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The simultaneous estimation and variable selection for Cox model has been discussed by several authors when one observes right-censored failure time data. However, there does not seem to exist an established procedure for interval-censored data, a more general and complex type of failure time data, except two parametric procedures. To address this, we propose a broken adaptive ridge (BAR) regression procedure that combines the strengths of the quadratic regularization and the adaptive weighted bridge shrinkage. In particular, the method allows for the number of covariates to be diverging with the sample size. Under some weak regularity conditions, unlike most of the existing variable selection methods, we establish both the oracle property and the grouping effect of the proposed BAR procedure. An extensive simulation study is conducted and indicates that the proposed approach works well in practical situations and deals with the collinearity problem better than the other oracle-like methods. An application is also provided.

We introduce a quantile-adaptive framework for nonlinear variable screening with high-dimensional heterogeneous data. This framework has two distinctive features: (1) it allows the set of active variables to vary across quantiles, thus making it more flexible to accommodate heterogeneity; (2) it is model-free and avoids the difficult task of specifying the form of a statistical model in a high dimensional space. Our nonlinear independence screening procedure employs spline approximations to model the marginal effects at a quantile level of interest. Under appropriate conditions on the quantile functions without requiring the existence of any moments, the new procedure is shown to enjoy the sure screening property in ultra-high dimensions. Furthermore, the quantile-adaptive framework can naturally handle censored data arising in survival analysis. We prove that the sure screening property remains valid when the response variable is subject to random right censoring. Numerical studies confirm the fine performance of the proposed method for various semiparametric models and its effectiveness to extract quantilespecific information from heteroscedastic data.

In analysis of survival data, the Accelerated Life Model (ALM) is one of the widely used semiparametric models, and we often encounter various types of censored survival data, such as right censored data, doubly censored data, interval censored data, partly interval-censored data, etc. For complicated types of censored data, the studies of statistical inferences on the ALM are very technical and challenging mathematically, thus up to now little work has been done. In this article, we extend the concept of weighted empirical likelihood (WEL) from univariate case to multivariate case, and we apply it to the ALM, which leads to an estimation approach, called weighted maximum likelihood estimator, as well as the WEL based confidence interval for the regression parameter. Our proposed procedures are applicable to various types of censored data under a unified framework, and some simulation results are presented.

The proportional hazards model (PH) is currently the most popular regression model for analyzing time-to-event data. Despite its popularity, the analysis of interval-censored data under the PH model can be challenging using many available techniques. This article presents a new method for analyzing interval-censored data under the PH model. The proposed approach uses a monotone spline representation to approximate the unknown nondecreasing cumulative baseline hazard function. Formulating the PH model in this fashion results in a finite number of parameters to estimate while maintaining substantial modeling flexibility. A novel expectation-maximization (EM) algorithm is developed for finding the maximum likelihood estimates of the parameters. The derivation of the EM algorithm relies on a two-stage data augmentation involving latent Poisson random variables. The resulting algorithm is easy to implement, robust to initialization, enjoys quick convergence, and provides closed-form variance estimates. The performance of the proposed regression methodology is evaluated through a simulation study, and is further illustrated using data from a large population-based randomized trial designed and sponsored by the United States National Cancer Institute.

This study focuses on estimating a nonparametric regression model with right-censored data when the covariate is subject to measurement error. To achieve this goal, it is necessary to solve the problems of censorship and measurement error ignored by many researchers. Note that the presence of measurement errors causes biased and inconsistent parameter estimates. Moreover, non-parametric regression techniques cannot be applied directly to right-censored observations. In this context, we consider an updated response variable using the Buckley–James method (BJM), which is essentially based on the Kaplan–Meier estimator, to solve the censorship problem. Then the measurement error problem is handled using the kernel deconvolution method, which is a specialized tool to solve this problem. Accordingly, three denconvoluted estimators based on BJM are introduced using kernel smoothing, local polynomial smoothing, and B-spline techniques that incorporate both the updated response variable and kernel deconvolution.The performances of these estimators are compared in a detailed simulation study. In addition, a real-world data example is presented using the Covid-19 dataset.

Doubly interval-censored data (DICD) often emerge in longitudinal studies, where the survival time, T = W − V, denotes the duration between two connected events: the initial event time (V) and the subsequent event time (W), both of which are subject to interval censoring (IC). Such data are prevalent in medical and epidemiological research, especially when event occurrences are observed only within specific intervals because of the nature of study designs or periodic assessments. Analysing DICD poses unique challenges: the lack of exact event times introduces complexities in modelling, estimation, and inference, which leads to biased regression parameter estimates and higher standard errors, if not handled appropriately. Existing methods often struggle with computational demands and theoretical constraints, particularly in scenarios involving small sample sizes or irregular censoring intervals. This study provides a comprehensive overview of the methods developed to analyse DICD, examining their strengths, limitations, and practical applications. We systematically reviewed the literature to achieve this goal, focusing on studies retrieved from PUBMED, Scopus, Embase, and CINAHL from database inception through June 2024. Among the 462 screened studies, 52 met the inclusion criteria, with applications of DICD most commonly arising in medical research. We distilled 8 key topic areas based on the synthesis of available literature and underscore the importance of understanding and appropriately analysing DICD to ensure accurate inferences and informed decision-making across various scientific disciplines. This review highlights how authors justify the use of DICD, the methods employed, and the limitations addressed, offering valuable insights into this specialized area of survival analysis.A review of the approaches created to manage DICD, including their advantages, disadvantages, and practical applications, is provided.The approach is extractive and is based on 8 key topic areas to analyse DICD appropriately.This study highlights the diverse methods employed for handling DICD in survival analysis and outlines how researchers have addressed DICD, consolidating all ideas into a cohesive overview.

In this article, we introduce a new continuous probability distribution called the Inverse Exponential Logistic Lehmann Type II distribution, derived from the Lehmann Type II alternative. The main objective is to apply this new distribution to survival analysis, specifically with right-censored data. We discuss various properties of the proposed distribution, including quantiles, skewness, kurtosis, moments, order statistics, and Rényi entropy. The distribution exhibits a hazard rate function with different shapes depending on the parameter values. Simulation studies were conducted to evaluate the performance of maximum likelihood estimates under a right censoring scheme. Finally, we illustrate the usefulness and flexibility of the proposed distribution by applying it to two real datasets and comparing its performance with that of other distributions. En este artículo, presentamos una nueva distribución de probabilidad continúa denominada distribución Exponencial Inversa Logística Lehmann Tipo II, derivada de la alternativa Lehmann Tipo II. El objetivo principal es aplicar esta nueva distribución al análisis de supervivencia, específicamente con datos censurados por la derecha. Discutimos diversas propiedades de la distribución propuesta, incluyendo cuantiles, asimetría, curtosis, momentos, estadísticos de orden y entropía de Rényi. La distribución exhibe una función de riesgo con diferentes formas dependiendo de los valores de los parámetros. Se realizaron estudios de simulación para evaluar el desempeño de las estimaciones obtenidas por el método de máxima verosimilitud bajo un esquema de censura por la derecha. Finalmente, ilustramos la utilidad y flexibilidad de la distribución propuesta mediante aplicaciones a dos conjuntos de datos reales, comparando su desempeño con otras distribuciones existentes.

In biomedical research, weighted logrank tests are frequently applied to compare two samples of randomly right censored survival times. We address the question how to combine a number of weighted logrank statistics to achieve good power of the corresponding survival test for a whole linear space or cone of alternatives, which are given by hazard rates. This leads to a new class of semiparametric projection tests that are motivated by likelihood ratio tests for an asymptotic model. We show that these tests can be carried out as permutation tests and discuss their asymptotic properties. A simulation study together with the analysis of a classical data set illustrates the advantages.

The proportional hazards mixture cure model is a popular analysis method for survival data where a subgroup of patients are cured. When the data are interval-censored, the estimation of this model is challenging due to its complex data structure. In this article, we propose a computationally efficient semiparametric Bayesian approach, facilitated by spline approximation and Poisson data augmentation, for model estimation and inference with interval-censored data and a cure rate. The spline approximation and Poisson data augmentation greatly simplify the MCMC algorithm and enhance the convergence of the MCMC chains. The empirical properties of the proposed method are examined through extensive simulation studies and also compared with the R package “GORCure”. The use of the proposed method is illustrated through analyzing a data set from the Aerobics Center Longitudinal Study.

This paper introduces a modified local linear estimator (LLR) for partially linear additive models (PLAM) when the response variable is subject to random right-censoring. In the case of modeling right-censored data, PLAM offers a more flexible and realistic approach to the estimation procedure by involving multiple parametric and nonparametric components. This differs from the widely used partially linear models that feature a univariate nonparametric function. The LLR method is employed to estimate unknown smooth functions using a modified backfitting algorithm, delivering a non-iterative solution for the right-censored PLAM. To address the censorship issue, three approaches are employed: synthetic data transformation (ST), Kaplan–Meier weights (KMW), and the kNN imputation technique (kNNI). Asymptotic properties of the modified backfitting estimators are detailed for both ST and KMW solutions. The advantages and disadvantages of these methods are discussed both theoretically and practically. Comprehensive simulation studies and real-world data examples are conducted to assess the performance of the introduced estimators. The results indicate that LLR performs well with both KMW and kNNI in the majority of scenarios, along with a real data example.