Censored Observations Research Articles

Confidence interval estimation for reliability of a two parameter Weibull distribution under complete and censored samples

Estimating the reliability function of the two parameter Weibull distribution is a critical task in various fields, providing essential insights into product longevity and optimizing maintenance strategies. Due to its adaptable parameters namely scale parameter α and shape parameter β, the Weibull distribution models diverse failure behaviours, from early-life defects to wear-out periods. By evaluating reliability at key time phases namely early life (t < 0.1α), useful life (0.1α ≤ t ≤ α), and end-of-life (t > α), this estimation process supports quality control, operational forecasting, and end-of-life planning. Such reliability assessments help minimize operational disruptions, improve cost management, and support strategic planning across industries where dependability and lifecycle management are essential, such as in manufacturing, healthcare, and technology sectors. Although it holds practical significance, the estimation of confidence interval (CI) for the reliability function of two parameter Weibull distribution has been relatively underexplored in the literature. This paper presents a new approach for constructing CI for the reliability function of the Weibull distribution using the generalized variable (GV) technique, applicable to both complete samples and type II singly right-censored samples. The empirical evaluation of this method indicates that it provides coverage probabilities that are closely aligned with the nominal level, even when dealing with small uncensored samples (as small as 5) and censored samples where the proportion of censored observations can reach 70%. In comparison, traditional methods for the Weibull distribution tend to yield less reliable or widely varied coverage probabilities for complete samples. The findings are demonstrated through practical examples. Keywords: Reliability, Confidence interval, Generalized Variable approach, Censoring.

A new control chart based on proportional hazards and frailty regression models for monitoring high‐quality processes with censored observations

AbstractImproving quality and reducing defects in various processes have led to the design of numerous control charts for monitoring count data. These charts are characterized by a large number of zero defects and are modeled with zero‐inflated distributions. Besides, it is important to consider the influence of key factors on the number of defects in some processes. This paper presents three monitoring scenarios that utilize cumulative sum (CUSUM) control charts in Phase II. These scenarios are valuable for monitoring high‐quality processes, particularly with censored observations. The first scenario uses a zero‐inflated Poisson (ZIP) distribution while the second one employs a proportional hazards regression model to account for observed variables. The third scenario combines the proportional hazards and frailty regression models to consider both observed and unobserved variables. The performance of all three control charts is evaluated by applying shifts to both parameters of the ZIP distribution separately and simultaneously. Extensive simulation studies are conducted and the effects of low, moderate, and high censoring rates are thoroughly studied. The results highlight the importance of considering influential variables for detecting early shifts, as neglecting them significantly impairs the control chart performance. Finally, a real case study, involving defect counts in printed rolls at a label printing factory, has been provided and discussed to show the application of the monitoring procedures.

US household demand system analysis for dairy milk products and plant‐based milk alternatives

AbstractUsing the QUAIDS model, we analyze interrelationships among dairy milk and plant‐based milk alternatives (PBMA) for US households from 2018 to 2020 using NielsenIQ. We adopt the Shonkwiler–Yen methodology to account for censored observations. PBMA demand is inelastic, while milk products show elastic demand. PBMA substitutes for traditional white milk and organic milk. Traditional flavored milk and PBMA as well as lactose‐free and organic milk are complements. PBMA and lactose‐free milk are independent goods. Demographic factors like income, household size, and education significantly affect budget share, alongside women, infants, and children participation and the pandemic.

Efficient ARL estimation for general control charts using censored run lengths

The average run length (ARL), the average number of in-control signals before an out-of-control signal occurs, is a critical measure of the performance of a control chart. Various methods have been explored for estimating the ARL, including Markov chain-based approximation, integration method, and the Monte Carlo method, especially for time-dependent charting statistics. Although computationally expensive, the Monte Carlo method is generic and applicable to all control charts. Typically, it involves choosing the maximum run length in advance and discarding iterations that fail to produce out-of-control signals to accommodate some unusually lengthy runs. However, these discarded runs provide information for estimating the run length. This paper introduces a new Monte Carlo approximation that retains failed iterations as Type I censored observations for ARL estimation. Our approach relies on the memoryless expectation of the run length distribution to have a simple and efficient ARL estimator. This assumption is necessary for mean estimation in Type I censored data and aligns with existing ARL approximations used in popular control charts like Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) charts. Numerical simulations demonstrate our method’s computational and statistical efficiency across the mean, median, EWMA, and CUSUM charts.

Bowel movement alterations predict the severity of diverticular disease and the risk of acute diverticulitis: a prospective, international st.

Patients with diverticular disease (DD) frequently have abnormal bowel movements. However, it is unknown whether the entity of these alterations is associated with the severity of DD. We aimed to assess bowel habits and their relationship with the severity of DD according to Diverticular Inflammation and Complication Assessment (DICA) classification, Combined Overview on Diverticular Assessment (CODA) score, and fecal calprotectin (FC). An international, multicenter, prospective cohort study was conducted in 43 centers. A 10-point visual analog scale (VAS) was used to assess the severity of constipation and diarrhea. The association of constipation and diarrhea with DICA classification, CODA score, and basal FC was tested using non-parametric tests. Survival methods for censored observations were applied to test the association of constipation and diarrhea with the incidence of acute diverticulitis over a 3-year follow-up. Of 871 patients with DD were included in the study. Of these, 208 (23.9%) and 199 (22.9%) reported a VAS score for constipation and diarrhea at least 3 at baseline, respectively. Higher constipation and diarrhea scores were associated with increasing DICA classification, CODA score and basal FC (P< 0.001). Constipation and diarrhea scores were independently associated with an increased hazard of developing acute diverticulitis (hazard ratio [HR]constipation = 1.15 per 1-VAS point increase, 95% confidence interval [CI], 1.04-1.27; P=0.004; and HRdiarrhea =1.14; 95% CI, 1.03-1.26; P=0.014, respectively). In newly diagnosed patients with DD, higher endoscopic and combined scores of DD severity were associated with higher scores of constipation and diarrhea at baseline. Both constipation and diarrhea were independent prognostic factors of acute diverticulitis.

Application of the Marshall-Olkin-Weibull logarithmic distribution to complete and censored data

In contemporary statistical research, there has been a notable surge of interest surrounding a suggested extension of the Marshall-Olkin-G distributions. The present extension exhibits a higher degree of flexibility in comparison to its parent distributions. In a similar manner, we present in this context an expansion of the Marshall-Olkin-G distributions proposed by statistical scholars. This study utilizes a specific variant of the extension known as the Marshall-Olkin-Weibull Logarithmic model, which is applied to both complete and censored data sets. It is evident that the aforementioned model has strong competitiveness in accurately characterizing both complete and censored observations in lifetime reliability issues, when compared to other comparative models discussed in this research work.

Composite event-free-survival as an endpoint in oncology drug evaluation: Review and guidance perspectives from the Haute Autorité de Santé (HAS)

BackgroundThe use of right-censored composite endpoints, such as progression-free survival, has been questioned in haemato-oncology trials due to potential bias in estimated treatment effect. This may impact the accuracy of health technology evaluations. We hypothesized that there is heterogeneity and potential sources of bias in the reporting of composite endpoints to health technology assessment (HTA) bodies. MethodsWe reviewed the submissions for reimbursement of oncology drugs in 2021 and 2022 that used a composite endpoint in the pivotal trial, after appraisal by the French HTA body. The retrieved information included the clinical study report, protocol, and statistical analysis plan submitted by the industry. All events of the composite endpoint and all causes of censored observations were measured. The design characteristics and treatment effect estimates were recorded. FindingsSeventy-six submissions were selected, including seven without a right-censored endpoint and four evaluating associations, resulting in 65 analysed records: 17 for haematological and 48 for solid tumours. Out these 65 submissions, 47 (72·3%) used a randomized controlled design, and 18 (27·7%) a non-comparative design. The most frequently used composite endpoint was progression-free survival, used in 54 (83·1%) of the submissions. Censoring was possibly informative in 51 (92·7%) cases, mostly due to the onset of new treatment (44/51, 86·3%) and/or discontinuation of follow-up (33/51, 64·7%). In contrast, 38 (58·5%) trials reported a quantification of censored observations, with only 12/51 (23·5%) quantifying the informative ones. The estimated treatment effect on the composite outcome increased with the amount of censoring, suggesting a higher benefit of the drug, but remained below that on survival with poor evidence of surrogacy (R-squared=0·23). InterpretationClinical study reports should be improved in terms of reporting censoring, while stakeholders should be aware of this potential source of bias. At a minimum, sensitivity analysis that ignores intercurrent events should be requested.

On the role of Volterra integral equations in self-consistent, product-limit, inverse probability of censoring weighted, and redistribution-to-the-right estimators for the survival function.

This paper reconsiders several results of historical and current importance to nonparametric estimation of the survival distribution for failure in the presence of right-censored observation times, demonstrating in particular how Volterra integral equations help inter-connect the resulting estimators. The paper begins by considering Efron's self-consistency equation, introduced in a seminal 1967 Berkeley symposium paper. Novel insights provided in the current work include the observations that (i) the self-consistency equation leads directly to an anticipating Volterra integral equation whose solution is given by a product-limit estimator for the censoring survival function; (ii) a definition used in this argument immediately establishes the familiar product-limit estimator for the failure survival function; (iii) the usual Volterra integral equation for the product-limit estimator of the failure survival function leads to an immediate and simple proof that it can be represented as an inverse probability of censoring weighted estimator; (iv) a simple identity characterizes the relationship between natural inverse probability of censoring weighted estimators for the survival and distribution functions of failure; (v) the resulting inverse probability of censoring weighted estimators, attributed to a highly influential 1992 paper of Robins and Rotnitzky, were implicitly introduced in Efron's 1967 paper in its development of the redistribution-to-the-right algorithm. All results developed herein allow for ties between failure and/or censored observations.

Inference for Bayesian Nonparametric Models with Binary Response Data via Permutation Counting

Since the beginning of Bayesian nonparametrics in the early 1970s, there has been a wide interest in constructing models for binary response data. Such data arise naturally in problems dealing with bioassay, current status data and sensitivity testing, and are equivalent to left and right censored observations if the inputs are one-dimensional. For models based on the Dirichlet process, inference is possible via Markov chain Monte Carlo (MCMC) simulations. However, there exist multiple processes based on different principles, for which such MCMC-based methods fail. Examples include logistic Gaussian processes and quantile pyramids. These require MCMC for posterior inference given exact observations, and thus become intractable when the data comprise both left and right censored observations. Here we present a new importance sampling algorithm for nonparametric models given exchangeable binary response data. It can be applied to any model from which samples can be generated, or even only approximately generated. The main idea behind the algorithm is to exploit the symmetries introduced by exchangeability. Calculating the importance weights turns out to be equivalent to evaluating the permanent of a certain class of (0,1)-matrix, which we prove can be done in polynomial time by deriving an explicit algorithm.

Competing risk multistate censored data modeling by propensity score matching method

The potential contribution of the paper is the use of the propensity score matching method for updating censored observations within the context of multi-state model featuring two competing risks.The competing risks are modelled using cause-specific Cox proportional hazard model.The simulation findings demonstrate that updating censored observations tends to lead to reduced bias and mean squared error for all estimated parameters in the risk of cause-specific Cox model.The results for a chemoradiotherapy real dataset are consistent with the simulation results.

Application of the New Extended Topp-Leone Distribution to Complete and Censored Data

One of the most important applications of statistical models is in analyzing survival data. In this study, we developed the Gamma Type Two Half Logistic Topp-Leone-G model using the technique earlier proposed by Zografos and Balakrishnan. Different characteristics of the proposed distribution are obtained. In order to estimate the model parameters based on complete and censored data, the maximum likelihood estimation method is used. Through Monte Carlo simulation, the performance of the estimators is evaluated. The proposed distribution's potential significance and applicability are empirically demonstrated using actual datasets. We found that our new distribution is a very competitive model for describing both complete and censored observations in survival analysis. The work demonstrated that in certain cases, our new model performed better than other parametric models with the same number of parameters.

Distributed Radar Multi-frame Detection with Local Censored Observations

Distributed Radar Multi-frame Detection with Local Censored Observations

Interval-specific censoring set adjusted Kaplan–Meier estimator

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.

Optimal Acceptance Sampling Testing Plan With Pivotal Quantity for Log-Location-Scale Distributions

Global market competition has led to manufacturers encountering a decision problem as the reliability of their products exceeds a given standard. Acceptance sampling tests (ASTs) can be expensive and time-consuming, especially for products with high reliability or quality. Thus, careful planning of the acceptance rule and determination of a suitable sample size for the test are important. In this article, an exact method for the optimal planning of ASTs is proposed for cases in which the product lifetimes follow a distribution in the general log-location-scale family of distributions. A novel procedure using the pivotal quantity is established based on the method-of-moments estimators of the model parameters, and the distribution of the reliability estimator is derived. An algorithm for obtaining the optimal sample size and the corresponding acceptability constant is presented in which the producer's and consumer's risks are constrained according to certain acceptance criteria. We apply the proposed method to a censored AST by generating censored observations with a quantile-filling method under Type-II censoring. The performance of the proposed AST with a complete or censored sample is studied and compared with an AST based on the maximum likelihood method. The robustness of the proposed AST is also examined under model misspecification. The results show that the proposed AST performs well under different scenarios.

TRAILBLAZER‐ALZ 3 – A Deeper Dive into Time‐to‐Event Trials

AbstractBackgroundThe pathophysiologic process of Alzheimer’s Disease (AD) is underway before cognitive decline becomes evident (i.e.; preclinical AD). Beginning treatment during this phase is believed to lead to beneficial outcomes in terms of disease progression. TRAILBLAZER‐ALZ 3 (TB3; NCT05026866) is an ongoing Phase 3 decentralized clinical trial assessing the effect of donanemab, a monoclonal antibody that removes amyloid plaques via microglial‐mediated clearance, versus placebo on clinical progression in preclinical AD. Clinical outcomes are assessed virtually by using central raters, psychometric examinations, and self‐administered tests. The primary endpoint of interest is the time to clinical progression as measured by the Clinical Dementia Rating scale global score (CDR‐GS).MethodTwo of the most frequently used methods to analyze time‐to‐event data are Kaplan‐Meier curves and Cox proportional hazards models. In TB3, the primary endpoint will be assessed via a Cox proportional hazard regression model. The key assumptions that will be made with this modeling approach are proportionality and censoring. Proportionality refers to the relative hazard being constant over time and how to treat censored observations, which refers to patients who do not reach the event during the observation period. While this approach has been used in fields such as oncology, we have adapted it for the assessment of time to clinical progression of AD cognitive decline. From this approach the hazard ratio, an estimate on the instantaneous risk, can be calculated. This measure can give insight, at a given time point, of the risk of progression of AD that a participant has.We will also look at additional considerations of collecting data in a decentralized remote manner, such as missing data due to technology issues, and highlight the approaches that will be used to analyze additional cognitive and biomarker data.ResultThis investigation will show that we have adapted analytic techniques to determine the time to clinical progression of AD as measured by an increase in CDR‐GS from baseline at 2 consecutive visits.ConclusionWe present an analytical method of assessing potential treatments to slow disease progression during the preclinical AD phase without requiring centralized assessment sites.

Look left, look right: censoring in clinical research.

In this methodology editorial, the problem of censored survival (or time-to-event) data in clinical research is discussed. In case of censored observations, part of the observation time for some participants in a study is unobserved, which means that measures such as an average survival time cannot be calculated. Instead, censored survival time should explicitly be accounted for in the analysis of a study, for example using the Kaplan-Meier method. Implications of censoring and how to deal with it in the analysis of a study or when reading a research paper are discussed.

Efficient non parametric spectral density estimation with censored observations

Spectral density estimation is a well-studied problem for the case of directly observed time series. If data are censored then add hoc methods, like ignoring censored observations or treatment them as missing and using imputation, are recommended. This article, for the first time in the literature, presents the theory and methodology of efficient non parametric spectral density estimation for censored time series. Recommended estimator is based on estimation of autocovariances for censored time series which is of interest on its own. Similarly to the case of direct observations, the theory and methodology are first developed for Gaussian time series, and then robustness of the estimator is verified for a larger class of mixing time series. Simulations and practical examples complement the theory.

A new goodness of fit test for gamma distribution with censored observations

In the present paper, we develop a new goodness of fit test for gamma distribution based on the fixed point characterization. We use U-Statistics theory to derive the test statistic. We discuss how the right censored observations are incorporated into the proposed test. The asymptotic properties of the test statistics in censored and uncensored cases are studied. We carry out a Monte Carlo simulation study to validate the finite sample performance of the proposed tests. We also illustrate the test procedures using real data sets.

Diverticular Inflammation and Complication Assessment classification, CODA score and fecal calprotectin in clinical assessment of patients with diverticular disease: A decision curve analysis.

The Diverticular Inflammation and Complication Assessment (DICA) classification and the Combined Overview on Diverticular Assessment (CODA) were found to be effective in predicting the outcomes of Diverticular Disease (DD). We ascertain whether fecal calprotectin (FC) can further aid in improving risk stratification. A three-year international, multicentre, prospective cohort study was conducted involving 43 Gastroenterology and Endoscopy centres. Survival methods for censored observations were used to estimate the risk of acute diverticulitis (AD) in newly diagnosed DD patients according to basal FC, DICA, and CODA. The net benefit of management strategies based on DICA, CODA and FC in addition to CODA was assessed with decision curve analysis, which incorporates the harms and benefits of using a prognostic model for clinical decisions. At the first diagnosis of diverticulosis/DD, 871 participants underwent FC measurement. FC was associated with the risk of AD at 3years (HR per each base 10 logarithm increase: 3.29; 95% confidence interval, 2.13-5.10) and showed moderate discrimination (c-statistic: 0.685; 0.614-0.756). DICA and CODA were more accurate predictors of AD than FC. However, FC showed high discrimination capacity to predict AD at 3months, which was not maintained at longer follow-up times. The decision curve analysis comparing the combination of FC and CODA with CODA alone did not clearly indicate a larger net benefit of one strategy over the other. FC measurement could be used as a complementary tool to assess the immediate risk of AD. In all other cases, treatment strategies based on the CODA score alone should be recommended.

Power analysis of approximation methods for parameter estimation in Cox regression model with longitudinal covariate and tied survival times

Cox regression model (CRM) with time-varying covariates is widely used in medical and health related studies to investigate the effects of longitudinal variables on survival. In this paper, tied survival refers to units in which different subjects have the same survival time, while the term interaction indicates the relationship between longitudinal covariate and survival time. Unlike previous studies, we calculate the statistical power of Wald χ 2 statistics to test the interaction term based on Monte Carlo (MC) simulations when Breslow, Efron, Discrete, and Exact approximation methods are used for handling tied survival times. A linear mixed effect model (LMM) is used to generate longitudinal covariate such as time-varying covariate in simulations. A numerical example is provided to illustrate the CRM with the interaction term between longitudinal covariate and survival time. Using extensive MC simulations under different conditions for censored proportion, type I error, and number of subjects, statistical power of Wald χ 2 statistics is calculated using four different methods in the CRM. Statistical power value calculated using Breslow method is usually lower than statistical power values calculated when the other three methods are used. The proportion of censored observations in survival analysis has an important effect on power calculations.