Model For Censored Data Research Articles

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.

Structure Identification in Varying-Coefficient Partially Linear Accelerated Failure Time Models via the Group MCP

The accelerated failure time (AFT) model is commonly used for the analysis of survival data in the presence of right censored due to the interpretability. In some practical cases, especially when some covariates are time-related, it is not realistic to assume the linear predictors in the AFT model. We propose a varying-coefficient partially linear AFT model for right censored data, allowing the nonlinear effects of covariates. To tackle challenges in estimation, we propose a penalized profile likelihood approach which utilizes a group minimax concave penalty to determine the nonlinear effects of covariates. Under the suitable conditions, we show that the proposed method can correctly select linear components and nonlinear components with high probability. Simulation results demonstrate the satisfactory performance of the proposed method in finite sample cases.

18F‑FDG PET/CT based radiomics features improve prediction of prognosis: multiple machine learning algorithms and multimodality applications for multiple myeloma

PurposeMultiple myeloma (MM), the second most hematological malignancy, have been studied extensively in the prognosis of the clinical parameters, however there are only a few studies have discussed the role of dual modalities and multiple algorithms of 18F-FDG (18F-fluorodeoxyglucose) PET/CT based radiomics signatures for prognosis in MM patients. We hope to deeply mine the utility of raiomics data in the prognosis of MM.MethodsWe extensively explored the predictive ability and clinical decision-making ability of different combination image data of PET, CT, clinical parameters and six machine learning algorithms, Cox proportional hazards model (Cox), linear gradient boosting models based on Cox’s partial likelihood (GB-Cox), Cox model by likelihood based boosting (CoxBoost), generalized boosted regression modelling (GBM), random forests for survival model (RFS) and support vector regression for censored data model (SVCR). And the model evaluation methods include Harrell concordance index, time dependent receiver operating characteristic (ROC) curve, and decision curve analysis (DCA).ResultsWe finally confirmed 5 PET based features, and 4 CT based features, as well as 6 clinical derived features significantly related to progression free survival (PFS) and we included them in the model construction. In various modalities combinations, RSF and GBM algorithms significantly improved the accuracy and clinical net benefit of predicting prognosis compared with other algorithms. For all combinations of various modalities based models, single-modality PET based prognostic models’ performance was outperformed baseline clinical parameters based models, while the performance of models of PET and CT combined with clinical parameters was significantly improved in various algorithms.Conclusion18F‑FDG PET/CT based radiomics models implemented with machine learning algorithms can significantly improve the clinical prediction of progress and increased clinical benefits providing prospects for clinical prognostic stratification for precision treatment as well as new research areas.

Wavelet Support Vector Censored Regression

Learning methods in survival analysis have the ability to handle censored observations. The Cox model is a predictive prevalent statistical technique for survival analysis, but its use rests on the strong assumption of hazard proportionality, which can be challenging to verify, particularly when working with non-linearity and high-dimensional data. Therefore, it may be necessary to consider a more flexible and generalizable approach, such as support vector machines. This paper aims to propose a new method, namely wavelet support vector censored regression, and compare the Cox model with traditional support vector regression and traditional support vector regression for censored data models, survival models based on support vector machines. In addition, to evaluate the effectiveness of different kernel functions in the support vector censored regression approach to survival data, we conducted a series of simulations with varying number of observations and ratios of censored data. Based on the simulation results, we found that the wavelet support vector censored regression outperformed the other methods in terms of the C-index. The evaluation was performed on simulations, survival benchmarking datasets and in a biomedical real application.

Extending multivariate Student's- semiparametric mixed models for longitudinal data with censored responses and heavy tails.

This article extends the semiparametric mixed model for longitudinal censored data with Gaussian errors by considering the Student's -distribution. This model allows us to consider a flexible, functional dependence of an outcome variable over the covariates using nonparametric regression. Moreover, the proposed model takes into account the correlation between observations by using random effects. Penalized likelihood equations are applied to derive the maximum likelihood estimates that appear to be robust against outlying observations with respect to the Mahalanobis distance. We estimate nonparametric functions using smoothing splines under an EM-type algorithm framework. Finally, the proposed approach's performance is evaluated through extensive simulation studies and an application to two datasets from acquired immunodeficiency syndrome clinical trials.

Survival models for right censored breast cancer data: theory, application and comparison

Background: Censoring frequently occurs in disease data analysis, which is a key characteristic of time to failure modeling. Typically, time to failure studies are conducted through non-parametric and semi-parametric modelling techniques. Parametric models provide more efficient estimates, but are seldomly used, because of some of the limitations and assumptions which need to be fulfilled to apply them. The aim of this study is to illustrate the theoretical and application limitations and performance of different flexible and standard parametric models to evaluate the prognostic value for mortality risk of breast cancer after recurrence among women. Methods: This article describes the theoretical properties of flexible parametric models and compares their performances to standard parametric models, by studying mortality in women diagnosed with breast cancer. We describe how time to failure data may be analyzed with nonlinear flexible models. In this regard, we apply fractional polynomials, spline models, piecewise exponential models, and piecewise exponential additive mixed models. We also illustrate properties of standard parametric models. All analyses have been conducted with multiple covariates to identify significant predictors. Information criteria have been used to evaluate performances of models. Results: Fractional polynomial and spline-based generalized additive models work well in capturing local fluctuations. Parameter estimation with a piecewise exponential additive mixed model (PAMM) as an extension of the piecewise exponential modelling (PEM) approach automatically penalizes model complexity, which is very helpful to avoid over fitting. Conclusions: Flexible parametric time to failure models are more efficient than standard parametric time to failure models. By incorporating time dependent covariates, PAMM is a good approach to perform in-depth studies of predictors over different finite intervals of follow-up time. Until now, this approach is rarely used in time to failure right censored studies.

A Class of Exponentiated Regression Model for Non Negative Censored Data with an Application to Antibody Response to Vaccine

In this paper, an asymmetric regression model for censored non-negative data based on the centred exponentiated log-skew-normal and Bernoulli distributions mixture is introduced. To connect the discrete part with the continuous distribution, the logit link function is used. The parameters of the model are estimated by using the likelihood maximum method. The score function and the information matrix are shown in detail. Antibody data from a study of the measles vaccine are used to illustrate applicability of the proposed model, and it was found the best fit to the data with respect to an others models used in the literature.

Mixture of linear experts model for censored data: A novel approach with scale-mixture of normal distributions

Mixture of linear experts (MoE) model is one of the widespread statistical frameworks for modeling, classification, and clustering of data. Built on the normality assumption of the error terms for mathematical and computational convenience, the classical MoE model has two challenges: (1) it is sensitive to atypical observations and outliers, and (2) it might produce misleading inferential results for censored data. The aim is then to resolve these two challenges, simultaneously, by proposing a robust MoE model for model-based clustering and discriminant censored data with the scale-mixture of normal (SMN) class of distributions for the unobserved error terms. An analytical expectation–maximization (EM) type algorithm is developed in order to obtain the maximum likelihood parameter estimates. Simulation studies are carried out to examine the performance, effectiveness, and robustness of the proposed methodology. Finally, a real dataset is used to illustrate the superiority of the new model.

Sure joint feature screening in nonparametric transformation model for right censored data

AbstractExisting screening procedures for right censored data either posit a specific model or adopt a marginal approach; hence, they are prone to model misspecification or erroneous screening. To address these problems, we develop a joint feature screening method in nonparametric transformation models for censored survival data. A sparsity‐restricted estimator is proposed using a smoothed partial rank objective function and an iterative hard thresholding algorithm. We rigorously show that with probability tending to 1, the proposed method is capable of retaining all relevant features in the model and is more desirable than marginal screening. Furthermore, because the transformation model encompasses many popular models, such as the Cox model, as special cases, the developed joint screening method is more robust than its competitors. Its finite sample performance is illustrated using both simulation studies and a real data example. We have implemented our method using Matlab and made it available through Github https://github.com/yiucla/SPR-SJS.

A Mortality Approach for Estimating the Probability of Default in Credit Risk

Credit risk is an important problem in banking, finance and insurance sectors. The financial institutions have to use information related to some specific characteristics of borrowers, such as borrower reputation, capital and capacity in order to make the right decision whether or not to grant credit. Regulatory capital allows banks to better capture unique risks and exposure cash flows. In this work, we propose a new approach to estimate the probability of default (PD) by using mortality tables based on progressive censored. The PD is a crucial value, which is used in computing the required capital against credit risk exposures. We use the internal rate approach and measure the PD based on time of default. Then we create a new model for Progressive censored data. The new model takes advantage simultaneously from both the progressively censored and Moody’s models, and where the objective is to compute the cumulative probability. The overall proposed approach is illustrated by examples to show its applicability and demonstrate its performance. Our research findings show that the PD based survival analysis for progressive censored increases each year similar to Moody’s. It impacts on worst –case default rate and the maturity adjustment.

A new approach to measure systemic risk: A bivariate copula model for dependent censored data

We propose a novel approach based on the Marshall–Olkin (MO) copula to estimate the impact of systematic and idiosyncratic components on cross-border systemic risk. To use the data on non-failed banks in the suggested method, we consider the time to bank failure as a censored variable. Therefore, we propose a pseudo-maximum likelihood estimation procedure for the MO copula for a Type I censored sample. We derive the log-likelihood function, the copula parameter estimator and the bootstrap confidence intervals. Empirical data on the banking system of three European countries (Germany, Italy and the UK) shows that the proposed censored model can accurately estimate the systematic component of cross-border systemic risk.

Substantial Bias in the Tobit Estimator: Making a Case for Alternatives

Censored outcome data are commonly encountered in criminology. Criminologists sometimes use the tobit model to address these censored data. While tobit models make more realistic demands of censored outcome data than ordinary least squares (OLS) regression, they require the researcher to make strong distributional assumptions. When these assumptions are not met, as is often the case in criminological data, tobit models yield biased and inconsistent estimates. We seek to demonstrate this substantial bias in simulation analyses and present easily applied alternative methods. The tobit model and semiparametric alternatives for censored outcome data are applied with simulated data under varying conditions. These simulations are followed with an empirical example using sentencing data. The bias from tobit can be corrected through application of semiparametric alternatives. Criminologists should begin their analyses of censored outcome data with the least restrictive of the available models (CLAD) before progressing to more efficient, but potentially biased, estimators.

Cash flow statements and firm value: Evidence from Taiwan

By studying cash flows from operating, investing, and financing activities, we explore the effect of these various cash flows on firm value by employing censored panel data models due to concerning panel data employed and characteristics of dependent variables. Results imply that firms raising funds for capital budgeting projects can enhance their firm value, resulting in cash inflows from financing activities and cash outflows to investing activities consistent with our cognitions. However, results reveal that cash inflows from operating activities may not be regarded as a positive signal different from the relevant studies. We infer that the market is increasingly competitive for Taiwanese enterprises due to more and more competitors from South Korea and China; in addition, we argue that firm value might not be enhanced if cash inflows from operating resulting from sales increased due to lower profit margin or purchases shrunk owing to market share declined.

Bayesian semiparametric failure time models for multivariate censored data with latent variables.

In this paper, we propose a semiparametric failure time model to analyze multivariate censored data with latent variables. The proposed model generalizes the conventional accelerated failure time model to accommodate latent risk factors that could be measured by multiple observed variables through a factor analysis and to incorporate additive nonparametric functions of observed and latent risk factors to examine their functional effects on multivariate failure times of interest. A Bayesian approach, along with Bayesian P-splines and Markov chain Monte Carlo techniques, is developed to estimate the unknown parameters and functions. The empirical performance of the proposed methodology is evaluated by a simulation study. An application to a study on the risk factors of two diabetes complications is presented.

A multiple imputation method based on weighted quantile regression models for longitudinal censored biomarker data with missing values at early visits

BackgroundIn patient-based studies, biomarker data are often subject to left censoring due to the detection limits, or to incomplete sample or data collection. In the context of longitudinal regression analysis, inappropriate handling of these issues could lead to biased parameter estimates. We developed a specific multiple imputation (MI) strategy based on weighted censored quantile regression (CQR) that not only accounts for censoring, but also missing data at early visits when longitudinal biomarker data are modeled as a covariate.MethodsWe assessed through simulation studies the performances of developed imputation approach by considering various scenarios of covariance structures of longitudinal data and levels of censoring. We also illustrated the application of the proposed method to the Prospective Study of Outcomes in Ankylosing spondylitis (AS) (PSOAS) data to address the issues of censored or missing C-reactive protein (CRP) level at early visits for a group of patients.ResultsOur findings from simulation studies indicated that the proposed method performs better than other MI methods by having a higher relative efficiency. We also found that our approach is not sensitive to the choice of covariance structure as compared to other methods that assume normality of biomarker data. The analysis results of PSOAS data from the imputed CRP levels based on our method suggested that higher CRP is significantly associated with radiographic damage, while those from other methods did not result in a significant association.ConclusionThe MI based on weighted CQR offers a more valid statistical approach to evaluate a biomarker of disease in the presence of both issues with censoring and missing data in early visits.

Additive risks regression model for middle censored exponentiated-exponential lifetime data

ABSTRACTJammalamadaka and Mangalam introduced middle censoring which refers to data arising in situations, where the exact lifetime becomes unobservable if it falls within a random censoring interval. In the present article, we propose an additive risks regression model for a lifetime data subject to middle censoring, where the lifetimes are assumed to follow exponentiated exponential distribution. The regression parameters are estimated using the Expectation-Maximization algorithm. Asymptotic normality of the estimator is proposed. We report a simulation study to assess the finite sample properties of the estimator. We then analyze a real-life data on survival times of larynx cancer patients studied by Karduan.

A flexible semiparametric regression model for bimodal, asymmetric and censored data

ABSTRACTIn this paper, we propose a new semiparametric heteroscedastic regression model allowing for positive and negative skewness and bimodal shapes using the B-spline basis for nonlinear effects. The proposed distribution is based on the generalized additive models for location, scale and shape framework in order to model any or all parameters of the distribution using parametric linear and/or nonparametric smooth functions of explanatory variables. We motivate the new model by means of Monte Carlo simulations, thus ignoring the skewness and bimodality of the random errors in semiparametric regression models, which may introduce biases on the parameter estimates and/or on the estimation of the associated variability measures. An iterative estimation process and some diagnostic methods are investigated. Applications to two real data sets are presented and the method is compared to the usual regression methods.

Identification of Panel Data Models with Endogenous Censoring

This paper analyzes the identification question in censored panel data models, where the censoring can depend on both observable and unobservable variables in arbitrary ways. Under some general conditions, we derive the tightest sets on the parameter of interest. These sets (which can be singletons) represent the limit of what one can learn about the parameter of interest given the model and the data in that every parameter that belongs to these sets is observationally equivalent to the true parameter. We consider two separate sets of assumptions, motivated by the previous literature, each controlling for unobserved heterogeneity with an individual specific (fixed) effect. The first imposes a stationarity assumption on the unobserved disturbance terms, along the lines of Manski (1987), and Honore (1993). The second is a nonstationary model that imposes a conditional independence assumption. For both models, we provide sufficient conditions for these models to point identify the parameters. Since our identified sets are defined through parameters that obey first order dominance, we outline easily implementable approaches to build confidence regions based on recent advances in Linton et.al.(2010) on bootstrapping tests of stochastic dominance. We also extend our results to dynamic versions of the censored panel models in which we consider lagged observed, latent dependent variables and lagged censoring indicator variables as regressors.

Empirical Likelihood for Censored Linear Regression and Variable Selection.

The linear regression model for right censored data, also known as the accelerated failure time model using the logarithm of survival time as the response variable, is a useful alternative to the Cox proportional hazards model. Empirical likelihood as a nonparametric approach has been demonstrated to have many desirable merits thanks to its robustness against model misspecification. However, the linear regression model with right censored data cannot directly benefit from the empirical likelihood for inferences mainly due to dependent elements in estimating equations of the conventional approach. In this paper, we propose an empirical likelihood approach with a new estimating equation for linear regression with right censored data. A nested coordinate algorithm with majorization is used for solving the optimization problems with nondifferentiable objective function. We show that the Wilks theorem holds for the new empirical likelihood. We also consider the variable selection problem with empirical likelihood when the number of predictors can be large. Since the new estimating equation is nondifferentiable, a quadratic approximation is applied to study the asymptotic properties of penalized empirical likelihood. We prove the oracle properties and evaluate the properties with simulated data. We apply our method to a SEER small intestine cancer dataset.

Efficient Sampling Methods for Truncated Multivariate Normal and Student-tDistributions Subject to Linear Inequality Constraints

Sampling from a truncated multivariate distribution subject to multiple linear inequality constraints is a recurring problem in many areas in statistics and econometrics, such as the order-restricted regressions, censored data models, and shape-restricted nonparametric regressions. However, the sampling problem remains nontrivial due to the analytically intractable normalizing constant of the truncated multivariate distribution. We first develop an efficient rejection sampling method for the truncated univariate normal distribution, and analytically establish its superiority in terms of acceptance rates compared to some of the popular existing methods. We then extend our methodology to obtain samples from a truncated multivariate normal distribution subject to convex polytope restriction regions. Finally, we generalize the sampling method to truncated scale mixtures of multivariate normal distributions. Empirical results are presented to illustrate the superior performance of our proposed Gibbs sampler in...