Estimation of Survival Function in Cox Regression Model Under Random Censoring From Both Sides

In this article we present three types of parametric–non parametric estimators for conditional survival function in Cox proportional hazards regression model when the lifetime of interest is subjected to random censorship from both sides. We prove consistency and asymptotic normality of estimators.     

Kernel Estimators for Additive Models with Dependent Observations from Random Fields

Nonparametric estimation of the regression function for additive models is investigated in cases where the observed data are dependent. An additive kernel estimator for the regression function under some general mixing conditions is proposed. Under the mixing conditions, the additive kernel estimator is shown to be asymptotically normal.     

Random Weighted Bootstrap Method for Recurrent Events with Informative Censoring

Using the data from the AIDS Link to Intravenous Experiences cohort study as an example, an informative censoring model was used to characterize the repeated hospitalization process of a group of patients. Under the informative censoring assumption, the estimators of the baseline rate function and the regression parameters were shown to be related to a latent variable. Hence, it becomes impractical to directly estimate the unknown quantities in the moments of the estimators for the bandwidth selection of a smoothing estimator and the construction of confidence intervals, which are respectively based on the asymptotic mean squared errors and the asymptotic distributions of the estimators. To overcome these difficulties, we develop a random weighted bootstrap procedure to select appropriate bandwidths and to construct approximated confidence intervals. One can see that our method is simple and faster to implement from a practical point of view, and is at least as accurate as other bootstrap methods. In this article, it is shown that the proposed method is useful through the performance of a Monte Carlo simulation. An application of our procedure is also illustrated by a recurrent event sample of intravenous drug users for inpatient cares over time.     

Homogeneity Tests for Related Samples Under Censoring

We propose nonparametric homogeneity tests for related samples against much wider than location (or scale) class of alternatives including possible crossings of marginal cumulative distribution functions. The tests can be used in the case of complete and censored samples. Asymptotic distribution of the test statistics is investigated.     

Conditional Maximum Likelihood and Interval Estimation for Two Weibull Populations under Joint Type-II Progressive Censoring

Comparative lifetime experiments are important when the object of a study is to determine the relative merits of two competing duration of life products. This study considers the interval estimation for two Weibull populations when joint Type-II progressive censoring is implemented. We obtain the conditional maximum likelihood estimators of the two Weibull parameters under this scheme. Moreover, simultaneous approximate confidence region based on the asymptotic normality of the maximum likelihood estimators are also discussed and compared with two Bootstrap confidence regions. We consider the behavior of probability of failure structure with different schemes. A simulation study is performed and an illustrative example is also given.     

Some asymptotic distribution results in time-sequential estimation of the mean exponential survival time

The asymptotic distribution of the stopping time N in a time-sequential procedure for the estimation of the mean exponential survival time given by Gardiner, Susarla, and van Ryzin (1986) is obtained. The same techniques used to obtain this asymptotic distribution of N are used to obtain the asymptotic distribution of the statistic representing the time-on-test expended per unit item in the study.     

Limit Theory for Random Coefficient First-Order Autoregressive Process

Random coefficient AR(1) processes are investigated where the random coefficient satisfies some suitable conditions. Conditional least squares estimator is shown to be consistent and to be asymptotically normality distributed. This extends the limit theory for stationary and near-stationary cases. Only second moments are assumed, as in the case of stationary autoregression models with fixed coefficient |ρ| < 1.     

Inference Under Right Censoring in a Discrete Setup

In this article, we consider the right random censoring scheme in a discrete setup when the lifetime and censoring variables are independent and have geometric distributions with means 1/θ₁ and 1/θ₂, respectively. We first obtain the Maximum Likelihood and Method of Moment estimators of the unknown parameters. We also find the Bayes and Posterior Regret Gamma Minimax estimators of the parameters for the two cases when the prior distributions are dependent and independent, assuming a squared error loss function. We then discuss the Proportional Hazard model, and obtain Maximum Likelihood estimators of the unknown parameters and derive the Bayes estimators assuming squared error loss using Markov Chain Monte Carlo methods.     

Estimation for the Parameters of the Pareto Distribution Under Progressive Censoring

In this article, progressive Type-II right censored sample from Pareto distribution is considered. Exact confidence region is derived for the parameters of the corresponding distribution under progressive censoring. Simulation study is performed to investigate the coverage probabilities of the proposed confidence region. Illustrative example is also given.     

Wavelet Analysis of Change Points in Nonparametric Hazard Rate Models Under Random Censorship

In this article, we consider detection and estimation of change points in nonparametric hazard rate models. Wavelet methods are utilized to develop a testing procedure for change points detection. The asymptotic properties of the test statistic are explored. When there exist change points in hazard function, we also propose estimators for the number, the locations, and the jump sizes of the change points. The asymptotic properties of these estimators are systematically derived. Some simulation examples are conducted to assess the finite sample performance of the proposed approach and to make comparisons with some existing methods. A real data analysis is provided to illustrate the new approach.     

Marginal Regression Analysis for Semi-Competing Risks Data Under Dependent Censoring

Abstract.  Multiple events data are commonly seen in medical applications. There are two types of events, namely terminal and non-terminal. Statistical analysis for non-terminal events is complicated due to dependent censoring. Consequently, joint modelling and inference are often needed to avoid the problem of non-identifiability. This article considers regression analysis for multiple events data with major interest in a non-terminal event such as disease progression. We generalize the technique of artificial censoring, which is a popular way to handle dependent censoring, under flexible model assumptions on the two types of events. The proposed method is applied to analyse a data set of bone marrow transplantation.     

Exact Interval Estimation for the Scale Family Under General Progressive Type-II Censoring

In this article, we consider a general progressively Type-II censored life test where the lifetime distribution of each test unit belongs to the scale family. We derive an exact confidence interval for the scale parameter. Using Monte Carlo simulation method, we assess the expected lower and upper limits of the proposed confidence interval for the exponential distribution. Finally, we present a numerical example to illustrate the proposed procedure.     

Semiparametric Proportional Mean Residual Life Model With Censoring Indicators Missing at Random

For right-censored survival data, the information that whether the observed time is survival or censoring time is frequently lost. This is the case for the competing risk data. In this article, we consider statistical inference for the right-censored survival data with censoring indicators missing at random under the proportional mean residual life model. Simple and augmented inverse probability weighted estimating equation approaches are developed, in which the nonmissingness probability and some unknown conditional expectations are estimated by the kernel smoothing technique. The asymptotic properties of all the proposed estimators are established, while extensive simulation studies demonstrate that our proposed methods perform well under the moderate sample size. At last, the proposed method is applied to a data set from a stage II breast cancer trial.     

Non‐parametric Copula Estimation Under Bivariate Censoring

In this paper, we consider non‐parametric copula inference under bivariate censoring. Based on an estimator of the joint cumulative distribution function, we define a discrete and two smooth estimators of the copula. The construction that we propose is valid for a large range of estimators of the distribution function and therefore for a large range of bivariate censoring frameworks. Under some conditions on the tails of the distributions, the weak convergence of the corresponding copula processes is obtained in l^∞([0,1]²). We derive the uniform convergence rates of the copula density estimators deduced from our smooth copula estimators. Investigation of the practical behaviour of these estimators is performed through a simulation study and two real data applications, corresponding to different censoring settings. We use our non‐parametric estimators to define a goodness‐of‐fit procedure for parametric copula models. A new bootstrap scheme is proposed to compute the critical values.     

Parameter Estimation for the Tail Distribution of a Random Sequence

The tail Y_t = X_t – u of a random sequence {X_t ∈ , t ∈ } with identically distributed X_t is approximated by the generalized Pareto distribution according to the extreme value theory, wherein Y_t occurs in clusters because of the dependence in the random sequence. Nevertheless, the parameters of the generalized Pareto distribution are estimated by the same methods as in the case of independent and identically distributed Y_t, provided that there is independence between the clusters of Y_t. The estimation variances and confidence intervals can be estimated by the jackknife method. The approaches are theoretically discussed and verified by extensive numerical researches.     

Bayes Estimation Based on Random Censored Data for Some Life Time Models Under Symmetric and Asymmetric Loss Functions

Censored data arise naturally in a number of fields, particularly in problems of reliability and survival analysis. There are several types of censoring; in this article, we shall confine ourselves to the right randomly censoring type. Under the Bayesian framework, we study the estimation of parameters in a general framework based on the random censored observations under Linear-Exponential (LINEX) and squared error loss (SEL) functions. As a special case, Weibull model is discussed and the admissibility of estimators of parameters verified. Finally, a simulation study is conducted based on Monte Carlo (MC) method for comparing estimated risks of the estimators obtained.