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.     

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.     

Nonparametric estimation with doubly censored and truncated data

Data from longitudinal studies in which an initiating event and a subsequent event occur in sequence are called doubly censored data if the time of both events is interval-censored. In some cases, the second event also suffers left-truncation. This article is concerned with using doubly censored and truncated data to estimate the distribution function F of the duration time, i.e. the elapsed time between the originating event and the subsequent event. An iterative procedure is proposed to obtain the estimate of F. A simulation study is conducted to investigate the performance of the proposed estimator. A modified data set is used to illustrate the proposed approach.     

Regression analysis of interval censored and doubly truncated data with linear transformation models

Doubly truncated data appear in a number of applications, including astronomy and survival analysis. For double-truncated data, the lifetime T is observable only when U ≤ T ≤ V, where U and V are the left-truncated and right-truncated time, respectively. In some situation, the lifetime T also suffers interval censoring. This paper considers the estimation of regression parameters under linear transformation models, in the presence of interval-censored and doubly truncated (ICDT) data. It is demonstrated that the approach of Zhang et al. (Can J Stat 33:61–70, 2005) can be extended to analyze ICDT data. The asymptotic properties of the proposed estimator are discussed. A simulation study is conducted to investigate the performance of the proposed estimator.     

A New,Fast Algorithm to Find the Regions of Possible Support for Bivariate Interval-Censored Data

The estimation of the nonparametric maximum likelihood estimate (NPMLE) of the bivariate distribution function on interval-censored data is a recent topic of research. Among other things, it provides a basic tool for checking a parametric model for the bivariate failure times. As a first step in the estimation of the NPMLE for bivariate interval-censored data, the regions of possible support—that is, the rectangles with nonzero mass—are calculated. For this step a new, fast algorithm is introduced here and compared with two existing algorithms. The advantages of our algorithm will be illustrated on the emergence times of permanent teeth on data from the longitudinal Signal® Tandmobiel study.     

区间数据的均值估计

本文在运用无偏转换思想找到区间数据均值估计的基础上,对所找到的估计量的方差进行了研究.针对区间截断情况1和区间截断情况2,找到了估计量方差有限的条件.当截断随机变量的分布在某种程度上比被截断随机变量的分布尾部更厚时,方差有限的估计量可以取到.     

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A cured model is a useful approach for analysing failure time data in which some subjects could eventually experience and others never experience the event of interest. All subjects in the test belong to one of the two groups: the susceptible group and the non-susceptible group. There has been considerable progress in the development of semi-parametric models for regression analysis of time-to-event data. However, most of the current work focuses on right-censored data, especially when the population contains a non-ignorable cured subgroup. In this paper, we propose a semi-parametric cure model for current status data. In general, treatments are developed to both increase the patients' chances of being cured and prolong the survival time among non-cured patients. A logistic regression model is proposed for whether the subject is in the susceptible group. An accelerated failure time regression model is proposed for the event time when the subject is in the non-susceptible group. An EM algorithm is used to maximize the log-likelihood of the observed data. Simulation results show that the proposed method can get efficient estimations.     

Panel‐based stratified cluster sampling and analysis for photovoltaic outdoor measurements

We study a stratified multisite cluster‐sampling panel time series approach in order to analyse and evaluate the quality and reliability of produced items, motivated by the problem to sample and analyse multisite outdoor measurements from photovoltaic systems. The specific stratified sampling in spatial clusters reduces sampling costs and allows for heterogeneity as well as for the analysis of spatial correlations due to defects and damages that tend to occur in clusters. The analysis is based on weighted least squares using data‐dependent weights. We show that this does not affect consistency and asymptotic normality of the least squares estimator under the proposed sampling design under general conditions. The estimation of the relevant variance–covariance matrices is discussed in detail for various models including nested designs and random effects. The strata corresponding to damages or manufacturers are modelled via a quality feature by means of a threshold approach. The analysis of outdoor electroluminescence images shows that spatial correlations and local clusters may arise in such photovoltaic data. Further, relevant statistics such as the mean pixel intensity cannot be assumed to follow a Gaussian law. We investigate the proposed inferential tools in detail by simulations in order to assess the influence of spatial cluster correlations and serial correlations on the test's size and power. ©2016 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.     

Additive hazards regression with random effects for clustered failure times

Additive hazards model with random effects is proposed for modelling the correlated failure time data when focus is on comparing the failure times within clusters and on estimating the correlation between failure times from the same cluster, as well as the marginal regression parameters. Our model features that, when marginalized over the random effect variable, it still enjoys the structure of the additive hazards model. We develop the estimating equations for inferring the regression parameters. The proposed estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Furthermore, the estimator of the baseline hazards function is proposed and its asymptotic properties are also established. We propose a class of diagnostic methods to assess the overall fitting adequacy of the additive hazards model with random effects. We conduct simulation studies to evaluate the finite sample behaviors of the proposed estimators in various scenarios. Analysis of the Diabetic Retinopathy Study is provided as an illustration for the proposed method.     

Semiparametric regression analysis for clustered doubly-censored data

This paper considers clustered doubly-censored data that occur when there exist several correlated survival times of interest and only doubly censored data are available for each survival time. In this situation, one approach is to model the marginal distribution of failure times using semiparametric linear transformation models while leaving the dependence structure completely arbitrary. We demonstrate that the approach of Cai et al. (Biometrika 87:867–878, 2000) can be extended to clustered doubly censored data. We propose two estimators by using two different estimated censoring weights. A simulation study is conducted to investigate the proposed estimators.