censored data modeling

This study addresses the challenge of accurately estimating relative variability—such as the coefficient of variation—for the power Lindley distribution under progressive Type-I interval censoring. It presents the first systematic investigation of estimation methods in this setting, integrating both frequentist and Bayesian paradigms. The proposed frequentist approaches include point estimators based on midpoint approximation, maximum likelihood, method of moments, nonlinear least squares, and Bootstrap resampling, along with asymptotic and Bootstrap confidence intervals. Bayesian inference is implemented via slice sampling for posterior analysis. Extensive simulations and a real-data application demonstrate that the proposed methods are effective and feasible, with the Bayesian approach consistently yielding superior estimation accuracy and stability across various censoring schemes and sample sizes, while also offering guidance for optimal inspection interval design.

This study addresses the challenge of quantifying uncertainty in survival analysis arising from censored data, small sample sizes, and population heterogeneity. The authors propose a model-agnostic Bayesian framework that circumvents reliance on a full likelihood specification and avoids sensitivity to parametric distributional assumptions. The approach integrates Bayesian bootstrapping with generalized Bayesian (Gibbs) posterior updating: nonparametric survival estimates are generated via Dirichlet-weighted resampling to capture sampling uncertainty, while prior information is incorporated through a loss-based updating rule to yield robust posterior inference. The framework is compatible with the Cox proportional hazards model, preserving the interpretability of hazard ratios. Simulation studies and real-data applications demonstrate its ability to effectively quantify uncertainty and flexibly leverage prior knowledge. An accompanying open-source R package, BayesBoots, has been released.

To address substantial bias in survival estimation and challenges in uncertainty quantification for interval-censored data, this paper proposes a hierarchical Bayesian modeling framework. First, an unbiased nonparametric survival distribution is recovered via the EM algorithm, benchmarked against the Turnbull NPMLE. Second, interpretable accelerated failure time (AFT) models—specifically Weibull or log-normal—are constructed, incorporating interval-censored likelihoods for covariate-adjusted prediction. Third, posterior uncertainty calibration, model comparison, and selection are jointly performed within a unified Bayesian framework. The method innovatively integrates EM-based initialization with Bayesian AFT inference, enabling simultaneous shape discovery, predictive optimization, and model evaluation. Simulation studies and analysis of ovarian cancer data demonstrate that the approach achieves minimal distribution recovery error, substantially improves predictive accuracy under correctly specified AFT models, yields well-calibrated uncertainty estimates via Bayesian inference, and supports robust model selection through Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO).

This study addresses the challenging problem of parameter estimation in generalized linear models with interval-censored covariates—a common yet methodologically underdeveloped issue in biomedical research. The authors propose GELc, a novel likelihood-based semiparametric approach that, for the first time, integrates an augmented Turnbull nonparametric estimator into the generalized linear modeling framework. By combining maximum likelihood estimation with asymptotic theory, the method establishes estimators that are consistent and asymptotically normal, enabling valid standard error computation. Extensive simulations demonstrate favorable finite-sample performance, with confidence intervals achieving nominal coverage rates. The practical utility of GELc is further confirmed through two real-data applications. The proposed methodology is publicly available as the R package ICenCov.

This study addresses the lack of exact inferential methods for reliability analysis of lifetime distributions—such as the Weibull and log-logistic—under Type-I censoring or small-sample settings. The authors propose a novel framework for exact parametric inference based on survival function reconstruction, overcoming limitations of conventional approaches that rely on asymptotic approximations or bootstrap techniques. For the first time, this method enables exact hypothesis testing and confidence interval construction for Type-I censored data across several widely used lifetime distributions. Extensive simulations demonstrate that the proposed approach substantially outperforms existing methods in both complete and censored data scenarios. Its practical utility is further corroborated through two real-world engineering case studies.

This study addresses the challenges posed by interval-censored data and the sensitivity of conventional maximum likelihood estimation to outliers in cyclic accelerated life testing (CyALT). Under the assumption that product lifetimes follow a log-normal distribution, the authors propose a robust inference method based on the weighted minimum density power divergence estimator (WMDPDE). The proposed approach achieves both high statistical efficiency and strong resistance to contamination. Notably, this work establishes the asymptotic theory and influence function of WMDPDE within the CyALT framework for the first time. Simulation studies demonstrate that WMDPDE substantially outperforms traditional methods in the presence of outliers while retaining high efficiency under clean data conditions. The practical applicability and robustness of the method are further confirmed through analysis of real-world air conditioner reliability data.

This study addresses a key limitation in traditional step-stress accelerated life testing (ALT) models, which assume product homogeneity and thus fail to capture heterogeneous aging behaviors that may emerge under high stress. The authors propose a hazard-rate-based heterogeneous step-stress ALT model that retains the homogeneity assumption at the initial stress level but introduces a finite mixture model at the second stress level to represent m latent subpopulations with distinct failure mechanisms. Parameter estimation under Type-II censoring is handled via the EM algorithm. Notably, this approach is the first to embed a finite mixture model within a hazard-rate framework, establishing an interpretable paradigm for heterogeneity modeling. The model rigorously reduces to the existing exponential heterogeneous model when the Weibull shape parameter equals one, confirming its theoretical generalizability. Simulations demonstrate that neglecting heterogeneity induces substantial bias in lifetime predictions across all quantiles, particularly at early failure quantiles.

This study addresses the challenge of stress-strength reliability assessment for multi-component systems under progressive Type-II censoring by developing a unified inferential framework that integrates maximum likelihood estimation, maximum product spacing, and Bayesian methods under the assumption of unit generalized Rayleigh distributions. The work innovatively proposes an optimal progressive censoring scheme based on three optimality criteria and enhances estimation accuracy through the synergistic use of the EM algorithm, Fisher information matrix, missing information principle, Markov chain Monte Carlo (MCMC) techniques, and optimal experimental design. Extensive simulation studies and real-data analysis demonstrate that the proposed methodology yields highly accurate reliability estimates and credible/confidence intervals while effectively identifying efficient censoring plans.

This study addresses the lack of a unified and interpretable modal regression framework for right-censored positive responses by proposing a parametric modal regression approach applicable to continuous positive distributions—namely Gamma, Beta, Weibull, Lognormal, and Inverse Gaussian. By analytically reparameterizing the density parameters as explicit functions of the conditional mode and integrating the censored log-likelihood for maximum likelihood estimation, the method establishes, for the first time, a closed-form mapping between the mode and a linear predictor under these distributions. The framework enables direct modeling of the conditional mode and facilitates asymptotic inference via the Fisher information matrix. Simulations confirm consistent parameter estimation, with bias and RMSE decreasing as sample size increases, and Wald confidence intervals achieving nominal coverage. The approach is successfully applied to real-world reliability data, and an accompanying R package, ModalCens, is made publicly available.

This study addresses the low power and poor stability of conventional Wald-type tests for interval-censored data in small-sample settings by proposing the first likelihood ratio test framework based on spline sieves. The method integrates spline sieve modeling with likelihood ratio testing and rigorously derives its asymptotic distribution, ensuring both theoretical validity and practical robustness. Simulation studies demonstrate that the proposed approach substantially improves statistical power while maintaining proper control of Type I error rates. Its applicability and advantages are further confirmed through analysis of real clinical data.