Interval-censored Failure Time Data Research Articles

Semiparametric analysis of nonparametric proportional hazards models with mixed dependent censored data

To construct a nonparametric proportional hazards (PH) model for mixed informative interval-censored failure time data for predicting the risks in heart transplantation surgeries. Based on the complexity of mixed informative interval-censored failure time data, we considered the interdependent relationship between failure time process and observation time process, constructed a nonparametric proportional hazards (PH) model to describe the nonlinear relationship between the risk factors and heart transplant surgery risks and proposed a two-step sieve estimation maximum likelihood algorithm. An estimation equation was established to estimate frailty variables using the observation process model. Ⅰ-spline and B-spline were used to approximate the unknown baseline hazard function and nonparametric function, respectively, to obtain the working likelihood function in the sieve space. The partial derivative of the model parameters was used to obtain the scoring equation. The maximum likelihood estimation of the parameters was obtained by solving the scoring equation, and a function curve of the impact of risk factors on the risk of heart transplantation surgery was drawn. Simulation experiment suggested that the estimated values obtained by the proposed method were consistent and asymptotically effective under various settings with good fitting effects. Analysis of heart transplant surgery data showed that the donor's age had a positive linear relationship with the surgical risk. The impact of the recipient's age at disease onset increased at first and then stabilized, but increased against at an older age. The donor-recipient age difference had a positive linear relationship with the surgical risk of heart transplantation. The nonparametric PH model established in this study can be used for predicting the risks in heart transplantation surgery and exploring the functional relationship between the surgery risks and the risk factors.

Variational Bayesian approach for analyzing interval-censored data under the proportional hazards model

Interval-censored failure time data frequently occur in medical follow-up studies among others and include right-censored data as a special case. Their analysis is much difficult than the analysis of the right-censored data due to their much more complicated structures and no partial likelihood. This article presents a variational Bayesian (VB) approach for analyzing such data under a proportional hazards model. The VB approach obtains a direct approximation of the posterior density. Compared to the Markov chain Monte Carlo (MCMC)-based sampling approaches, the VB approach achieves enhanced computational efficiency without sacrificing estimation accuracy. An extensive simulation study is conducted to compare the performance of the proposed methods with two main Bayesian methods currently available in the literature and the classic proportional hazards model and indicates that they work well in practical situations.

Modeling the association of bivariate interval-censored data under the additive hazards model

. Bivariate interval-censored failure time data occurs in many fields such as medical followup studies. In this article, we propose an estimation procedure for the association between two related interval-censored survival times when they follow a copula model jointly and the additive hazards model marginally. A simulation study was conducted for assessing the finite sample performance of the presented method and suggests that it works well in practical situations. The proposed method is applied to the AIDS Clinical Trial Group (ACTG) 181 data that motivated this research.

Regression analysis of multivariate interval-censored failure time data with a cured subgroup and informative censoring

Multivariate interval-censored failure time data occur when a failure time study involves several related failure times of interest and only interval-censored observations are available for each of them. Although a great deal of literature has been established for their regression analysis, there does not seem to exist an approach that applies to the situation where there exist both a cured subgroup and informative censoring, the focus of this paper. For the problem, a class of semiparametric transformation non-mixture cure models is presented and a two-step estimation procedure is proposed. For the implementation of the proposed method, an EM algorithm is developed. Numerical results suggest that the proposed method works well for practical situations and an application is provided.

Variable Selection for Length-Biased and Interval-Censored Failure Time Data

Length-biased failure time data occur often in various biomedical fields, including clinical trials, epidemiological cohort studies and genome-wide association studies, and their analyses have been attracting a surge of interest. In practical applications, because one may collect a large number of candidate covariates for the failure event of interest, variable selection becomes a useful tool to identify the important risk factors and enhance the estimation accuracy. In this paper, we consider Cox’s proportional hazards model and develop a penalized variable selection technique with various popular penalty functions for length-biased data, in which the failure event of interest suffers from interval censoring. Specifically, a computationally stable and reliable penalized expectation-maximization algorithm via two-stage data augmentation is developed to overcome the challenge in maximizing the intractable penalized likelihood. We establish the oracle property of the proposed method and present some simulation results, suggesting that the proposed method outperforms the traditional variable selection method based on the conditional likelihood. The proposed method is then applied to a set of real data arising from the Prostate, Lung, Colorectal and Ovarian cancer screening trial. The analysis results show that African Americans and having immediate family members with prostate cancer significantly increase the risk of developing prostate cancer, while having diabetes exhibited a significantly lower risk of developing prostate cancer.

A new frailty-based GEE approach of the informatively case K interval-censored failure time data

Interval-censored failure time data are commonly encountered in many fields and some methods and models have been proposed for them in the literature. In the real situations, interval censoring is informative. For this problem, we propose a new frailty-based generalized estimating equation (GEE) method of the proportional hazards (PH) model with the informatively case K interval-censored failure time data. In this article, a frailty-based generalized estimating equation is developed that can yield an unbiased estimator of the cumulative hazards function. The observation process of the proposed method does not need a non homogeneous Poisson process used in many existing literatures. The asymptotic properties of the proposed method are established, and an extensive simulation study is conducted to assess the performance of the proposed procedure. In addition, an application to an AIDS clinical trial data set is presented.

A new approach for semi-parametric regression analysis of bivariate interval-censored outcomes from case-cohort studies

Interval-censored failure time data frequently occur in many areas and a great deal of literature on their analyses has been established. In this article, we discuss the situation where one faces bivariate interval-censored data arising from case-cohort studies, which are commonly used as a tool to save costs when disease incidence is low and covariates are difficult to obtain. For this problem, a class of copula-based semi-parametric models is presented and for estimation, a sieve weighted maximum likelihood estimation procedure is developed. The resulting estimators of regression parameters are shown to be strongly consistent and asymptotically normal. Furthermore, the proposed method is generalized to the situation of non rare diseases. A simulation study is conducted to assess the finite sample performance of the proposed method and suggests that it performs well in practice.

Estimation of complier causal treatment effects under the case–cohort studies with interval-censored failure time data

It has attracted a great deal of interest in randomized survival studies to assess the causal treatment effect under non-compliance with time-to-event outcomes. In this paper, the problem when one faces case–cohort studies for which covariates are usually too expensive to be measured or obtained for the full cohort and also the disease rate is generally low is considered. Furthermore, only interval-censored data may be available for the failure event of interest, a situation for which there does not seem to exist an established estimation procedure. To address the problem, a sieve inverse probability weighting estimation procedure is proposed, and the resulting estimators are shown to be consistent and asymptotically normal. A simulation study is conducted to evaluate the finite sample performance of the proposed approach and suggests that it works well in practice. In addition, the method is applied to a breast cancer screening study.

Group variable selection for the Cox model with interval-censored failure time data.

Group variable selection is often required in many areas, and for this many methods have been developed under various situations. Unlike the individual variable selection, the group variable selection can select the variables in groups, and it is more efficient to identify both important and unimportant variables or factors by taking into account the existing group structure. In this paper, we consider the situation where one only observes interval-censored failure time data arising from the Cox model, for which there does not seem to exist an established method. More specifically, a penalized sieve maximum likelihood variable selection and estimation procedure is proposed and the oracle property of the proposed method is established. Also, an extensive simulation study is performed and suggests that the proposed approach works well in practical situations. An application of the method to a set of real data isprovided.

Estimation of complier causal treatment effects with informatively interval-censored failure time data

Estimation of complier causal treatment effects with informatively interval-censored failure time data

Estimation of accelerated hazards models based on case K informatively interval-censored failure time data

The accelerated hazards model is one of the most commonly used models for regression analysis of failure time data and this is especially the case when, for example, the hazard functions may have monotonicity property. Correspondingly a large literature has been established for its estimation or inference when right-censored data are observed. Although several methods have also been developed for its inference based on interval-censored data, they apply only to limited situations or rely on some assumptions such as independent censoring. In this paper, we consider the situation where one observes case K interval-censored data, the type of failure time data that occur most in, for example, medical research such as clinical trials or periodical follow-up studies. For inference, we propose a sieve borrow-strength method and in particular, it allows for informative censoring. The asymptotic properties of the proposed estimators are established. Simulation studies demonstrate that the proposed inference procedure performs well. The method is applied to a set of real data set arising from an AIDS clinical trial.

Semiparametric regression analysis of length-biased and partly interval-censored data with application to an AIDS cohort study.

Length-biased data occur often in many scientific fields, including clinical trials, epidemiology surveys and genome-wide association studies, and many methods have been proposed for their analysis under various situations. In this article, we consider the situation where one faces length-biased and partly interval-censored failure time data under the proportional hazards model, for which it does not seem to exist an established method. For the estimation, we propose an efficient nonparametric maximum likelihood method by incorporating the distribution information of the observed truncation times. For the implementation of the method, a flexible and stable EM algorithm via two-stage data augmentation is developed. By employing the empirical process theory, we establish the asymptotic properties of the resulting estimators. A simulation study conducted to assess the finite-sample performance of the proposed method suggests that it works well and is more efficient than the conditional likelihood approach. An application to an AIDS cohort study is also provided.

Combined estimating equation approaches for the additive hazards model with left-truncated and interval-censored data.

Interval-censored failure time data arise commonly in various scientific studies where the failure time of interest is only known to lie in a certain time interval rather than observed exactly. In addition, left truncation on the failure event may occur and can greatly complicate the statistical analysis. In this paper, we investigate regression analysis of left-truncated and interval-censored data with the commonly used additive hazards model. Specifically, we propose a conditional estimating equation approach for the estimation, and further improve its estimation efficiency by combining the conditional estimating equation and the pairwise pseudo-score-based estimating equation that can eliminate the nuisance functions from the marginal likelihood of the truncation times. Asymptotic properties of the proposed estimators are discussed including the consistency and asymptotic normality. Extensive simulation studies are conducted to evaluate the empirical performance of the proposed methods, and suggest that the combined estimating equation approach is obviously more efficient than the conditional estimating equation approach. We then apply the proposed methods to a set of real data for illustration.

A semi-parametric weighted likelihood approach for regression analysis of bivariate interval-censored outcomes from case-cohort studies.

The case-cohort design was developed to reduce costs when disease incidence is low and covariates are difficult to obtain. However, most of the existing methods are for right-censored data and there exists only limited research on interval-censored data, especially on regression analysis of bivariate interval-censored data. Interval-censored failure time data frequently occur in many areas and a large literature on their analyses has been established. In this paper, we discuss the situation of bivariate interval-censored data arising from case-cohort studies. For the problem, a class of semiparametric transformation frailty models is presented and for inference, a sieve weighted likelihood approach is developed. The large sample properties, including the consistency of the proposed estimators and the asymptotic normality of the regression parameter estimators, are established. Moreover, a simulation is conducted to assess the finite sample performance of the proposed method and suggests that it performs well in practice.

Partially Linear Additive Hazards Regression for Bivariate Interval-Censored Data

In this paper, we discuss regression analysis of bivariate interval-censored failure time data that often occur in biomedical and epidemiological studies. To solve this problem, we propose a kind of general and flexible copula-based semiparametric partly linear additive hazards models that can allow for both time-dependent covariates and possible nonlinear effects. For inference, a sieve maximum likelihood estimation approach based on Bernstein polynomials is proposed to estimate the baseline hazard functions and nonlinear covariate effects. The resulting estimators of regression parameters are shown to be consistent, asymptotically efficient and normal. A simulation study is conducted to assess the finite-sample performance of this method and the results show that it is effective in practice. Moreover, an illustration is provided.

A New Model-Free Feature Screening Procedure for Ultrahigh-Dimensional Interval-Censored Failure Time Data

A New Model-Free Feature Screening Procedure for Ultrahigh-Dimensional Interval-Censored Failure Time Data

Estimation of linear transformation cure models with informatively interval-censored failure time data

Linear transformation models have been one type of models commonly used for regression analysis of failure time data partly due to their flexibility. More recently they have been generalised to the case where there may exist a cured subgroup or the censoring may be informative. In this paper, we consider a more complicated and general situation where both a cured subgroup and informative censoring, or more specifically informative interval censoring, exist. As pointed out in the literature, the analysis that fails to take into account either the cured subgroup or the informative censoring can yield biased estimation or misleading conclusions. For the problem, a three-component mixture cure model is presented and we develop a two-step estimation procedure with the use of B-splines to approximate unknown functions. The proposed approach is quite flexible and can be easily implemented. Also the proposed estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and suggests that the method works well for practical situations. Furthermore a real application is provided to illustrate the proposed methodology.

Regression Analysis of Multivariate Interval-Censored Failure Time Data under Transformation Model with Informative Censoring

We consider a regression analysis of multivariate interval-censored failure time data where the censoring may be informative. To address this, an approximated maximum likelihood estimation approach is proposed under a general class of semiparametric transformation models, and in the method, the frailty approach is employed to characterize the informative interval censoring. For the implementation of the proposed method, we develop a novel EM algorithm and show that the resulting estimators of the regression parameters are consistent and asymptotically normal. To evaluate the empirical performance of the proposed estimation procedure, we conduct a simulation study, and the results indicate that it performs well for the situations considered. In addition, we apply the proposed approach to a set of real data arising from an AIDS study.

Efficient estimation for accelerated failure time model with interval-censored data in the presence of a cured subgroup

As the alternative of Cox model, the accelerated failure time (AFT) model, which simply regresses the logarithm of the survival time over the covariates, is commonly used in the analysis of interval-censored data. In this paper, we propose a novel two-component mixture-cure model for the interval-censored failure time data in the presence of a cure fraction. Specifically, the first component is a logistic regression model that describes the cure rate, and the second component is a semiparametric accelerated failure time model that describes the failure time of interest for the uncured subjects. An efficient semiparametric procedure is developed to estimate parameters in the considered model. We propose a penalized sieve maximum likelihood estimation approach with Bernstein polynomials to estimate the regression parameters quickly and accurately and the proposed procedure does not rely on the assumption of the distribution of the measurement error. The asymptotic properties of the resulting estimators are established. Extensive simulation studies conducted indicate that the proposed procedure works well for practical situations. In addition, AIDS data analysis is provided for illustration of the proposed method.

Joint analysis of informatively interval-censored failure time and panel count data.

Interval-censored failure time and panel count data, which frequently arise in medical studies and social sciences, are two types of important incomplete data. Although methods for their joint analysis have been available in the literature, they did not consider the observation process, which may depend on the failure time and/or panel count of interest. This study considers a three-component joint model to analyze interval-censored failure time, panel counts, and the observation process within a unique framework. Gamma and distribution-free frailties are introduced to jointly model the interdependency among the interval-censored data, panel count data, and the observation process. We propose a sieve maximum likelihood approach coupled with Bernstein polynomial approximation to estimate the unknown parameters and baseline hazard function. The asymptotic properties of the resulting estimators are established. An extensive simulation study suggests that the proposed procedure works well for practical situations. An application of the method to a real-life dataset collected from a cardiac allograft vasculopathy study is presented.