Estimation of the linear EV model with censored data

In this paper, a censored linear errors-in-variables model is investigated. The asymptotic normality of the unknown parameter's estimator is obtained. Two empirical log-likelihood ratio statistics for the unknown parameter in the model are suggested. It is proved that the proposed statistics are asymptotically chi-squared under some mild conditions, and hence can be used to construct the confidence regions of the parameter of interest. Finite sample performance of the proposed method is illustrated in a simulation study.     

On goodness-of-fit tests for Aalen's additive model based on left-truncated right-censored or doubly censored data

ABSTRACT

Gandy and Jensen (2005 Gandy, A., Jensen, U. (2005). On goodness-of-fit tests for Aalen's additive risk model. Scan. J. Stat. 32:425–445.[Crossref], [Web of Science ®] , [Google Scholar]) proposed goodness-of-fit tests for Aalen's additive risk model. In this article, we demonstrate that the approach of Gandy and Jensen (2005 Gandy, A., Jensen, U. (2005). On goodness-of-fit tests for Aalen's additive risk model. Scan. J. Stat. 32:425–445.[Crossref], [Web of Science ®] , [Google Scholar]) can be applied to left-truncated right-censored (LTRC) data and doubly censored data. A simulation study is conducted to investigate the performance of the proposed tests. The proposed tests are illustrated using heart transplant data.     

Reliability of a soccer player based on the bivariate Rayleigh distribution with right censored and ignorable missing data

In this paper, we study the performance of a soccer player based on analysing an incomplete data set. To achieve this aim, we fit the bivariate Rayleigh distribution to the soccer dataset by the maximum likelihood method. In this way, the missing data and right censoring problems, that usually happen in such studies, are considered. Our aim is to inference about the performance of a soccer player by considering the stress and strength components. The first goal of the player of interest in a match is assumed as the stress component and the second goal of the match is assumed as the strength component. We propose some methods to overcome incomplete data problem and we use these methods to inference about the performance of a soccer player.     

A proportional hazards model for the analysis of doubly censored competing risks data

ABSTRACT

Competing risks data are common in medical research in which lifetime of individuals can be classified in terms of causes of failure. In survival or reliability studies, it is common that the patients (objects) are subjected to both left censoring and right censoring, which is refereed as double censoring. The analysis of doubly censored competing risks data in presence of covariates is the objective of this study. We propose a proportional hazards model for the analysis of doubly censored competing risks data, using the hazard rate functions of Gray (1988 Gray, R.J. (1988). A class of k-sample tests for comparing the cumulative incidence of a competing risk. Ann. Statist. 16:1141–1154.[Crossref], [Web of Science ®] , [Google Scholar]), while focusing upon one major cause of failure. We derive estimators for regression parameter vector and cumulative baseline cause specific hazard rate function. Asymptotic properties of the estimators are discussed. A simulation study is conducted to assess the finite sample behavior of the proposed estimators. We illustrate the method using a real life doubly censored competing risks data.     

A modified chi-square test for Bertholon model with censored data

In this work, we propose the construction of a chi-squared goodness-of-fit test in censored data case, for Bertholon model which can analyse various competing risks of failure or death. This test is based on a modification of the Nikulin-Rao-Robson (NRR) statistic proposed by Bagdonavicius and Nikulin (2011a Bagdonavicius, V., Nikulin, M. (2011a). Chi-squared tests for general composite hypotheses from censored samples. Comptes Rendus Mathématiques: Series I 349(3–4):219–223. [Google Scholar], 2011b Bagdonavicius, V., Nikulin, M. (2011b). Chi-squared goodness-of-fit test for right censored data. International Journal of Applied Mathematics and Statistics 24:30–50. [Google Scholar]) for censored data. We applied this test to numerical examples from simulated samples and real data.     

Methods of Statistical Inference for Median Regression Models with Doubly Censored Data

Recently, least absolute deviations (LAD) estimator for median regression models with doubly censored data was proposed and the asymptotic normality of the estimator was established. However, it is invalid to make inference on the regression parameter vectors, because the asymptotic covariance matrices are difficult to estimate reliably since they involve conditional densities of error terms. In this article, three methods, which are based on bootstrap, random weighting, and empirical likelihood, respectively, and do not require density estimation, are proposed for making inference for the doubly censored median regression models. Simulations are also done to assess the performance of the proposed methods.     

Cure rate model with bivariate interval censored data

A mixture model is proposed to analyze a bivariate interval censored data with cure rates. There exist two types of association related with bivariate failure times and bivariate cure rates, respectively. A correlation coefficient is adopted for the association of bivariate cure rates and a copula function is applied for bivariate survival times. The conditional expectation of unknown quantities attributable to interval censored data and cure rates are calculated in the E-step in ES (Expectation-Solving algorithm) and the marginal estimates and the association measures are estimated in the S-step through a two-stage procedure. A simulation study is performed to evaluate the suggested method and a real data from HIV patients is analyzed as a real data example.     

A semiparametric shock model for a pair of event-related dependent censored failure times

In this paper, we propose a semiparametric shock model for two dependent failure times where the risk indicator of one failure time plays the part of a time-varying covariate for the other one. According to Hougaard [2000. Analysis of Multivariate Survival Data. Springer, New York], the dependence between the two failure times is therefore of event-related type.     

Empirical likelihood ratio confidence intervals in terms of cumulative hazard function for left-truncated and right-censored data

Abstract

Based on the approach of Pan and Zhou, we demonstrate that empirical likelihood ratios in terms of cumulative hazard function for left-truncated and right-censored (LTRC) data can be used to form confidence intervals for the parameters that are linear functionals of the cumulative hazard function. Simulation studies indicate that the empirical likelihood ratio based confidence intervals work well in finite samples.     

Estimation of bivariate and marginal distributions with censored data

Summary. Consider a pair of random variables, both subject to random right censoring. New estimators for the bivariate and marginal distributions of these variables are proposed. The estimators of the marginal distributions are not the marginals of the corresponding estimator of the bivariate distribution. Both estimators require estimation of the conditional distribution when the conditioning variable is subject to censoring. Such a method of estimation is proposed. The weak convergence of the estimators proposed is obtained. A small simulation study suggests that the estimators of the marginal and bivariate distributions perform well relatively to respectively the Kaplan–Meier estimator for the marginal distribution and the estimators of Pruitt and van der Laan for the bivariate distribution. The use of the estimators in practice is illustrated by the analysis of a data set.     

Inference on semiparametric transformation model with general interval-censored failure time data

Failure time data occur in many areas and in various censoring forms and many models have been proposed for their regression analysis such as the proportional hazards model and the proportional odds model. Another choice that has been discussed in the literature is a general class of semiparmetric transformation models, which include the two models above and many others as special cases. In this paper, we consider this class of models when one faces a general type of censored data, case K informatively interval-censored data, for which there does not seem to exist an established inference procedure. For the problem, we present a two-step estimation procedure that is quite flexible and can be easily implemented, and the consistency and asymptotic normality of the proposed estimators of regression parameters are established. In addition, an extensive simulation study is conducted and suggests that the proposed procedure works well for practical situations. An application is also provided.     

Foundational issues concerning the analysis of censored data

The common approach to analyzing censored data utilizes competing risk models; a class of distribution is first chosen and then the sufficient statistics are identified! An operational Bayesian approach (Barlow 1993) for analyzing censored data would require a somewhat different methodology. In this approach, we first determine potentially observable parameters of interest. We then determine the data summaries (sufficient statistics) for these parameters. Tsai (1994) suggests that the observed sample frequency is sufficient for predicting the population frequency. Invariant probability measures (likelihoods), conditional on the parameters of interest, are then derived based on the principle of sufficiency and the principle of insufficient reason.Research partially supported by the Army Research Office (DAAL03-91-G-0046) grant to the University of California at Berkeley.     

Maximum likelihood estimation for the proportional odds model with mixed interval-censored failure time data

This article discusses regression analysis of mixed interval-censored failure time data. Such data frequently occur across a variety of settings, including clinical trials, epidemiologic investigations, and many other biomedical studies with a follow-up component. For example, mixed failure times are commonly found in the two largest studies of long-term survivorship after childhood cancer, the datasets that motivated this work. However, most existing methods for failure time data consider only right-censored or only interval-censored failure times, not the more general case where times may be mixed. Additionally, among regression models developed for mixed interval-censored failure times, the proportional hazards formulation is generally assumed. It is well-known that the proportional hazards model may be inappropriate in certain situations, and alternatives are needed to analyze mixed failure time data in such cases. To fill this need, we develop a maximum likelihood estimation procedure for the proportional odds regression model with mixed interval-censored data. We show that the resulting estimators are consistent and asymptotically Gaussian. An extensive simulation study is performed to assess the finite-sample properties of the method, and this investigation indicates that the proposed method works well for many practical situations. We then apply our approach to examine the impact of age at cranial radiation therapy on risk of growth hormone deficiency in long-term survivors of childhood cancer.     

Nonparametric estimation of the bivariate cdf for arbitrarily censored data

Right, left or interval censored multivariate data can be represented by an intersection graph. Focussing on the bivariate case, the authors relate the structure of such an intersection graph to the support of the nonparametric maximum likelihood estimate (NPMLE) of the cumulative distribution function (CDF) for such data. They distinguish two types of non‐uniqueness of the NPMLE: representational, arising when the likelihood is unaffected by the distribution of the estimated probability mass within regions, and mixture, arising when the masses themselves are not unique. The authors provide a brief overview of estimation techniques and examine three data sets.     

Statistical analysis of data from dilution assays with censored correlated counts

Frequently, count data obtained from dilution assays are subject to an upper detection limit, and as such, data obtained from these assays are usually censored. Also, counts from the same subject at different dilution levels are correlated. Ignoring the censoring and the correlation may provide unreliable and misleading results. Therefore, any meaningful data modeling requires that the censoring and the correlation be simultaneously addressed. Such comprehensive approaches of modeling censoring and correlation are not widely used in the analysis of dilution assays data. Traditionally, these data are analyzed using a general linear model on a logarithmic-transformed average count per subject. However, this traditional approach ignores the between-subject variability and risks, providing inconsistent results and unreliable conclusions. In this paper, we propose the use of a censored negative binomial model with normal random effects to analyze such data. This model addresses, in addition to the censoring and the correlation, any overdispersion that may be present in count data. The model is shown to be widely accessible through the use of several modern statistical software.     

Estimation in the Cox proportional hazards model with doubly censored and truncated data

In longitudinal studies, the proportional hazard model is often used to analyse covariate effects on the duration time, defined as the elapsed time between the first and second event. In this article, we consider the situation when the first event suffers partly interval-censoring and the second event suffers left-truncation and right-censoring. We proposed a two-step estimation procedure for estimating the regression coefficients of the proportional model. A simulation study is conducted to investigate the performance of the proposed estimator.     

Exact inference for a simple step-stress model with Type-II hybrid censored data from the exponential distribution

In reliability and life-testing experiments, the researcher is often interested in the effects of extreme or varying stress factors such as temperature, voltage and load on the lifetimes of experimental units. Step-stress test, which is a special class of accelerated life-tests, allows the experimenter to increase the stress levels at fixed times during the experiment in order to obtain information on the parameters of the life distributions more quickly than under normal operating conditions. In this paper, we consider a new step-stress model in which the life-testing experiment gets terminated either at a pre-fixed time (say, _Tm+1$T_{m+1}$) or at a random time ensuring at least a specified number of failures (say, r out of n). Under this model in which the data obtained are Type-II hybrid censored, we consider the case of exponential distribution for the underlying lifetimes. We then derive the maximum likelihood estimators (MLEs) of the parameters assuming a cumulative exposure model with lifetimes being exponentially distributed. The exact distributions of the MLEs of parameters are obtained through the use of conditional moment generating functions. We also derive confidence intervals for the parameters using these exact distributions, asymptotic distributions of the MLEs and the parametric bootstrap methods, and assess their performance through a Monte Carlo simulation study. Finally, we present two examples to illustrate all the methods of inference discussed here.     

A class of nonparametric bivariate survival function estimators for randomly censored and truncated data

This paper proposes a class of nonparametric estimators for the bivariate survival function estimation under both random truncation and random censoring. In practice, the pair of random variables under consideration may have certain parametric relationship. The proposed class of nonparametric estimators uses such parametric information via a data transformation approach and thus provides more accurate estimates than existing methods without using such information. The large sample properties of the new class of estimators and a general guidance of how to find a good data transformation are given. The proposed method is also justified via a simulation study and an application on an economic data set.