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??In survival analysis, most existing approaches for analysing right-censored failure time data assume that the censoring time is independent of the failure time. However, investigators often face problems involving dependent censoring, i.e., failure time and censoring time are possibly dependent and they may be censored one another, especially in clinical trials. Without accounting for such dependence, survival distributions cannot be estimated consistently. Numerous attempts to model this dependence have been made. Among them, copula models are of particular interest because of their simple structure. Proportional hazard model analysis for informative right-censored data has been discussed in this paper. An Archimedean copula is assumed for the joint distribution function of failure time and censoring time variables. Under the conditions of identifiability of the parameter of the Archimedean copula, the maximum likelihood estimators of the parameter of Archimedean copula, the parameters and the cumulative hazard function of PH model are worked out. Extensive simulation studies show that the feasibility of the proposed method and the consistency of the estimators.     

Nonparametric estimation of interval-censored failure time data in the presence of informative censoring

Nonparametric estimation of a survival function is one of the most commonly asked questions in the analysis of failure time data and for this, a number of procedures have been developed under various types of censoring structures (Kalbfleisch and Prentice, 2002). In particular, several algorithms are available for interval-censored failure time data with independent censoring mechanism (Sun, 2006; Turnbull, 1976). In this paper, we consider the interval-censored data where the censoring mechanism may be related to the failure time of interest, for which there does not seem to exist a nonparametric estimation procedure. It is well-known that with informative censoring, the estimation is possible only under some assumptions. To attack the problem, we take a copula model approach to model the relationship between the failure time of interest and censoring variables and present a simple nonparametric estimation procedure. The method allows one to conduct a sensitivity analysis among others.     

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In this paper, a nonparametric method for reliability of the stress-strength model is proposed when the dependent stress variable and strength variable are subject to right censoring. The dependence between variables is measured by the common Farlie-Gumbel-Morgenstern copula function and Clayton copula function. Using the empirical process theory, consistency and asymptotic normality of the proposed estimator is established in this paper. The results of numerical simulation show that the proposed method performs well in the case of finite sample. The method proposed in this paper has a wide application prospect in practice.     

Adjusted Log-rank Test with Double Inverse Weighting under Dependent Censoring

It is a common issue to compare treatment-specific survival and the weighted log-rank test is the most popular method for group comparison. However, in observational studies, treatments and censoring times are usually not independent, which invalidates the weighted log-rank tests. In this paper, we propose adjusted weighted log-rank tests in the presence of non-random treatment assignment and dependent censoring. A double-inverse weighted technique is developed to adjust the weighted log-rank tests. Specifically, inverse probabilities of treatment and censoring weighting are involved to balance the baseline treatment assignment and to overcome dependent censoring, respectively. We derive the asymptotic distribution of the proposed adjusted tests under the null hypothesis, and propose a method to obtain the critical values. Simulation studies show that the adjusted log-rank tests have correct sizes whereas the traditional weighted log-rank tests may fail in the presence of non-random treatment assignment and dependent censoring. An application to oropharyngeal carcinoma data from the Radiation Therapy Oncology Group is provided for illustration.     

A novel means of estimating quantiles for 2-parameter Weibull distribution under the right random censoring model

Censoring models are frequently used in reliability analysis to reduce experimental time. The three types of censoring models are type-I, type-II and random censoring. In this study, we focus on the right random censoring model. In this model, if the failure time exceeds its associated censoring time, then the failure time becomes a censored observation. In this case, many authors (see: Lee, Statistical Methods for Survival Data Analysis, 2nd Edition, Wiley, New York, 1992; Lawless, Statistical Models and Methods for Lifetime Data, Wiley, New York, 1982; Miller, Survival Analysis, Wiley, New York, 1981, among others) considered using the observed censoring time to impute the censored observation which, however, underestimates the true failure time. Herein, two methods to impute the censored observations are proposed in a right random censoring model for a 2-parameter Weibull distribution. By a Monte Carlo simulation, the quantile estimates are calculated to assess the performance of the proposed imputation methods with respect to their relative mean square error. Simulation results indicate that the two imputation methods proposed herein are superior to the method proposed by the above authors if the shape parameter of Weibull distribution exceeds 1, except for the lower quantiles.     

Piecewise Linear Approximations for Cure Rate Models and Associated Inferential Issues

Cure rate models offer a convenient way to model time-to-event data by allowing a proportion of individuals in the population to be completely cured so that they never face the event of interest (say, death). The most studied cure rate models can be defined through a competing cause scenario in which the random variables corresponding to the time-to-event for each competing causes are conditionally independent and identically distributed while the actual number of competing causes is a latent discrete random variable. The main interest is then in the estimation of the cured proportion as well as in developing inference about failure times of the susceptibles. The existing literature consists of parametric and non/semi-parametric approaches, while the expectation maximization (EM) algorithm offers an efficient tool for the estimation of the model parameters due to the presence of right censoring in the data. In this paper, we study the cases wherein the number of competing causes is either a binary or Poisson random variable and a piecewise linear function is used for modeling the hazard function of the time-to-event. Exact likelihood inference is then developed based on the EM algorithm and the inverse of the observed information matrix is used for developing asymptotic confidence intervals. The Monte Carlo simulation study demonstrates the accuracy of the proposed non-parametric approach compared to the results attained from the true correct parametric model. The proposed model and the inferential method is finally illustrated with a data set on cutaneous melanoma.     

Joint modeling for mixed-effects quantile regression of longitudinal data with detection limits and covariates measured with error,with application to AIDS studies

It is very common in AIDS studies that response variable (e.g., HIV viral load) may be subject to censoring due to detection limits while covariates (e.g., CD4 cell count) may be measured with error. Failure to take censoring in response variable and measurement errors in covariates into account may introduce substantial bias in estimation and thus lead to unreliable inference. Moreover, with non-normal and/or heteroskedastic data, traditional mean regression models are not robust to tail reactions. In this case, one may find it attractive to estimate extreme causal relationship of covariates to a dependent variable, which can be suitably studied in quantile regression framework. In this paper, we consider joint inference of mixed-effects quantile regression model with right-censored responses and errors in covariates. The inverse censoring probability weighted method and the orthogonal regression method are combined to reduce the biases of estimation caused by censored data and measurement errors. Under some regularity conditions, the consistence and asymptotic normality of estimators are derived. Finally, some simulation studies are implemented and a HIV/AIDS clinical data set is analyzed to to illustrate the proposed procedure.     

Asymptotics for non-parametric likelihood estimation with doubly censored multivariate failure times

This paper considers non-parametric estimation of a multivariate failure time distribution function when only doubly censored data are available, which occurs in many situations such as epidemiological studies. In these situations, each of multivariate failure times of interest is defined as the elapsed time between an initial event and a subsequent event and the observations on both events can suffer censoring. As a consequence, the estimation of multivariate distribution is much more complicated than that for multivariate right- or interval-censored failure time data both theoretically and practically. For the problem, although several procedures have been proposed, they are only ad-hoc approaches as the asymptotic properties of the resulting estimates are basically unknown. We investigate both the consistency and the convergence rate of a commonly used non-parametric estimate and show that as the dimension of multivariate failure time increases or the number of censoring intervals of multivariate failure time decreases, the convergence rate for non-parametric estimate decreases, and is slower than that with multivariate singly right-censored or interval-censored data.     

Semiparametric quantile regression with random censoring

This paper considers estimation and inference in semiparametric quantile regression models when the response variable is subject to random censoring. The paper considers both the cases of independent and dependent censoring and proposes three iterative estimators based on inverse probability weighting, where the weights are estimated from the censoring distribution using the Kaplan–Meier, a fully parametric and the conditional Kaplan–Meier estimators. The paper proposes a computationally simple resampling technique that can be used to approximate the finite sample distribution of the parametric estimator. The paper also considers inference for both the parametric and nonparametric components of the quantile regression model. Monte Carlo simulations show that the proposed estimators and test statistics have good finite sample properties. Finally, the paper contains a real data application, which illustrates the usefulness of the proposed methods.

     

Smoothing estimation of rate function for recurrent event data with informative censoring

This paper proposes kernel estimation of the occurrence rate function for recurrent event data with informative censoring. An informative censoring model is considered with assumptions made on the joint distribution of the recurrent event process and the censoring time without modeling the censoring distribution. Under the validity of the informative censoring model, we also show that an estimator based on the assumption of independent censoring becomes inappropriate and is generally asymptotically biased. To investigate the asymptotic properties of the proposed estimator, the explicit form of its asymptotic mean squared risk and the asymptotic normality are derived. Meanwhile, the empirical consistent smoothing estimator for the variance function of the estimator is suggested. The performance of the estimators are also studied through Monte Carlo simulations. An epidemiological example of intravenous drug user data is used to show the influence of informative censoring in the estimation of the occurrence rate functions for inpatient cares over time.