Censored Data Research Articles

SurvLoss: A New Survival Loss Function for Neural Networks to Process Censored Data

SurvLoss: A New Survival Loss Function for Neural Networks to Process Censored Data

Fuzzy Evaluation Model for Lifetime Performance Using Type-I Censoring Data

As global warming becomes increasingly serious, humans start to consider how to coexist with the natural environment. People become more and more aware of environmental protection and sustainable development. Therefore, in the pursuit of economic growth, it has become a consensus that enterprises should be responsible for the social and ecological environment. Regarding the manufacturing of electronic devices, as long as both component production quality and assembly quality are ensured, consumers can be provided with high-quality, safe, and efficient products. In light of this trend, enhancing product availability and reliability can reduce costs and carbon emissions resulting from repairing or replacing components, thus becoming a vital factor for corporate and environmental sustainability. Accordingly, enterprises enhance their economic benefits as well as have the effects of energy conservation and waste reduction by extending products’ service lifetime and increasing their added value. According to several studies, it takes a long time to retrieve electronic products’ lifetime data. Moreover, acquiring complete samples is often challenging. Consequently, when analyzing real cases, samples are usually collected using censoring techniques. The type-I right censoring data is suitable for industrial processes. Thus, this study utilized type-I right censoring sample data to estimate the lifetime performance index. It usually takes a large amount of time to access lifetime data for electronic products and it is often impossible to obtain complete samples since the size of the sample is usually small. Hence, to avoid misjudgment caused by sampling errors, this study followed suggestions from existing research and applied fuzzy tests built on confidence intervals to establish a fuzzy evaluation model for the lifetime performance index. This model helps relevant electronic industries not only evaluate the lifetime of their electronic components but also instantly seize opportunities for improvement.

Parameter estimation of Chen distribution under improved adaptive type-II progressive censoring

ABSTRACT This study focuses on the estimation of the two unknown parameters of Chen distribution, characterized by a bathtub-shaped hazard rate function, within an improved adaptive type-II progressive censored data framework. Maximum likelihood estimation is proposed for the two parameters, and the establishment of approximate confidence intervals is based on asymptotic normality. Bayesian estimation is also conducted under both symmetric and asymmetric loss functions, utilizing the proposed importance sampling and Metropolis–Hastings algorithm. Lastly, the performance of various estimation methods is evaluated through Monte Carlo simulation experiments, and the proposed estimation approach is illustrated using a real dataset.

Advancing Bayesian Inference: Fitting Type I Half-logistic Nadarajah-Haghighi Distribution and its Comparison with Related Distributions for Censored Survival Data

In recent years, the field of Bayesian modeling of generalized distributions has garnered substantial attention. This surge in interest can be attributed to the remarkable strides made in computational capabilities and the enhanced accessibility of sophisticated software tools. This study aims to apply Bayesian inference methods to the Type I Half-logistic Nadarajah- Haghighi model and compares it with the Exponential model and the Type I Half-logistic Exponential model. These distributions are analyzed and fitted to censored survival data using the probabilistic programming language STAN. To incorporate censored mechanisms within the STAN framework, customized codes are developed. The models are then compared using fully Bayesian model selection methods.. KEYWORDS :Censored data, Nadarajah-Haghighi distribution, Type I half-logistic family, LOOIC, WAIC, STAN.

Analysis of a new extension version of the exponential model using improved adaptive progressive censored data and its applications

This article covers the issue of evaluating the two shape parameters and reliability metrics of a novel Kumaraswamy-exponential lifetime distribution, whose density exhibits a left-skewed, right-skewed, or symmetric shape, through a type-II improved adaptive progressively censored sample. Both conventional and Bayesian viewpoints are used to evaluate the various parameters, which include point and interval estimations. While the estimation of one of the shape parameters requires a numerical solution, the other shape parameter estimation can be carried out in closed form by the classical method. Besides, the likelihood method’s asymptotic traits are employed to provide interval estimations for all parameters. Leveraging the Markov chain Monte Carlo process, the symmetric squared loss function and independent gamma priors are taken into account for calculating Bayes points and the highest posterior density interval estimations. To illustrate the accuracy, compare estimation methods, and show the applicability of the various suggested methods, a simulation examination and a pair of applications are looked at. In the end, four accuracy indicators are taken into consideration to figure out the best progressive censoring pattern. The numerical results indicate that when collecting samples using the suggested censored procedure, it is advisable to use the Bayesian estimation approach for evaluating the Kumaraswamy-exponential distribution.

On Modi-Exponential Distribution under Conventional Type-I and Type-II Censoring

In this article, a new Modi-Exponential distribution is considered under Type-I and Type-II censoring. Some statistical and reliability characteristics of the distribution are specified. Statistical inferences of the Modi-Exponential parameters based on Type-I and Type-II censored data are discussed. The maximum likelihood estimation method is used for estimation of unknown parameters along with reliability characteristics. Asymptotic confidence intervals are also obtained for interval estimation. Monte-Carlo Simulation study is performed to study the performances of estimators. Further, two real data sets are provided to illustrate the results.. KEYWORDS :Censoring, Maximum likelihood estimation, Confidence bounds, Simulation.

Assessing heterogeneity in surrogacy using censored data.

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.

Statistical Inference Using Partially Accelerated Life Test Model for the Weibull Population Mean Unified Hybrid Censored Data

In this paper, estimates of the parameters and the acceleration factor of a new distribution known as the Weibull Population Mean Distribution (WPMD) are explored. We propose the use of the model suggested by Abd-Elrahman [A better alternative to the generalized Bilal distribution: A new model and applications, Int. J. Reliab. Qual. Saf. Eng. 30(6) (2023) 2350027, doi: 10.1142/S0218539323500274] for estimating these parameters. To accomplish this, we employ the maximum likelihood estimation method via a Constant-Stress Partially Accelerated Life Test (CSPALT) model. In this study, we have utilized Unified Hybrid (UH) censored data obtained from the WPMD. Confidence intervals for the model parameters and the acceleration factor are constructed based on the approximate Fisher information matrix. The average and Mean Squared Error (MSE) of estimates are computed to evaluate the performance of the proposed method under the CSPALT model. Additionally, a real data set is provided for illustrative purposes, and a numerical analysis of the UH Censoring Scheme (UHCS) is carried out. Finally, concluding remarks are presented.

ECG-surv: A deep learning-based model to predict time to 1-year mortality from 12-lead electrocardiogram

Electrocardiogram (ECG) abnormalities have demonstrated potential as prognostic indicators of patient survival. However, the traditional statistical approach is constrained by structured data input, limiting its ability to fully leverage the predictive value of ECG data in prognostic modeling. This study aims to introduce and evaluate a deep-learning model to simultaneously handle censored data and unstructured ECG data for survival analysis. We herein introduce a novel deep neural network called ECG-surv, which includes a feature extraction neural network and a time-to-event analysis neural network. The proposed model is specifically designed to predict the time to 1-year mortality by extracting and analyzing unique features from 12-lead ECG data. ECG-surv was evaluated using both an independent test set and an external set, which were collected using different ECG devices. The performance of ECG-surv surpassed that of the Cox proportional model, which included demographics and ECG waveform parameters, in predicting 1-year all-cause mortality, with a significantly higher concordance index (C-index) in ECG-surv than in the Cox model using both the independent test set (0.860 [95% CI: 0.859- 0.861] vs. 0.796 [95% CI: 0.791- 0.800]) and the external test set (0.813 [95% CI: 0.807- 0.814] vs. 0.764 [95% CI: 0.755- 0.770]). ECG-surv also demonstrated exceptional predictive ability for cardiovascular death (C-index of 0.891 [95% CI: 0.890- 0.893]), outperforming the Framingham risk Cox model (C-index of 0.734 [95% CI: 0.715-0.752]). ECG-surv effectively utilized unstructured ECG data in a survival analysis. It outperformed traditional statistical approaches in predicting 1-year all-cause mortality and cardiovascular death, which makes it a valuable tool for predicting patient survival.

Empirical likelihood MLE for joint modeling right censored survival data with longitudinal covariates

Empirical likelihood MLE for joint modeling right censored survival data with longitudinal covariates

Bayesian extension of the Weibull AFT shared frailty model with generalized family of distributions for enhanced survival analysis using censored data

ABSTRACT 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.

Structure of hybrid censoring schemes and its implications

AbstractIn this paper, structural properties of (progressive) hybrid censoring schemes are established by studying the possible data scenarios resulting from the hybrid censoring scheme. The results illustrate that the distributions of hybrid censored random variables can be immediately derived from the cases of Type-I and Type-II censored data. Furthermore, it turns out that results in likelihood and Bayesian inference are also obtained directly which explains the similarities present in the probabilistic and statistical analysis of these censoring schemes. The power of the approach is illustrated by applying the approach to the quite complex unified Type-II (progressive) hybrid censoring scheme. Finally, it is shown that the approach is not restricted to (progressively Type-II censored) order statistics and that it can be extended to almost any kind of ordered data.

Analysis of generalized type-II progressively hybrid Lindley-exponential data and its modeling in physics, engineering, and management

The life test is guaranteed to end at a predetermined time using a novel type-II generalized progressively hybrid censoring method that is investigated when the test participants’ lifetime model has a two-parameter Lindley-exponential (LndE) distribution. The LndE characteristics are estimated using Bayes and maximum likelihood inference techniques when the suggested censored data are present. By employing the normal approximation of each unknown quantity, the estimated confidence intervals are also constructed. Additionally, independent gamma density priors are used to generate the Bayesian estimators under symmetrical (squared error) loss. Since the likelihood function is formulated in a difficult manner, the Bayes estimators and their corresponding greatest posterior density intervals cannot be computed theoretically, but they may be evaluated using Markov-chain Monte Carlo algorithms. The most progressive design is then determined by applying four optimality criteria. Using Monte Carlo comparisons, the efficiency of the proposed estimating processes is evaluated, and some suggestions are made. In the end, the usefulness of the suggested methods that may be applied in practical situations is demonstrated by analyzing three distinct applications: physics, engineering, and management. When the experimenter’s primary concern is the test’s duration, the numerical findings revealed that the sampling strategy is adaptable and incredibly successful in finishing the experiment in a variety of realistic scenarios.

Variable selection and subgroup analysis for high-dimensional censored data

This paper proposes a penalized method for high-dimensional variable selection and subgroup identification in the Tobit model. Based on Olsen's [(1978). Note on the uniqueness of the maximum likelihood estimator for the Tobit model. Econometrica: Journal of the Econometric Society, 46(5), 1211–1215. https://doi.org/10.2307/1911445] convex reparameterization of the Tobit negative log-likelihood, we develop an efficient algorithm for minimizing the objective function by combining the alternating direction method of multipliers (ADMM) and generalised coordinate descent (GCD). We also establish the oracle properties of our proposed estimator under some mild regularity conditions. Furthermore, extensive simulations and an empirical data study are conducted to demonstrate the performance of the proposed approach.

Model averaging for right censored data with measurement error.

This paper studies a novel model averaging estimation issue for linear regression models when the responses are right censored and the covariates are measured with error. A novel weighted Mallows-type criterion is proposed for the considered issue by introducing multiple candidate models. The weight vector for model averaging is selected by minimizing the proposed criterion. Under some regularity conditions, the asymptotic optimality of the selected weight vector is established in terms of its ability to achieve the lowest squared loss asymptotically. Simulation results show that the proposed method is superior to the other existing related methods. A real data example is provided to supplement the actual performance.

Advancements in Laplace transform techniques: Performing non-parametric hypothesis testing on real-world data through statistical analysis

This research delves into the exploration of a statistical testing approach grounded in Laplace transform techniques specifically tailored for the New Better than Used Laplace transform order (NBUL) class of life distributions. The developed test exhibits versatility, accommodating both complete and censored data, and critical values are systematically calculated for its application. Beyond the methodological presentation, our study investigates the test’s statistical power and explores Pitman’s asymptotic efficiency concerning various alternative distributions. Comparative analyses with other tests within the same class contribute to a comprehensive understanding of the proposed approach. To demonstrate practical applicability, we apply this novel testing technique to authentic engineering and medical datasets. The outcomes of these applications serve as illustrative examples, showcasing the effectiveness and relevance of the proposed methodology in real-world scenarios.

Modeling arsenic in European topsoils with a coupled semiparametric (GAMLSS-RF) model for censored data

Arsenic (As) is a versatile heavy metalloid trace element extensively used in industrial applications. As is carcinogen, poses health risks through both inhalation and ingestion, and is associated with an increased risk of liver, kidney, lung, and bladder tumors. In the agricultural context, the repeated application of arsenical products leads to elevated soil concentrations, which are also affected by environmental and management variables. Since exposure to As poses risks, effective assessment tools to support environmental and health policies are needed. However, the most comprehensive soil As data available, the Land Use/Cover Area frame statistical Survey (LUCAS) database, contains severe limitations due to high detection limits. Although within International Organization for Standardization standards, the detection limits preclude the adoption of standard methodologies for data analysis. The present work focused on developing a new method to model As contamination in European soils using LUCAS soil samples. We introduce the GAMLSS-RF model, a novel approach that couples Random Forests with Generalized Additive Models for Location, Scale, and Shape. The semiparametric model can capture non-linear interactions among input variables while accommodating censored and non-censored observations and can be calibrated to include information from other campaign databases. After fitting and validating a spatial model, we produced European-scale As concentration maps at a 250 m spatial resolution and evaluated the patterns against reference values (i.e., two action levels and a background concentration). We found a significant variability of As concentration across the continent, with lower concentrations in Northern countries and higher concentrations in Portugal, Spain, Austria, France and Belgium. By overcoming limitations in existing databases and methodologies, the present approach provides an alternative way to handle highly censored data. The model also consists of a valuable probabilistic tool for assessing As contamination risks in soils, contributing to informed policy-making for environmental and health protection.

Classical and Bayesian inference of inverted modified Lindley distribution based on progressive type-II censoring for modeling engineering data

This paper investigates statistical inferences for product lifetimes following the inverted modified Lindley distribution, utilizing progressive Type-II censored data. The estimation of model parameters employs the maximum likelihood method, complemented by the construction of approximate confidence intervals. Bayesian estimates are also explored, incorporating squared error and linear exponential loss functions with noninformative priors. To approximate Bayes estimates, the proposal presents Gibbs sampling based on the MCMC algorithm. This results in the generation of the greatest posterior density credible intervals for the parameters. A real data analysis is conducted to validate the accuracy of all the models and methods discussed. Finally, computational studies using Monte Carlo simulations are presented to compare the suggested estimators.

County‐Level Evaluation of Large‐Scale Gridded Data Sets of Irrigated Area Over China

AbstractThe reliability of irrigated area (IA) information dominates the performance of irrigation water use and crop modeling accuracy. IA is typically mapped using Food and Agriculture Organization (FAO) agricultural census and remote sensing indices. Recent advances in machine learning and sampling techniques further improve IA mapping. However, the relative performances of different IA mapping approaches and their capability in capturing long‐term IA temporal variability remain unknown. Here, 1861 county‐level IA information from Government Censored Data (GCD) during 2000–2021 are collected, cross‐validated, and employed to evaluate commonly used gridded IA data sets. Results show that IA data sets based on the direct interpolation of FAO agricultural census can accurately capture the spatial distribution of IA. However, FAO statistics are only available in a particular year, which cannot capture inter‐annual irrigation variations. In contrast, IA products solely based on vegetation indices are prone to positive biases over humid regions due to the lack of contrast in vegetation dynamics. Overall, the latest GCD‐based machine learning IA data sets are relatively more accurate, but they are also problematic in estimating IA trends due to the use of temporally static training samples. Such biases are tightly related to agricultural suitability (AS calculated using precipitation and potential evapotranspiration). This suggests that AS should be employed as an endogenous variable in future machine learning based IA mapping algorithms.

Nonparametric density estimation over its unknown support for right censored data

The long-standing problem of nonparametric density estimation of the lifetime of interest over its unknown support, when only right-censored observations are available, is considered. Two cases, when the support of the lifetime of interest is a proper subset of the support of censoring variable and when the supports are the same, are explored. An orthogonal series density estimation, over a random interval defined by a specially chosen sequence of order statistics, is proposed and rates of the mean integrated squared error convergence are evaluated.