Presence Of Right-censored Data Research Articles

Divergences based Bayesian inference with censored data

. In this work, we deal with some Bayesian inference problems in the presence of right censored data. First, we propose a dual ϕ−divergence Bayes type estimators for parametric models and we establish their asymptotic normality. To establish this result, we need a uniform strong law of large numbers that we prove as well. Then, we consider the problem of prior distributions construction for model selection using ϕ−divergences. Finally, we consider the problem of the predictive density estimation on the basis of ϕ−divergences. We apply an expansion result of the generalized Bayesian predictive density on two parametric models widely used in survival analysis, namely the Weibull and the inverse Weibull model, under right censoring. We also check the performances of our proposed methods through simulations and real data applications. The results of these studies show that our proposed dual ϕ−divergence Bayes type estimators are more robust than other Bayesian estimators. Moreover, the generalized Bayesian predictive density performs better than the classical estimative density especially for the inverse Weibull model.

Improved Bayesian Inferences for Right-Censored Birnbaum–Saunders Data

This work focuses on making Bayesian inferences for the two-parameter Birnbaum–Saunders (BS) distribution in the presence of right-censored data. A flexible Gibbs sampler is employed to handle the censored BS data in this Bayesian work that relies on Jeffrey’s and Achcar’s reference priors. A comprehensive simulation study is conducted to compare estimates under various parameter settings, sample sizes, and levels of censoring. Further comparisons are drawn with real-world examples involving Type-II, progressively Type-II, and randomly right-censored data. The study concludes that the suggested Gibbs sampler enhances the accuracy of Bayesian inferences, and both the amount of censoring and the sample size are identified as influential factors in such analyses.

Measuring the Recovery Performance of a Portfolio of NPLs

The objective of the present paper is to propose a new method to measure the recovery performance of a portfolio of non-performing loans (NPLs) in terms of recovery rate and time to liquidate. The fundamental idea is to draw a curve representing the recovery rates over time, here assumed discretized, for example, in years. In this way, the user can get simultaneously information about recovery rate and time to liquidate of the portfolio. In particular, it is discussed how to estimate such a curve in the presence of right-censored data, e.g., when the NPLs composing the portfolio have been observed in different time periods, with a method based on an algorithm that is usually used in the construction of survival curves. The curves obtained are smoothed with nonparametric statistical learning techniques. The effectiveness of the proposal is shown by applying the method to simulated and real financial data. The latter are about some portfolios of Italian unsecured NPLs taken over by a specialized operator.

Model Checking with Right Censored Data Using Relative Belief Ratio.

Model checking is a topic of special interest in statistics. When data are censored, the problem becomes more difficult. This paper employs the relative belief ratio and the beta-Stacy process to develop a method for model checking in the presence of right-censored data. The proposed method for the given model of interest compares the concentration of the posterior distribution to the concentration of the prior distribution using a relative belief ratio. We propose a computational algorithm for the method and then illustrate the method through several data analysis examples.

Discrete Bilal Distribution in the Presence of Right-Censored Data and a Cure Fraction

The statistical literature presents many continuous probability distributions with only one parameter, which are extensively used in the analysis of lifetime data, such as the exponential, the Lindley, and the Rayleigh distributions. Alternatively, the use of discretized versions of these distributions can provide a better fit for the data in many applications. As the novelty of this study, we present inferences for the discrete Bilal distribution (DB) with one parameter introduced by Altun et al. (2020) in the presence of right-censored data and cure fraction. We assume standard maximum likelihood methods based on asymptotic normality of the maximum likelihood estimators and also a Bayesian approach based on MCMC (Markov Chain Monte Carlo) simulation methods to get inferences for the parameters of the discrete BD distribution. The use of the proposed model was illustrated with three examples considering real medical lifetime data sets. From these applications, we concluded that the proposed model based on the discrete DB distribution has good performance even with the inclusion of a cure fraction in comparison to other existing discrete models, such as the DsFx-I, Lindley, Rayleigh, and Burr-Hatke probability distributions. Moreover, the model can be easily implemented in standard existing software, such as the R package. Under a Bayesian approach, we assumed a gamma prior distribution for the parameter of the DB discrete distribution. We also provided a brief sensitivity analysis assuming the half-normal distribution in place of the gamma distribution for the parameter of the DB distribution. From the obtained results of this study, we can conclude that the proposed methodology can be very useful for researchers dealing with medical discrete lifetime data in the presence of right-censored data and cure fraction.

Modifying Weighted Kaplan-Meier Test for Two-Sample Survival Comparison


 
 
 This paper presents an approach to improving the weighted Kaplan-Meier test statistics in order to make it a more useful tool for a long-term comparison of two underlying survival distributions in the presence of right-censored data. The procedures are based on the use of some weight function that involves the percentage of censored data as a component. Some versatile procedures for the alternative, not pre-specified, are also discussed. Numerical simulations are conducted to investigate the performance of the proposed procedures. For illustration, the procedures are applied to real-world data in clinical trials, where patients with tongue cancer are divided into two groups according to tumor DNA.
 
 
 

Assessing the adequacy of the gompertz regression model in the presence of right censored data

The Gompertz distribution is often used to model human mortality and establish actuarial tables. Cox-Snell residual is the most general practice to evaluate the model adequacy. However, standard statistical procedures are not amenable to handle the censored observations. Therefore, this research investigates the adequacy of the two parameter Gompertz parametric survival model that was extended to incorporate with fixed covariate in the presence of right censored data. Performance of the model is assessed and compared at various combinations of sample sizes and censoring proportions via simulation study. The newly proposed modifications to the Cox-Snell residuals based on the geometric mean and harmonic mean as well as the jackknife means were compared with Cox-Snell and Modified Cox-Snell residuals via simulation studies at different settings. The log-cumulative hazard plot of residuals is obtained by plotting the proposed residuals against the cumulative hazard function to assess the model’s fit. Based on the model adequacy study, we found out that jackknife geometric mean and jackknife harmonic mean outperform CS, MCS, GMCS and HMCS residuals.

Fiducial Inference on the Right Censored Birnbaum–Saunders Data via Gibbs Sampler

In this article, we implement a flexible Gibbs sampler to make inferences for two-parameter Birnbaum–Saunders (BS) distribution in the presence of right-censored data. The Gibbs sampler is applied on the fiducial distributions of the BS parameters derived using the maximum likelihood, methods of moments, and their bias-reduced estimates. A Monte-Carlo study is conducted to make comparisons between these estimates for Type-II right censoring with various parameter settings, sample sizes, and censoring percentages. It is concluded that the bias-reduced estimates outperform the rest with increasing precision. Higher sample sizes improve the overall accuracy of all the estimates while the amount of censoring shows a negative effect. Further comparisons are made with existing methods using two real-world examples.

Bayesian Computational Methods for Sampling from the Posterior Distribution of a Bivariate Survival Model, Based on AMH Copula in the Presence of Right-Censored Data.

In this paper, we study the performance of Bayesian computational methods to estimate the parameters of a bivariate survival model based on the Ali–Mikhail–Haq copula with marginal distributions given by Weibull distributions. The estimation procedure was based on Monte Carlo Markov Chain (MCMC) algorithms. We present three version of the Metropolis–Hastings algorithm: Independent Metropolis–Hastings (IMH), Random Walk Metropolis (RWM) and Metropolis–Hastings with a natural-candidate generating density (MH). Since the creation of a good candidate generating density in IMH and RWM may be difficult, we also describe how to update a parameter of interest using the slice sampling (SS) method. A simulation study was carried out to compare the performances of the IMH, RWM and SS. A comparison was made using the sample root mean square error as an indicator of performance. Results obtained from the simulations show that the SS algorithm is an effective alternative to the IMH and RWM methods when simulating values from the posterior distribution, especially for small sample sizes. We also applied these methods to a real data set.

Likelihood-based inference for the transmuted log-logistic model in the presence of right-censored data

ABSTRACTAlthough new transmuted distributions have been widely proposed in the last few years, it is rarely to find those class of models applied in survival analysis in the presence of censored lifetimes. In this context, we are concerned in applying the transmuted log-logistic model in the study of discharge times of patients treated with the Linezolid drug. For model fitting, we use and compare different profile likelihood methods. Analysis of residuals and influence are also presented. All results are validated in a simulation study by considering the bootstrap techniques.

Prediction errors for state occupation and transition probabilities in multi-state models.

In this paper, we consider the estimation of prediction errors for state occupation probabilities and transition probabilities for multistate time-to-event data. We study prediction errors based on the Brier score and on the Kullback-Leibler score and prove their properness. In the presence of right-censored data, two classes of estimators, based on inverse probability weighting and pseudo-values, respectively, are proposed, and consistency properties of the proposed estimators are investigated. The second part of the paper is devoted to the estimation of dynamic prediction errors for state occupation probabilities for multistate models, conditional on being alive, and for transition probabilities. Cross-validated versions are proposed. Our methods are illustrated on the CSL1 randomized clinical trial comparing prednisone versus placebo for liver cirrhosis patients.

Aircraft re-routing optimization and performance assessment under uncertainty

The need for aircraft re-routing arises when there is disruption in the system, such as when an airport is closed due to extreme weather. In this paper, we investigate a simulation-based approach to optimize the aircraft re-routing process, by considering multiple sources of uncertainty. The proposed approach has four main components: system simulation, uncertainty representation, aircraft re-routing algorithm, and system performance assessment. Several sources of uncertainty are accounted for in this approach, related to incoming aircraft, space availability in neighboring airports, radar performance, and communication delays. An aircraft re-routing optimization model is formulated to make periodic re-routing decisions with the objective of minimizing the overall distance travelled by all the aircraft, subject to the system resources. We analyze the performance of this aircraft re-routing system using system failure time as the metric. Since the simulation time is limited, right-censored data arises with respect to system failure time. A novel methodology is developed to compute the lower bound of system failure time in the presence of right-censored data, and to analyze the sensitivity of the system performance metric to the uncertain variables relating to the aircraft, radars, nearby airports, and communication system. Since the simulation is time-consuming, we build a Support Vector Regression (SVR) surrogate model to efficiently construct the system failure time distribution.

An extension of generalized pairwise comparisons for prioritized outcomes in the presence of censoring.

Generalized pairwise comparisons have been proposed to permit a comprehensive assessment of several prioritized outcomes between two groups of observations. This procedure estimates Δ, the net chance of a better outcome with treatment than with control by comparing the patients outcomes among all possible pairs taking one patient from the treatment group and one patient from the control group. For time to event outcomes, the standard procedure of generalized pairwise comparisons is analogous to the Gehan's modification of the Mann-Whitney test which is biased in presence of censored observation and less powerful than Efron's modification of this test. We adapt Efron's modification to generalized pairwise comparisons. We show how a pairwise contribution to Δ can be calculated from the estimates of the survival function in the presence of right-censored data. We performed a simulation study to assess the bias, the type I error and the power of the new procedure. The estimate of Δ with the new procedure is only slightly biased even in presence of heavy censoring. We also show how this bias can be corrected when only one time-to-event outcome is analyzed. The new procedure has higher power in most cases compared to the standard procedure.

Bayesian estimation of the limiting availability in the presence of right-censored data

This work presents a Bayesian approach for estimating the limiting availability of an one-unit repairable system when the data are subject to right censorship. It is assumed that the failure and repair times of the components are independent exponential random variables. A conjugate Bayesian analysis is performed considering an informative and non informative prior distributions. Simulations are presented to study the performance of the Bayesian solutions. Some observations are made in relation to the maximum likelihood method. The Weibull case is also discussed.

Implementing ReliefF filters to extract meaningful features from genetic lifetime datasets

BackgroundThe analysis of survival data allows to evaluate whether in a population the genetic exposure is related to the time until an event occurs. Owing to the complexity of common human diseases, there is the incipient need to develop bioinformatics tools to properly model non-linear high-order interactions in lifetime datasets. These tools, such as the survival dimensionality reduction algorithm, may suffer from extreme computational costs in large-scale datasets. Herein, we address the problem of estimating the quality of attributes, so as to extract relevant features from lifetime datasets and to scale down their size. MethodsThe ReliefF algorithm was modified and adjusted to compensate for the loss of information due to censoring, introducing reclassification and weighting schemes. Synthetic lifetime two-locus epistatic datasets of 500 attributes, 400–800 individuals and different degrees of cumulative heritability and censorship were generated. The capability of the survival ReliefF algorithm (sReliefF) and of a tuned sReliefF approach to properly select the causative pair of attributes was evaluated and compared to univariate selection based on Cox scores. Results/conclusionssReliefF methods efficiently scaled down the simulated datasets, whilst univariate selection performed no better than random choice. These approaches may help to reduce the computational cost and to improve the classification task of algorithms that model high-order interactions in presence of right-censored data. Availability: http://sourceforge.net/projects/sdrproject/files/sReliefF/.

Survival dimensionality reduction (SDR): development and clinical application of an innovative approach to detect epistasis in presence of right-censored data

BackgroundEpistasis is recognized as a fundamental part of the genetic architecture of individuals. Several computational approaches have been developed to model gene-gene interactions in case-control studies, however, none of them is suitable for time-dependent analysis. Herein we introduce the Survival Dimensionality Reduction (SDR) algorithm, a non-parametric method specifically designed to detect epistasis in lifetime datasets.ResultsThe algorithm requires neither specification about the underlying survival distribution nor about the underlying interaction model and proved satisfactorily powerful to detect a set of causative genes in synthetic epistatic lifetime datasets with a limited number of samples and high degree of right-censorship (up to 70%). The SDR method was then applied to a series of 386 Dutch patients with active rheumatoid arthritis that were treated with anti-TNF biological agents. Among a set of 39 candidate genes, none of which showed a detectable marginal effect on anti-TNF responses, the SDR algorithm did find that the rs1801274 SNP in the FcγRIIa gene and the rs10954213 SNP in the IRF5 gene non-linearly interact to predict clinical remission after anti-TNF biologicals.ConclusionsSimulation studies and application in a real-world setting support the capability of the SDR algorithm to model epistatic interactions in candidate-genes studies in presence of right-censored data.Availability: http://sourceforge.net/projects/sdrproject/

Testing additivity in nonparametric regression under random censorship

In this paper, we are concerned with nonparametric estimation of the multivariate regression function in the presence of right censored data. More precisely, we propose a statistic which is shown to be asymptotically normally distributed under the additive assumption, and which could then be used to test for additivity in the multivariate censored regression setting.

Uniform limit laws of the logarithm for estimators of the additive regression function in the presence of right censored data

It has been recently shown that nonparametric estimators of the additive regression function could be obtained in the presence of right censoring by coupling the marginal integration method with initial kernel-type Inverse Probability of Censoring Weighted estimators of the multivariate regression function \citeDebbarhViallon3. In this paper, we get the exact rate of strong uniform consistency for such estimators. Our uniform limit laws especially lead to the construction of asymptotic simultaneous 100% confidence bands for the true regression function.

Resampling Procedures to Compare Two Survival Distributions in the Presence of Right-Censored Data

SUMMARY In this simulation study, the accuracy of the size of four classes of test procedures asymptotic normal test, permutation test, bootstrap hypothesis test, and bootstrap interval test were compared using the logrank and Prentice-Wilcoxon two sample test statistics. Sample sizes of 20 and 50 per group were used. Twenty observations per group yielded differences in the test procedures. When the Prentice-Wilcoxon test statistic was employed, the asymptotic test procedure was the most accurate; resampling procedures did not improve upon its accuracy. Using the logrank test statistic, the permutation or bootstrap hypothesis testing procedures were closest to the nominal significance level. The more popular asymptotic normal logrank test was consistently anticonservative. When the number of observations in each group was increased to 50, the test procedures were comparable. Power comparisons were also examined. The test with the greatest power was dependent upon the two survival patterns and the choice of test statistic.