival curve tests, and they will be more useful when considering higher censoring rates. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the inferential procedures within both classical and Bayesian frameworks for the generalized logistic distribution under a random censoring model. For randomly censored data, our main goals were to develop maximum likelihood estimators and construct confidence intervals using the Fisher information matrix for the unknown parameters. Additionally, we developed Bayes estimators with gamma priors, addressing both squared error and general entropy loss functions. We also calculated Bayesian credible intervals for the parameters. These methods were applied to two real datasets with random censoring to provide valuable insights. Finally, we conducted a simulation analysis to assess the effectiveness of the estimated values. [ABSTRACT FROM AUTHOR]

Censored data, where the event time is partially observed, are challenging for survival probability estimation. In this article, we introduce a novel nonparametric fiducial approach to interval-censored data, including right-censored, current status, case II censored, and mixed case censored data. The proposed approach leveraging a simple Gibbs sampler has a useful property of being "one size fits all," that is, the proposed approach automatically adapts to all types of noninformative censoring mechanisms. As shown in the extensive simulations, the proposed fiducial confidence intervals significantly outperform existing methods in terms of both coverage and length. In addition, the proposed fiducial point estimator has much smaller estimation errors than the nonparametric maximum likelihood estimator. Furthermore, we apply the proposed method to Austrian rubella data and a study of hemophiliacs infected with the human immunodeficiency virus. The strength of the proposed fiducial approach is not only estimation and uncertainty quantification but also its automatic adaptation to a variety of censoring mechanisms. for this article are available online. [ABSTRACT FROM AUTHOR]

Background: Mild cognitive impairment (MCI) patients are at a high risk of developing Alzheimer's disease and related dementias (ADRD) at an estimated annual rate above 10%. It is clinically and practically important to accurately predict MCI-to-dementia conversion time. Objective: It is clinically and practically important to accurately predict MCI-to-dementia conversion time by using easily available clinical data. Methods: The dementia diagnosis often falls between two clinical visits, and such survival outcome is known as interval-censored data. We utilized the semi-parametric model and the random forest model for interval-censored data in conjunction with a variable selection approach to select important measures for predicting the conversion time from MCI to dementia. Two large AD cohort data sets were used to build, validate, and test the predictive model. Results: We found that the semi-parametric model can improve the prediction of the conversion time for patients with MCI-to-dementia conversion, and it also has good predictive performance for all patients. Conclusions: Interval-censored data should be analyzed by using the models that were developed for interval- censored data to improve the model performance. [ABSTRACT FROM AUTHOR]

The paper introduces a nonparametric estimator for the regression function of left truncated and right censored data, achieved through minimising the mean squared relative error. Under α-mixing condition, strong uniform convergence of the estimator is established with a rate over a compact set. An extensive simulation study is conducted to assess the estimator's performance, comparing its efficiency to that of the classical regression estimator for finite samples across various scenarios. Moreover, a real world application is presented to demonstrate the practical utility of the proposed estimator. [ABSTRACT FROM AUTHOR]

Phase IV clinical trials are designed to monitor long-term side effects of medical treatment. For instance, childhood cancer survivors treated with chest radiation and/or anthracycline are often at risk of developing cardiotoxicity during their adulthood. Often the primary focus of a study could be on estimating the cumulative incidence of a particular outcome of interest such as cardiotoxicity. However, it is challenging to evaluate patients continuously and usually, this information is collected through cross-sectional surveys by following patients longitudinally. This leads to interval-censored data since the exact time of the onset of the toxicity is unknown. Rai et al. computed the transition intensity rate using a parametric model and estimated parameters using maximum likelihood approach in an illness-death model. However, such approach may not be suitable if the underlying parametric assumptions do not hold. This manuscript proposes a semi-parametric model, with a logit relationship for the treatment intensities in two groups, to estimate the transition intensity rates within the context of an illness-death model. The estimation of the parameters is done using an EM algorithm with profile likelihood. Results from the simulation studies suggest that the proposed approach is easy to implement and yields comparable results to the parametric model. [ABSTRACT FROM AUTHOR]

Purpose: Crime data analysis has gained significant interest due to its peculiarities. One key characteristic of property crimes is the uncertainty surrounding their exact temporal location, often limited to a time window. Methods: This study introduces a spatio-temporal logistic regression model that addresses the challenges posed by temporal uncertainty in crime data analysis. Inspired by the aoristic method, our Bayesian approach allows for the inclusion of temporal uncertainty in the model. Results: To demonstrate the effectiveness of our proposed model, we apply it to both simulated datasets and a dataset of residential burglaries recorded in Valencia, Spain. We compare our proposal with a complete cases model, which excludes temporally-uncertain events, and also with alternative models that rely on imputation procedures. Our model exhibits superior performance in terms of recovering the true underlying crime risk. Conclusions: The proposed modeling framework effectively handles interval-censored temporal observations while incorporating covariate and space–time effects. This flexible model can be implemented to analyze crime data with uncertainty in temporal locations, providing valuable insights for crime prevention and law enforcement strategies. [ABSTRACT FROM AUTHOR]

The transformation model with partly interval-censored data offers a highly flexible modeling framework that can simultaneously support multiple common survival models and a wide variety of censored data types. However, the real data may contain unexplained heterogeneity that cannot be entirely explained by covariates and may be brought on by a variety of unmeasured regional characteristics. Due to this, we introduce the conditionally autoregressive prior into the transformation model with partly interval-censored data and take the spatial frailty into account. An efficient Markov chain Monte Carlo method is proposed to handle the posterior sampling and model inference. The approach is simple to use and does not include any challenging Metropolis steps owing to four-stage data augmentation. Through several simulations, the suggested method's empirical performance is assessed and then the method is used in a leukemia study. [ABSTRACT FROM AUTHOR]

In this paper, we study the robust estimation and empirical likelihood for the regression parameter in generalized linear models with right censored data. A robust estimating equation is proposed to estimate the regression parameter, and the resulting estimator has consistent and asymptotic normality. A bias-corrected empirical log-likelihood ratio statistic of the regression parameter is constructed, and it is shown that the statistic converges weakly to a standard $ \chi ^2 $ χ 2 distribution. The result can be directly used to construct the confidence region of regression parameter. We use the bias correction method to directly calibrate the empirical log-likelihood ratio, which does not need to be multiplied by an adjustment factor. We also propose a method for selecting the tuning parameters in the loss function. Simulation studies show that the estimator of the regression parameter is robust and the bias-corrected empirical likelihood is better than the normal approximation method. An example of a real dataset from Alzheimer's disease studies shows that the proposed method can be applied in practical problems. [ABSTRACT FROM AUTHOR]

Censorship is one of the main forms of political coercion deployed by modern states to control and regulate public expression. In this article, we examine the political censorship of China's intellectual public space, which has long been underexplored. We apply unsupervised machine learning to examine the database of a leading intellectual portal website, which serves as an archive of both published and censored intellectual writings between 2000 and 2020 and includes over 740 million Chinese characters. We identify a strategic censorship mechanism that consists of thematic and persona censorship elements. Thematic censorship involves the state filtering out writing that competes with the official policy narrative, historiography, and values. Persona censorship involves the complete muting of individual intellectuals who have previously made derogatory attacks on the supreme leaders of the Communist Party, which represents a symbolic act of open defiance. [ABSTRACT FROM AUTHOR]

This study examined the estimations of Weibull distribution using progressively first-failure censored data, under the assumption that removals follow the beta-binomial distribution. Classical and Bayesian approaches for estimating unknown model parameters have been established. The estimations included scale and shape parameters, reliability and failure rate metrics as well as betabinomial parameters. Estimations were considered from both point and interval viewpoints. The Bayes estimates were developed by using the squared error loss and generating samples for the posterior distribution through the Markov Chain Monte Carlo technique. Two interval estimation approaches are considered: approximate confidence intervals based on asymptotic normality of likelihood estimates and Bayes credible intervals. To investigate the performance of classical and Bayesian estimations, a simulation study was considered by various kinds of experimental settings. Furthermore, two examples related to real datasets were thoroughly investigated to verify the practical importance of the suggested methodologies. [ABSTRACT FROM AUTHOR]

Various goodness-of-fit tests are designed based on the so-called information matrix equivalence: if the assumed model is correctly specified, two information matrices that are derived from the likelihood function are equivalent. In the literature, this principle has been established for the likelihood function with fully observed data, but it has not been verified under the likelihood for censored data. In this manuscript, we prove the information matrix equivalence in the framework of semiparametric copula models for multivariate censored survival data. Based on this equivalence, we propose an information ratio (IR) test for the specification of the copula function. The IR statistic is constructed via comparing consistent estimates of the two information matrices. We derive the asymptotic distribution of the IR statistic and propose a parametric bootstrap procedure for the finite-sample P-value calculation. The performance of the IR test is investigated via a simulation study and a real data example. [ABSTRACT FROM AUTHOR]

There is often a presence of random change points (RCPs) with varying timing of hazard rate change among patients in survival analysis within oncology trials. This is in contrast to fixed change points in piecewise constant hazard models, where the timing of hazard rate change remains the same for all subjects. However, currently there is a lack of appropriate statistical methods to effectively tackle this particular issue. This article presents novel statistical methods that aim to characterize these complex survival models. These methods allow for the estimation of important features such as the probability of an event occurring and being censored, and the expected number of events within the clinical trial, prior to any specific time, and within specific time intervals. They also derive expected survival time and parametric expected survival and hazard functions for subjects with any finite number of RCPs. Simulation studies validate these methods and demonstrate their reliability and effectiveness. Real clinical data from an oncology trial is also used to apply these methods. The applications of these methods in oncology trials are extensive, including estimating hazard rates and rate parameters of RCPs, assessing treatment switching, delayed onset of immunotherapy, and subsequent anticancer therapies. They also have value in clinical trial planning, monitoring, and sample size adjustment. The expected parametric survival and hazard functions provide a thorough understanding of the behaviors and effects of RCPs in complex survival models. [ABSTRACT FROM AUTHOR]

In analysis of survival data, the Accelerated Life Model (ALM) is one of the widely used semiparametric models, and we often encounter various types of censored survival data, such as right censored data, doubly censored data, interval censored data, partly interval-censored data, etc. For complicated types of censored data, the studies of statistical inferences on the ALM are very technical and challenging mathematically, thus up to now little work has been done. In this article, we extend the concept of weighted empirical likelihood (WEL) from univariate case to multivariate case, and we apply it to the ALM, which leads to an estimation approach, called weighted maximum likelihood estimator, as well as the WEL based confidence interval for the regression parameter. Our proposed procedures are applicable to various types of censored data under a unified framework, and some simulation results are presented. [ABSTRACT FROM AUTHOR]

In survival analysis, the Accelerated Failure Time (AFT) shared frailty model is a widely used framework for analyzing time-to-event data while accounting for unobserved heterogeneity among individuals. This paper extends the traditional Weibull AFT shared frailty model using half logistic-G family of distributions (Type I, Type II and Type II exponentiated) through Bayesian methods. This approach offers flexibility in capturing covariate influence and handling heavy-tailed frailty distributions. Bayesian inference with MCMC provides parameter estimates and credible intervals. Simulation studies show improved model predictive performance compared to existing models, and real-world applications demonstrate its practical utility. In summary, our Bayesian Weibull AFT shared frailty model with Type I, Type II and Type II exponentiated half logistic-G family distributions enhances time-to-event data analysis, making it a versatile tool for survival analysis in various fields using STAN in R. [ABSTRACT FROM AUTHOR]

It is the purpose of this paper to propose a novel clustering technique tailored to randomly censored data in reliability/survival analysis. It is based on an underlying mixture model of Weibull distributions and consists in estimating its parameters by means of a variant of the Expectation–Maximization method in the presence of random censorship. Beyond the description of the algorithm, model selection issues are addressed and we investigate its performance from an empirical perspective by applying it to possibly strongly censored (synthetic and real) survival data. The experiments carried out provide strong empirical evidence that our algorithm performs better than alternative methods standing as natural competitors in this framework. [ABSTRACT FROM AUTHOR]

In reliability and life analysis, the accelerated life test is frequently used because it can reduce cost and obtain additional reliability and lifetime information. In addition, when a unit fails in a life test, there are often two or more risk factors related to the cause of the failure. In this article, we consider the inference from a step-stress-accelerated life test with competing risks using progressive type-II censored data. Based on the assumption that the parameters affected by stress follow a log-linear model with the stress level, the proportional hazard model with the Kumaraswamy distribution is established. The point estimation of the unknown parameters is derived using maximum likelihood and Bayesian methods. Accordingly, the logarithmic asymptotic confidence and the highest posterior density credible intervals are derived and constructed. Moreover, the algorithm for multi-parameter sampling and simulation technology based on this model is given. Simulation results show that the proposed methods have good performance. In light of the estimates of the parameters, the estimated reliability function under normal conditions can be expressed, and its images under different methods are drawn. Last, a real dataset and a set of simulated data are presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

Consider a situation where one is interested in estimating the density of a survival time that is subject to random right censoring and measurement errors. This happens often in practice, like in public health (pregnancy length), medicine (duration of infection), ecology (duration of forest fire), among others. We assume a classical additive measurement error model with Gaussian noise and unknown error variance and a random right censoring scheme. Under this setup, we develop minimal conditions under which the assumed model is identifiable when no auxiliary variables or validation data are available, and we offer a flexible estimation strategy using Laguerre polynomials for the estimation of the error variance and the density of the survival time. The asymptotic normality of the proposed estimators is established, and the numerical performance of the methodology is investigated on both simulated and real data on gestational age. [ABSTRACT FROM AUTHOR]

Accelerated life tests play a very critical role in reliability analysis because highly reliable products are being produced with recent advanced technologies to sustain the market demand and competition. A progressive-stress accelerated life test is one of the kinds of accelerated life tests that allows applied stress to change continuously. Considering the importance of progressive-stress accelerated life tests, this paper deals with progressive-stress accelerated life tests when the lifetimes of units follow the log-logistic distribution and are progressively type-II censored where the associated scale parameter conforms to the inverse power law. Different estimators of model parameters are derived using maximum likelihood and Bayesian methods. Interval estimation is also considered. In the sequel, approximate confidence, bootstrap, and Bayes credible intervals are constructed. Bayes estimators are obtained under squared error, LINEX, and entropy loss functions using proper and improper prior distributions. A simulation study is conducted based on various censoring schemes. The coverage percentages and interval widths are computed via Monte Carlo simulations. Bayes predictive estimates and intervals are also obtained. Finally, two different accelerated life test data are analyzed for illustration purposes. [ABSTRACT FROM AUTHOR]

The exponential distribution can provide a simple and appealing survival-time model in reliability analysis and life tests. Due to certain experimental designs, time limitations, budgetary requirements, and other reasons, however, only censored data can be obtained. In this paper, we propose a novel estimation procedure for the mean survival time of an exponential distribution under a sequential censoring scheme, which can be treated as a combination of type I censoring and type II censoring. The procedure makes a trade-off between estimation error and sampling cost, using the minimum number of observations. An extensive set of Monte Carlo simulations is conducted to further validate its remarkable performance. To demonstrate the practical applicability, we then implement this newly proposed procedure to assess the reliability of various Backblaze's hard disk models. [ABSTRACT FROM AUTHOR]

Consider the semiparametric linear regression estimation problem with right-censored data. Under right censoring, the Buckley–James estimator (BJE) is the standard extension of the least squares estimator. Moreover, an iterative algorithm for the BJE has been implemented in R package called rms. We show that it often does not yield a solution, even if a consistent BJE exists. Yu and Wong (J Stat Comput Simul 72:451–460, 2002) proposed another algorithm to find all possible BJEs. The latter algorithm is modified in this paper so that it indeed finds all BJEs when the underlying regression parameter vector is identifiable. We show that some of these BJE's can be inconsistent. Thus it is important to decide how to select a proper BJE such that it is consistent if the parameter is identifiable. We suggest either choose one close to the modified semi-parametric maximum likelihood estimator (Yu and Wong in Technometrics 47:34–42, 2005) or a finite boundary point if there are infinitely many BJEs. [ABSTRACT FROM AUTHOR]

Interval-censored failure time data frequently occur in many areas and a great deal of literature on their analyses has been established. In this article, we discuss the situation where one faces bivariate interval-censored data arising from case-cohort studies, which are commonly used as a tool to save costs when disease incidence is low and covariates are difficult to obtain. For this problem, a class of copula-based semi-parametric models is presented and for estimation, a sieve weighted maximum likelihood estimation procedure is developed. The resulting estimators of regression parameters are shown to be strongly consistent and asymptotically normal. Furthermore, the proposed method is generalized to the situation of non rare diseases. A simulation study is conducted to assess the finite sample performance of the proposed method and suggests that it performs well in practice. [ABSTRACT FROM AUTHOR]

Up to now, almost all existing methods for joint modeling survival data and longitudinal data rely on parametric/semiparametric assumptions on longitudinal covariate process, and the resulting inferences critically depend on the validity of these assumptions that are difficult to verify in practice. The kernel method-based procedures rely on choices of kernel function and bandwidth, and none of the existing methods provides estimate for the baseline distribution in proportional hazards model. This article proposes a proportional hazards model for joint modeling right censored survival data and intensive longitudinal data taking into account of within-subject historic change patterns. Without any parametric/semiparametric assumptions or use of kernel method, we derive empirical likelihood-based maximum likelihood estimators and partial likelihood estimators for the regression parameter and the baseline distribution function. We develop stable computing algorithms and present some simulation results. Analyses of real dataset are conducted for smoking cessation data and liver disease data. [ABSTRACT FROM AUTHOR]

This paper is concerned with applying the Bayesian and E-Bayesian approaches to estimating the unknown parameters of the modified Topp–Leone–Chen distribution under a progressive Type-II censored sample plan. The paper explores the complexities of different estimating methods and investigates the behavior of the estimates through some computations. The Bayes and E-Bayes estimators are obtained under two distinct loss functions, the balanced squared error loss function, as a symmetric loss function, and the balanced linear exponential loss function, as an asymmetric loss function. The estimators are derived using gamma prior and uniform hyperprior distributions. A numerical illustration is given to examine the theoretical results through using the Metropolis–Hastings algorithm of the Markov chain Monte Carlo method of simulation by the R programming language. Finally, real-life data sets are applied to prove the flexibility and applicability of the model. [ABSTRACT FROM AUTHOR]

This note develops a generalized k$$ k $$‐variate hazard function for censored data in survival analysis. It introduces a generalized recursive formula, extending the bivariate and trivariate cases introduced by Clayton and Cuzick (1985, Journal of the Royal Statistical Society: Series A (General), 148(2):82–108) and Kittani (1995, Journal of Mathematical Sciences, 67–74), respectively. The newly developed function is explicitly specified by k$$ k $$ association parameters and k$$ k $$ marginal hazard functions. [ABSTRACT FROM AUTHOR]

Life categories and probability distributions are part of a new field in reliability that has emerged as a result of the daily generation of data that has become more complex across practical fields. This study demonstrated how well the U-statistics technique can be applied to real-world testing problems, producing more efficient processes that are on par with or even more successful than conventional approaches. Furthermore, there was room for improvement in the performance of these methods. An approach tending toward normalcy was supported by comparing a unique U-statistic test with the used better than age in moment generating ordering (UBAmgf) test statistic, In this manuscript, a novel nonparametric technique has been developed to test the belonging of a dataset to a distribution of a new statistical class survival function, the moment generating function for used better than aged (UBAmgf). This type of test was crucial in practical life, such as implementing a specific strategy of proposed therapy for a particular disease, deeming it futile if the survival data was exponential (accepting H0) (the suggested therapeutic approach does not exhibit positive or negative effects on the patients). Once the survival data was UBAmgf, the treatment or device or system employed yields an expected overall current value better or higher than the older device governed by the asymptotic survival function (discussed in the Applications section). The appropriateness of the proposed statistical test's application range was properly determined by calculating its test efficiency and critical values and comparing them with other tests, whether in complete or censored data. Finally, we applied this proposed test technique in the manuscript to a different set of real data in both cases. [ABSTRACT FROM AUTHOR]

As a common semiparametric mode, the partially linear additive model has flexible structures, and it has been widely used in practice. In this paper, we study the quantile regression estimation of the model when its responses are censored. In particular, we consider a more general censoring framework, which allows different types of censoring (left, right, double, or interval censoring) simultaneously. Based on the general principles of data augmentation, we propose a unified iterative algorithm, where the censored data is imputed by sampling data from the quantile process, and regression parameters are refitted by using bootstrap samples. Monte Carlo simulations are conducted to verify the finite-sample properties of the method, and the results show its good performance. The application to Boston housing price data further illustrates the advantages of this method in practice. [ABSTRACT FROM AUTHOR]

Despite its drawbacks, the complete case analysis is commonly used in regression models with incomplete covariates. Understanding when the complete case analysis will lead to consistent parameter estimation is vital before use. Our aim here is to demonstrate when a complete case analysis is consistent for randomly right-censored covariates and to discuss the implications of its use even when consistent. Across the censored covariate literature, different assumptions are made to ensure a complete case analysis produces a consistent estimator, which leads to confusion in practice. We make several contributions to dispel this confusion. First, we summarize the language surrounding the assumptions that lead to a consistent complete case estimator. Then, we show a unidirectional hierarchical relationship between these assumptions, which leads us to one sufficient assumption to consider before using a complete case analysis. Lastly, we conduct a simulation study to illustrate the performance of a complete case analysis with a right-censored covariate under different censoring mechanism assumptions, and we demonstrate its use with a Huntington disease data example. [ABSTRACT FROM AUTHOR]

Determining whether a surrogate marker can be used to replace a primary outcome in a clinical study is complex. While many statistical methods have been developed to formally evaluate a surrogate marker, they generally do not provide a way to examine heterogeneity in the utility of a surrogate marker. Similar to treatment effect heterogeneity, where the effect of a treatment varies based on a patient characteristic, heterogeneity in surrogacy means that the strength or utility of the surrogate marker varies based on a patient characteristic. The few methods that have been recently developed to examine such heterogeneity cannot accommodate censored data. Studies with a censored outcome are typically the studies that could most benefit from a surrogate because the follow‐up time is often long. In this paper, we develop a robust nonparametric approach to assess heterogeneity in the utility of a surrogate marker with respect to a baseline variable in a censored time‐to‐event outcome setting. In addition, we propose and evaluate a testing procedure to formally test for heterogeneity at a single time point or across multiple time points simultaneously. Finite sample performance of our estimation and testing procedure are examined in a simulation study. We use our proposed method to investigate the complex relationship between change in fasting plasma glucose, diabetes, and sex hormones using data from the diabetes prevention program study. [ABSTRACT FROM AUTHOR]