Uncensored Data Research Articles

Reliability Analysis for Unknown Age Class of Lifetime Distribution with Real Applications in Medical Science

Analyzing the reliability of the aging class of life distribution provides important information about how long a product lasts and sustainability measures that are essential for determining the environmental impact and formulating resource-saving plans. The study emphasizes the goodness-of-fit technique of the nonparametric test for the NBRUmgf class because age data are crucial for applications. Evaluations were conducted using the test’s asymptotic properties and Pitman efficiency methodology for some selected asymmetric probability models, and the outcomes were compared with those of alternative methods. We assessed the test’s power against widely used reliability distributions for some well-known alternative asymmetric distributions, including the Weibull, Gamma, and linear failure rate (LFR) distributions, and provided percentiles for both censored and uncensored data. This study shows the efficacy of the test in various sectors using real-world datasets and comprehensive tables of test statistics.

Left, Right, Midpoint and Random Point Imputation Techniques for Weibull Regression Model with Right and Interval-Censored Data”

The research explores several imputation techniques, namely left, right, midpoint and random imputations for the MLE of the Weibull regression model with covariate for uncensored, right, and interval-censored data. A simulation study is conducted to obtain the parameter estimates of the model with different imputation techniques, sample sizes, and censoring proportions and its performance are evaluated using bias, standard error (SE), and root mean square error (RMSE). The simulation result indicates that midpoint imputation technique outperformed other techniques based on the lowest RMSE values. Finally, the model was fit to diabetic nephropathy data were fitted to the model using selected imputation techniques. The result concluded that the Weibull regression model may provide a good fit to the data and that the covariate, gender has a significant effect on the survival time of patient kidneys.

Order Statistics and ML Estimators of a 3-Component Mixture of Power Distribution: A Simulation Study

The probability density functions of , and order statistics are explored in this study. Also, the moments, their mean and variance of , and order statistics are derived. The Maximum Likelihood (ML) method is employed to estimate the parameters, and a system of non-linear equations is solved to derive the limiting expressions of the ML estimators and their variances, utilizing Fisher’s information matrix. A detailed numerical analysis of the ML estimators’ performance is carried out through a Monte Carlo simulation for various sample sizes, test termination times, and parameter values. Additionally, the practical applicability of the 3-component mixture of Power distributions is demonstrated by estimating the ML parameters using real-world data. The study's results indicated that maximum likelihood estimators based on complete (uncensored) data perform significantly better than those based on censored data. Additionally, the estimators derived from uncensored data are more dependable and precise.

Data Tells the Truth: A Knowledge Distillation Method for Genomic Survival Analysis by Handling Censoring

Survival analysis is a critical tool for cancer research, yet handling censored data remains challenging due to supervision bias and inaccurate hazard estimates. To address these issues, we propose a simple but effective method termed KD, which employs knowledge distillation using uncensored data to rectify the supervision bias in censored data. This approach leverages the combined power of both rectified censored data and uncensored data to improve survival prediction accuracy. Remarkably, our KD method not only effectively harnesses censored data but also better reflects clinical reality, demonstrating its immense value in survival analysis. We applied our KD method to 19 target cancer sites using The Cancer Genome Atlas (TCGA) dataset. Our results consistently outperform traditional machine learning and deep learning-based methods across both target cancer sites and independent cancer cohorts. More importantly, our data-driven approach enables the model to extract hidden information from censored data, leading to conclusions that align more closely with clinical knowledge and scenarios. This validation of our KD method’s effectiveness highlights the substantial value of rational censored data usage, providing valuable insights for cancer research and clinical decisions. All data and codes are freely available at: https://datatellstruth.github.io/.

Maximal entropy prior for the simple step‐stress accelerated test

AbstractThe step‐stress procedure is a popular accelerated test used to analyze the lifetime of highly reliable components. This paper considers a simple step‐stress accelerated test assuming a cumulative exposure model with uncensored lifetime data following a Weibull distribution. The maximum likelihood approach is often used to analyze accelerated stress test data. Another approach is to use the Bayesian inference, which is useful when there is limited data available. In this paper, the parameters of the model are estimated based on the objective Bayesian viewpoint using non‐informative priors. Our main aim is to propose the maximal data information prior (MDIP) presented by Zellner (1984) as an alternative prior to the conventional independent gamma priors for the unknown parameters, in situations where there is little or no a priori knowledge about the parameters. We also obtain the Bayes estimators based on both classes of priors, assuming three different loss functions: square error loss function (SELF), linear‐exponential loss function (LINEX), and generalized entropy loss function (GELF). The proposed MDIP prior is compared with the gamma priors via Monte Carlo simulations by examining their biases and mean square errors under the three loss functions, and coverage probability. Additionally, we employ the Markov Chain Monte Carlo (MCMC) algorithm to extract characteristics of marginal posterior distributions, such as the Bayes estimator and credible intervals. Finally, a real lifetime data is presented to illustrate the proposed methodology.

Deep Survival Analysis With Latent Clustering and Contrastive Learning.

Survival analysis is employed to analyze the time before the event of interest occurs, which is broadly applied in many fields. The existence of censored data with incomplete supervision information about survival outcomes is one key challenge in survival analysis tasks. Although some progress has been made on this issue recently, the present methods generally treat the instances as separate ones while ignoring their potential correlations, thus rendering unsatisfactory performance. In this study, we propose a novel Deep Survival Analysis model with latent Clustering and Contrastive learning (DSACC). Specifically, we jointly optimize representation learning, latent clustering and survival prediction in a unified framework. In this way, the clusters distribution structure in latent representation space is revealed, and meanwhile the structure of the clusters is well incorporated to improve the ability of survival prediction. Besides, by virtue of the learned clusters, we further propose a contrastive loss function, where the uncensored data in each cluster are set as anchors, and the censored data are treated as positive/negative sample pairs according to whether they belong to the same cluster or not. This design enables the censored data to make full use of the supervision information of the uncensored samples. Through extensive experiments on four popular clinical datasets, we demonstrate that our proposed DSACC achieves advanced performance in terms of both C-index (0.6722, 0.6793, 0.6350, and 0.7943) and Integrated Brier Score (IBS) (0.1616, 0.1826, 0.2028, and 0.1120).

A novel nonparametric time-dependent precision-recall curve estimator for right-censored survival data.

In order to assess prognostic risk for individuals in precision health research, risk prediction models are increasingly used, in which statistical models are used to estimate the risk of future outcomes based on clinical and nonclinical characteristics. The predictive accuracy of a risk score must be assessed before it can be used in routine clinical decision making, where the receiver operator characteristic curves, precision-recall curves, and their corresponding area under the curves are commonly used metrics to evaluate the discriminatory ability of a continuous risk score. Among these the precision-recall curves have been shown to be more informative when dealing with unbalanced biomarker distribution between classes, which is common in rare event, even though except one, all existing methods are proposed for classic uncensored data. This paper is therefore to propose a novel nonparametric estimation approach for the time-dependent precision-recall curve and its associated area under the curve for right-censored data. A simulation is conducted to show the better finite sample property of the proposed estimator over the existing method and a real-world data from primary biliary cirrhosis trial is used to demonstrate the practical applicability of the proposedestimator.

The New Odd Burr III -G power series class of distributions: properties and applications to censored and uncensored data

The New Odd Burr III -G power series class of distributions: properties and applications to censored and uncensored data

CenTime: Event-conditional modelling of censoring in survival analysis

Survival analysis is a valuable tool for estimating the time until specific events, such as death or cancer recurrence, based on baseline observations. This is particularly useful in healthcare to prognostically predict clinically important events based on patient data. However, existing approaches often have limitations; some focus only on ranking patients by survivability, neglecting to estimate the actual event time, while others treat the problem as a classification task, ignoring the inherent time-ordered structure of the events. Additionally, the effective utilisation of censored samples−data points where the event time is unknown− is essential for enhancing the model’s predictive accuracy. In this paper, we introduce CenTime, a novel approach to survival analysis that directly estimates the time to event. Our method features an innovative event-conditional censoring mechanism that performs robustly even when uncensored data is scarce. We demonstrate that our approach forms a consistent estimator for the event model parameters, even in the absence of uncensored data. Furthermore, CenTime is easily integrated with deep learning models with no restrictions on batch size or the number of uncensored samples. We compare our approach to standard survival analysis methods, including the Cox proportional-hazard model and DeepHit. Our results indicate that CenTime offers state-of-the-art performance in predicting time-to-death while maintaining comparable ranking performance. Our implementation is publicly available at https://github.com/ahmedhshahin/CenTime.

A new non-parametric hypothesis testing with reliability analysis applications to model some real data

Due to the essential necessities of current technology and contemporary sciences, a methodical approach to investigating every occurrence or action occurring in the world was required. As a result, it makes sense that such an approach would be required in the investigation of the reliability of technological systems and products. In actuality, there are instances when system parts gradually deteriorate over time t, at which point the system needs to be updated by replacing the spare parts. Although renewal tries to improve system usability, it is unable to restore the system to its prior state. We discovered that an entirely novel domain of reliability known as classes of life distributions has emerged as a result of the growth of criteria for determining the success or failure of dependability over the previous few decades. Moreover, the other nonparametric tests of life distribution lack test efficiency and have low test power. On the other hand, based on that approach, the non-parametric statistical test utilized in this study evaluates different types of treatment by examining failure behavior in the survival data that was collected. As a result, in this ivestigation, we have developed a novel test of life distribution in this study that considers the power and effectiveness of the test. In order to compare data belonging to the harmonic new better than used in expectation (HNBUE) class with data that follow an exponential distribution, this article suggests nonparametric tests for both censored and uncensored data. The higher percentile points of the test statistics are collected, and the suggested test's normality is verified. The Pitman asymptotic relative efficiency (PARE) and powers of proposed test are calculated a few well-known alternative asymmetric models. Three asymmetric real-world data sets are examined to demonstrate the paper's findings.

Manual censoring of impedance tracings by the Wingate consensus reduces the number of impedance episodes, impacting on reflux categorization.

The Lyon consensus classifies the evidence of gastroesophageal reflux (GERD) based on endoscopic features and results of pH/impedance monitoring (pH-MII) including the post-reflux swallow-induced peristaltic wave index (PSPWI) and mean nocturnal baseline impedance (MNBI). The Wingate consensus established criteria to reduce inter-reviewer variability when assessing reflux episodes and PSPWI by impedance. This study aims to assess the influence of the Wingate criteria on the different pH-MII parameters obtained by automated analysis. Thirty consecutive pH-MII off PPI were reviewed according to Wingate criteria. Number of impedance episodes and PSPWI were compared before and after censoring from automatic analysis. Reflux categorization according to Lyon consensus between censored and uncensored data was compared. Pearson correlations between impedance parameters and censored episodes were calculated. Censoring the tracings significantly reduced the number of reflux episodes (66 [42-90.25] vs. 44.5 [21.5-61.5], p = 0.0105). Reasons for censoring were as follows: 1/ anterograde episode: 9.5 [6-13], 2/ impedance drop <50%: 1 [0-3], 3/ duration <4 s: 1 [0-2], 4/ <2 distal channels: 2.5 [1-4], and 5/ artifacts: 2 [1-5]. Censored episodes were in majority non-acid (16.5 [13-26.5] vs. 2 [0-4], p < 0.00001). Censoring altered the categorization of impedance episodes (<40 episodes, 6 vs. 13 for resp. uncensored vs. censored tracings, 40-80 episodes: 13 vs. 13, and >80 episodes: 11 vs. 4, p = 0.0264), but not the symptom index, the symptom association probability, or the categorization according to the Lyon consensus. Nevertheless, individual tracings were affected. The percentage of censored episodes was inversely correlated with the number of acidic impedance episodes (r = -0.62, p = 0.0002). Manual interpretation of impedance tracings based on the Wingate consensus reduces the number of impedance episodes, impacting on reflux categorization. Acidic reflux episodes are less likely to be censored, harboring a potential at improving automatic pH-MII analysis.

Impact of Inbreeding and Ancestral Inbreeding on Longevity Traits in German Brown Cows.

A recent study on the population structure of the German Brown population found increasing levels of classical and ancestral inbreeding coefficients. Thus, the aim of this study was to determine the effects of inbreeding depression and purging on longevity traits using classical and ancestral inbreeding coefficients according to Kalinowski (2002) (Fa_Kal, FNew), Ballou (1997) (Fa_Bal), and Baumung (2015) (Ahc). For this purpose, uncensored data of 480,440 cows born between 1990 and 2001 were available. We analyzed 17 longevity traits, including herd life, length of productive life, number of calvings, lifetime and effective lifetime production for milk, fat, and protein yield, the survival to the 2nd, 4th, 6th, 8th, and 10th lactation number, and the culling frequencies due to infertility, or udder and foot and leg problems. Inbreeding depression was significant and negative for all traits but for culling due to udder and to foot and leg problems. When expressed in percentages of genetic standard deviations, inbreeding depression per 1% increase in inbreeding was -3.61 to -10.98%, -2.42 to -2.99%, -2.21 to -4.58%, and 5.13% for lifetime production traits, lifetime traits, survival rates, and culling due to infertility, respectively. Heterosis and recombination effects due to US Brown Swiss genes were positive and counteracted inbreeding depression. The effects of FNew were not significantly different from zero, while Fa_Kal had negative effects on lifetime and lifetime production traits. Similarly, the interaction of F with Fa_Bal was significantly negative. Thus, purging effects could not be shown for longevity traits in German Brown. A possible explanation may be seen in the breed history of the German Brown, that through the introgression of US Brown Swiss bulls ancestral inbreeding increased and longevity decreased. Our results show, that reducing a further increase in inbreeding in mating plans is advisable to prevent a further decline in longevity due to inbreeding depression, as purging effects were very unlikely in this population.

Model checks for two-sample location-scale

Two-sample location-scale refers to a model that permits a pair of standardised random variables to have a common base distribution. Function-based hypothesis testing in these models refers to formal tests based on distributions functions, or direct transformations thereof, that would help decide whether or not two samples come from some location-scale family of distributions. For uncensored data, an approach of testing based on plug-in empirical likelihood (PEL) is carried out with sample means and standard deviations as the plug-ins. The method extends to censored data, where censoring adjusted moment estimators provide the requisite plug-ins. The large sample null distribution of the PEL statistic is derived. Since it is not distribution free, a two-sample location-scale appropriate resampling is employed to obtain thresholds needed for the testing. Numerical studies are carried out to investigate the performance of the proposed method. Real examples are presented for both the uncensored and censored cases.

Sea turtle egg yolk and albumen as biomonitoring matrices for maternal burdens of organic pollutants

To establish the use of eggs as biomonitoring tools for maternal body burdens, we investigated the mother-to-egg ratio of 56 PCB, 12 OCP and 34 PBDE unique compounds from maternal plasma into replicate egg yolk and albumen samples in the loggerhead turtle (Caretta caretta) as a case study of a threatened migratory marine species. We applied robust Regression on Order Statistics to fully account for the information in both censored and uncensored data. Our results added new insights into the use of yolk as a suitable biomonitoring matrix; the difference between yolk and albumen which were previously analysed as a homogeneous mixture; and the value of accounting for censored data. Overall, compound-specific mother-to-egg ratios need to be considered when translating yolk levels back to maternal pollution burdens, and when assessing the risk to the subsequent generations of turtle embryos.

The NBRULC Reliability Class: Mathematical Theory and Goodness-of-Fit Testing with Applications to Asymmetric Censored and Uncensored Data

The majority of approaches proposed in the past few decades to solve life test problems have differed markedly from those used for closely related, yet broader, issues. Due to the complexity of data that are generated each day in many practical domains, as a result of the development of scales for rating the success or failure of reliability, a new domain of reliability has been created. This domain is referred to as life classes, where specific probability distributions are presented. In this study, it is shown that the use of the quality-of-fit technique to solve problems involving life testing makes sense, and produces simpler processes that are roughly equivalent or superior to those used in traditional procedures. They may also behave better in limited samples. This work investigates a novel quality-of-fit test statistic; it is based on an exponential transform and is compared to the best renewal used Laplace test in increasing convex ordering (NBRULC). Evidence for approach normality is provided. The calculated variables include powers, Pitman asymptotic effectiveness, and critical points. Methods on how to handle censored data were also studied. Our experiments have real-world applications in the fields of medicine and engineering.

A New Right-Skewed One-Parameter Distribution with Mathematical Characterizations, Distributional Validation, and Actuarial Risk Analysis, with Applications

Skewed probability distributions are important when modeling skewed data sets because they provide a way to describe the shape of the distribution and estimate the likelihood of extreme events. Asymmetric probability distributions have the potential to handle and assess problems in actuarial risk assessment and analysis. To that end, we present a new right-skewed one-parameter distribution. In this work and for this purpose, a right-skewed probability distribution was derived and analyzed. The new distribution outperformed the exponential distribution, the Pareto distribution, the Chen distribution, and others in the field of actuarial risk analysis. Some useful key risk indicators are considered and analyzed to analyze the risks and for comparison with the competitive model. Several actuarial risk functions and indicators are evaluated and analyzed using the U.K. insurance claims data set. The process of risk assessment and analysis was carried out using a comprehensive simulation. For the purposes of distributional validity, a modified chi-squared type test is presented and employed in the testing process. The new, modified chi-squared type test that is used is simply an extension of the Rao–Robson–Nikulin test. In this work, the distributional validity is presented and analyzed under right-skewed censored and uncensored data sets.

MSMpred: interactive modelling and prediction of individual evolution via multistate models

BackgroundModelling the course of a disease regarding severe events and identifying prognostic factors is of great clinical relevance. Multistate models (MSM) can be used to describe diseases or processes that change over time using different states and the transitions between them. Specifically, they are useful to analyse a disease with an increasing degree of severity, that may precede death. The complexity of these models changes depending on the number of states and transitions taken into account. Due to that, a web tool has been developed making easier to work with those models.ResultsMSMpred is a web tool created with the shiny R package that has two main features: 1) to allow to fit a MSM from specific data; 2) to predict the clinical evolution for a given subject. To fit the model, the data to be analysed must be upload in a prespecified format. Then, the user has to define the states and transitions as well as the covariates (e.g., age or gender) involved in each transition. From this information, the app returns histograms or barplots, as appropriate, to represent the distributions of the selected covariates and boxplots to show the patient’ length of stay (for uncensored data) in each state. To make predictions, the values of selected covariates from a new subject at baseline has to be provided. From these inputs, the app provides some indicators of the subject’s evolution such as the probability of 30-day death or the most likely state at a fixed time. Furthermore, visual representations (e.g., the stacked transition probabilities plot) are given to make predictions more understandable.ConclusionsMSMpred is an intuitive and visual app that eases the work of biostatisticians and facilitates to the medical personnel the interpretation of MSMs.

Reliability Class Testing and Hypothesis Specification: NBRULC−t∘ Characterizations with Applications for Medical and Engineering Data Modeling

Due to the complexity of the data being generated day in and day out in many practical domains, as a result of the development of scales for rating the success or failure of reliability, a new domain of reliability called the classes of life and determinant probability distributions has been presented. This article introduces novel statistical probability models for the reliability class of life test under different reliability processes in the age range t∘. Several probabilistic properties and features were derived and rigorously screened to test the new reliability class. According to the U-statistic, a novel hypothesis test was created to evaluate the exponentiality property. The comparative efficiency of the test according to Pitman’s asymptotic efficiency was examined and compared with other reliability classes. To prove the superiority of the new reliability class, some probability models were utilized, including the Weibull, Makeham, gamma, and linear failure rate models. Moreover, critical point simulations of the null Monte Carlo distribution and some applications of the censored and uncensored data were implemented to validate the class test listed by the reliability analysis.

DAmcqrnn: An approach to censored monotone composite quantile regression neural network estimation

Quantile regression neural network (QRNN) model has recently become popular in solving complex nonlinear problems, but the quantile curves achieved by QRNN model may cross each other, leading to unreliable results. To remedy this defect, monotone composite quantile regression neural network (MCQRNN) model is more attractive with non-crossing quantile predictions. However, few works have been involved in the literature to apply MCQRNN model for censoring issues. Based on the data augmentation algorithm, this study presents an iterative estimation method, which is a three-step alternating process, for censored MCQRNN model. Step 1 imputes the censored data through a data augmentation procedure. Step 2 updates the MCQRNN model with the imputed data. Step 3 makes predictions by the updated MCQRNN model. Simulation studies and real data application demonstrate that our proposed method is not only superior to the available censored methods with respect to quantile loss and C-index, but also yields very close prediction results to those obtained by full uncensored data. Avoiding the quantile crossing problem, the proposed method is more flexible to cope with different types of censoring, overcoming the limitation that the existing censored methods only work for single censoring type with unbelievable predictions caused by the crossing phenomenon.

A New Reliability Class-Test Statistic for Life Distributions under Convolution, Mixture and Homogeneous Shock Model: Characterizations and Applications in Engineering and Medical Fields

Over the past few decades, a new area of reliability known as classes of life distributions has developed as a result of the creation of metrics for evaluating the success or failure of reliability. This paper proposes a new reliability class-test statistic for life distributions. In some reliability processes, such as convolution, mixture, and homogeneous shock models, the closure characteristics of the proposed class-test statistic are investigated. To compare the proposed class-test against some competitive tests, the Weibull, linear failure rate (LFR), and Makeham distributions are evaluated. In addition, the relationship between sample size, level of confidence, and critical values is considered to assess the efficacy of the proposed class-test. Furthermore, a Monte Carlo null distribution critical points simulation and some applications of the censored and uncensored data are performed to demonstrate the validity of the proposed class-test in reliability analysis.