Interval-censored Failure Time Data Research Articles

Regression analysis of case K interval-censored failure time data in the presence of informative censoring.

Interval-censored failure time data occur in many fields such as demography, economics, medical research, and reliability and many inference procedures on them have been developed (Sun, 2006; Chen, Sun, and Peace, 2012). However, most of the existing approaches assume that the mechanism that yields interval censoring is independent of the failure time of interest and it is clear that this may not be true in practice (Zhang et al., 2007; Ma, Hu, and Sun, 2015). In this article, we consider regression analysis of case K interval-censored failure time data when the censoring mechanism may be related to the failure time of interest. For the problem, an estimated sieve maximum-likelihood approach is proposed for the data arising from the proportional hazards frailty model and for estimation, a two-step procedure is presented. In the addition, the asymptotic properties of the proposed estimators of regression parameters are established and an extensive simulation study suggests that the method works well. Finally, we apply the method to a set of real interval-censored data that motivated this study.

Power and sample size calculations for interval-censored survival analysis.

We propose a method for calculating power and sample size for studies involving interval-censored failure time data that only involves standard software required for fitting the appropriate parametric survival model. We use the framework of a longitudinal study where patients are assessed periodically for a response and the only resultant information available to the investigators is the failure window: the time between the last negative and first positive test results. The survival model is fit to an expanded data set using easily computed weights. We illustrate with a Weibull survival model and a two-group comparison. The investigator can specify a group difference in terms of a hazards ratio. Our simulation results demonstrate the merits of these proposed power calculations. We also explore how the number of assessments (visits), and thus the corresponding lengths of the failure intervals, affect study power. The proposed method can be easily extended to more complex study designs and a variety of survival and censoring distributions.

Regression Analysis of Left-truncated and Case I Interval-censored Data with the Additive Hazards Model

In recent years the analysis of interval-censored failure time data has attracted a great deal of attention and such data arise in many fields including demographical studies, economic and financial studies, epidemiological studies, social sciences, and tumorigenicity experiments. This is especially the case in medical studies such as clinical trials. In this article, we discuss regression analysis of one type of such data, Case I interval-censored data, in the presence of left-truncation. For the problem, the additive hazards model is employed and the maximum likelihood method is applied for estimations of unknown parameters. In particular, we adopt the sieve estimation approach that approximates the baseline cumulative hazard function by linear functions. The resulting estimates of regression parameters are shown to be consistent and efficient and have an asymptotic normal distribution. An illustrative example is provided.

A Two-Sample Parametric Test for Partly Interva-Censored Data with Nonproportional Hazard

In clinical trials and engineering studies that are followed by periodic follow-ups, it is predominantly to have partly interval-censored failure time data. Partly interval-censored failure time data is composed of exact observations and interval-censored observations. This paper discusses two-sample parametric comparison of reliability function in the existence of partly interval-censored failure time data. We have constructed a score test and likelihood ratio test for this kind of failure time data under piecewise exponential distribution by using multiple imputation technique. Simulation study is established to assess the proposed test, which indicates that the presented procedure works well. Finally, an example is given for illustration purposes.

Semiparametric regression analysis for time-to-event marked endpoints in cancer studies

In cancer studies the disease natural history process is often observed only at a fixed, random point of diagnosis (a survival time), leading to a current status observation (Sun (2006). The statistical analysis of interval-censored failure time data. Berlin: Springer.) representing a surrogate (a mark) (Jacobsen (2006). Point process theory and applications: marked point and piecewise deterministic processes. Basel: Birkhauser.) attached to the observed survival time. Examples include time to recurrence and stage (local vs. metastatic). We study a simple model that provides insights into the relationship between the observed marked endpoint and the latent disease natural history leading to it. A semiparametric regression model is developed to assess the covariate effects on the observed marked endpoint explained by a latent disease process. The proposed semiparametric regression model can be represented as a transformation model in terms of mark-specific hazards, induced by a process-based mixed effect. Large-sample properties of the proposed estimators are established. The methodology is illustrated by Monte Carlo simulation studies, and an application to a randomized clinical trial of adjuvant therapy for breast cancer.

Hazard ratio estimation for two‐sample case under interval‐censored failure time data

This paper discusses two-sample comparison in the case of interval-censored failure time data. For the problem, one common approach is to employ some nonparametric test procedures, which usually give some p-values but not a direct or exact quantitative measure of the survival or treatment difference of interest. In particular, these procedures cannot provide a hazard ratio estimate, which is commonly used to measure the difference between the two treatments or samples. For interval-censored data, a few nonparametric test procedures have been developed, but it does not seem to exist as a procedure for hazard ratio estimation. Corresponding to this,we present two procedures for nonparametric estimation of the hazard ratio of the two samples for interval-censored data situations. They are generalizations of the corresponding procedures for right-censored failure time data. An extensive simulation study is conducted to evaluate the performance of the two procedures and indicates that they work reasonably well in practice. For illustration, they are applied to a set of interval-censored data arising from a breast cancer study.

Survival Model for Partly Interval-Censored Data with Application to Anti D in Rhesus D Negative Studies

This paper discusses regression analysis of partly interval-censored failure time data, which is occur in many fields including demographical, epidemiological, financial, medical and sociological studies. For the problem, we focus on the situation where the survival time of interest can be described by the additive hazards model in the present of partly interval-censored. A major advantage of the approach is its simplicity and it can be easily implemented by using R software. Simulation studies are conducted which indicate that the approach performs well for practical situations and comparable to the existing methods. The methodology is applied to a set of partly interval-censored failure time data arising from anti D in Rhesus D negative studies.

Simple estimation procedures for regression analysis of interval-censored failure time data under the proportional hazards model

Interval-censored failure time data occur in many fields including epidemiological and medical studies as well as financial and sociological studies, and many authors have investigated their analysis (Sun, The statistical analysis of interval-censored failure time data, 2006; Zhang, Stat Modeling 9:321-343, 2009). In particular, a number of procedures have been developed for regression analysis of interval-censored data arising from the proportional hazards model (Finkelstein, Biometrics 42:845-854, 1986; Huang, Ann Stat 24:540-568, 1996; Pan, Biometrics 56:199-203, 2000). For most of these procedures, however, one drawback is that they involve estimation of both regression parameters and baseline cumulative hazard function. In this paper, we propose two simple estimation approaches that do not need estimation of the baseline cumulative hazard function. The asymptotic properties of the resulting estimates are given, and an extensive simulation study is conducted and indicates that they work well for practical situations.

Efficient Estimation for Linear Transformation Models with Current Status Data

Linear transformation models provide a class of flexible models for regression analysis of failure time data and several methods have been proposed for fitting them to right-censored failure time data (Chen, 2002; Cheng et al., 1995; Yin and Zeng, 2006). This article considers the fitting of these models to current status data, a special type of interval-censored failure time data. We derive the maximum likelihood estimates and their information bound and establish the efficiency of the estimates. Simulation studies show that the approach is appropriate for practical use and an application is given to illustrate the approach.

Additive Transformation Models for Multivariate Interval-Censored Data

Tong, et al. (2008) considered multivariate (clustered) interval-censored failure time data that occur when there exist several correlated survival times of interest and only interval-censored data are available for each survival time. Assuming that covariates affect the hazard rate linearly, they developed a marginal inference approach using the additive hazards model. In this article, based on the idea of Zeng and Cai (2010), we consider a general class of additive transformation model, which relaxes the linear assumption. Using working independence likelihood, we present an inference approach for regression analysis of multivariate interval-censored data. A simulation study is conducted to investigate the performance of the proposed estimator. We apply the proposed method to the data set from the Diabetic Retinopathy Study.

Parametric Tests for Partly Interval-censored Failure Time Data under Weibull Distribution via Multiple Imputation

The statistical problem considered in this article is the parametric treatment comparison when partly interval-censored failure time data exist. Partly interval-censored failure time data are composed of exact observations and interval-censored observations. This phenomenon often occurs in clinical trials and health studies that require periodic following up with patients. The authors constructed a score test and likelihood ratio test for this type of failure time data under Weibull distributions using multiple imputation technique. A simulation study and a modified secondary data set from breast cancer study are used to assess the proposed test and illustrate the differences between the two tests. The results indicate that the presented procedure works well for both tests, but the likelihood ratio test is better than the score test in certain situations.

Empirical likelihood for linear transformation models with interval-censored failure time data

For regression analysis of interval-censored failure time data, Zhang et al. (2005) [40] proposed an estimating equation approach to fit linear transformation models. In this paper, we develop two empirical likelihood (EL) inference approaches for the regression parameters based on the generalized estimating equations. The limiting distributions of log-empirical likelihood ratios are derived and empirical likelihood confidence intervals for any specified component of regression parameters are obtained. We carry out extensive simulation studies to compare the proposed methods with the method discussed by Zhang et al. (2005) [40]. The simulation results demonstrate that the EL and jackknife EL methods for linear transformation models have better performance than the existing normal approximation method based on coverage probability of confidence intervals in most cases, and they enable us to overcome an under-coverage problem for the confidence intervals of the regression parameters using a normal approximation when sample sizes are small and right censoring is heavy. Two real data examples are provided to illustrate our procedures.

The Statistical Analysis of Interval-Censored Failure Time Data with Applications

The analysis of survival data is a major focus of statistics. Interval censored data reflect uncertainty as to the exact times the units failed within an interval. This type of data frequently comes from tests or situations where the objects of interest are not constantly monitored. Thus events are known only to have occurred between the two observation periods. Interval censoring has become increasingly common in the areas that produce failure time data. This paper explores the statistical analysis of interval-censored failure time data with applications. Three different data sets, namely Breast Cancer, Hemophilia, and AIDS data were used to illustrate the methods during this study. Both parametric and nonparametric methods of analysis are carried out in this study. Theory and methodology of fitted models for the interval-censored data are described. Fitting of parametric and non-parametric models to three real data sets are considered. Results derived from different methods are presented and also compared.

Semiparametric Regression Analysis of Clustered Interval-Censored Failure Time Data with Informative Cluster Size

Clustered interval-censored failure time data are commonly encountered in many medical settings. In such situations, one issue that often arises in practice is that the cluster size is related to the risk for the outcome of interest. It is well-known that ignoring the informativeness of the cluster size can result in biased parameter estimates. In this article, we consider regression analysis of clustered interval-censored data with informative cluster size with the focus on semiparametric methods. For the problem, two approaches are presented and investigated. One is a within-cluster resampling procedure and the other is a weighted estimating equation approach. Unlike previously published methods, the new approaches take into account cluster sizes and heterogeneous correlation structures without imposing strong parametric assumptions. A simulation experiment is carried out to evaluate the performance of the proposed approaches and indicates that they perform well for practical situations. The approaches are applied to a lymphatic filariasis study that motivated this study.

Sieve Estimation for the Cox Model with Clustered Interval-Censored Failure Time Data

Clustered interval-censored failure time data occur when the failure times of interest are clustered into small groups and known only to lie in certain intervals. A number of methods have been proposed for regression analysis of clustered failure time data, but most of them apply only to clustered right-censored data. In this paper, a sieve estimation procedure is proposed for fitting a Cox frailty model to clustered interval-censored failure time data. In particular, a two-step algorithm for parameter estimation is developed and the asymptotic properties of the resulting sieve maximum likelihood estimators are established. The finite sample properties of the proposed estimators are investigated through a simulation study and the method is illustrated by the data arising from a lymphatic filariasis study.

Regression analysis of clustered interval-censored failure time data with the additive hazards model

This paper discusses regression analysis of clustered failure time data, which means that the failure times of interest are clustered into small groups instead of being independent. Clustering occurs in many fields such as medical studies. For the problem, a number of methods have been proposed, but most of them apply only to clustered right-censored data. In reality, the failure time data is often interval-censored. That is, the failure times of interest are known only to lie in certain intervals. We propose an estimating equation-based approach for regression analysis of clustered interval-censored failure time data generated from the additive hazards model. A major advantage of the proposed method is that it does not involve the estimation of any baseline hazard function. Both asymptotic and finite sample properties of the proposed estimates of regression parameters are established and the method is illustrated by the data arising from a lymphatic filariasis study.

A new class of generalized log rank tests for interval-censored failure time data

This paper discusses nonparametric comparison of survival functions when one observes only interval-censored failure time data (Peto and Peto, 1972; Sun, 2006; Zhao et al., 2008). For the problem, a few procedures have been proposed in the literature. However, most of the existing test procedures determine the test results or p-values based on ad hoc methods or the permutation approach. Furthermore for the test procedures whose asymptotic distributions have been derived, the results are only for the null hypothesis. In other words, no nonparametric test procedure exists that has a known asymptotic distribution under the alternative hypothesis and thus can be employed to carry out the power and test size calculation. In this paper, a new class of generalized log-rank tests is proposed and their asymptotic distributions are derived under both null and alternative hypotheses. A simulation study is conducted to assess their performance for finite sample situations and an illustrative example is provided.

Nonparametric estimation of current status data with dependent censoring

This paper discusses nonparametric estimation of a survival function when one observes only current status data (McKeown and Jewell, Lifetime Data Anal 16:215-230, 2010; Sun, The statistical analysis of interval-censored failure time data, 2006; Sun and Sun, Can J Stat 33:85-96, 2005). In this case, each subject is observed only once and the failure time of interest is observed to be either smaller or larger than the observation or censoring time. If the failure time and the observation time can be assumed to be independent, several methods have been developed for the problem. Here we will focus on the situation where the independent assumption does not hold and propose two simple estimation procedures under the copula model framework. The proposed estimates allow one to perform sensitivity analysis or identify the shape of a survival function among other uses. A simulation study performed indicates that the two methods work well and they are applied to a motivating example from a tumorigenicity study.

Analysis of interval‐censored disease progression data via multi‐state models under a nonignorable inspection process

Irreversible multi-state models provide a convenient framework for characterizing disease processes that arise when the states represent the degree of organ or tissue damage incurred by a progressive disease. In many settings, however, individuals are only observed at periodic clinic visits and so the precise times of the transitions are not observed. If the life history and observation processes are not independent, the observation process contains information about the life history process, and more importantly, likelihoods based on the disease process alone are invalid. With interval-censored failure time data, joint models are nonidentifiable and data analysts must rely on sensitivity analyses to assess the effect of the dependent observation times. This paper is concerned, however, with the analysis of data from progressive multi-state disease processes in which individuals are scheduled to be seen at periodic pre-scheduled assessment times. We cast the problem in the framework used for incomplete longitudinal data problems. Maximum likelihood estimation via an EM algorithm is advocated for parameter estimation. Simulation studies demonstrate that the proposed method works well under a variety of situations. Data from a cohort of patients with psoriatic arthritis are analyzed for illustration.

Regression analysis of clustered interval-censored failure time data with informative cluster size

Correlated or clustered failure time data often occur in medical studies, among other fields ( Cai and Prentice, 1995; Kalbfleisch and Prentice, 2002), and sometimes such data arise together with interval censoring ( Wang et al., 2006). Furthermore, the failure time of interest may be related to the cluster size. For example, Williamson et al. (2008) discussed such an example arising from a lymphatic filariasis study. A simple and common approach to the analysis of these data is to simplify or convert interval-censored data to right-censored data due to the lack of proper inference procedures for direct analysis of these data. In this paper, two procedures are presented for regression analysis of clustered failure time data that allow both interval censoring and informative cluster size. Simulation studies are conducted to evaluate the presented approaches and they are applied to a motivating example.