Interval-censored Failure Time Data Research Articles

Improving estimation efficiency of case-cohort studies with interval-censored failure time data.

The case-cohort design is a commonly used cost-effective sampling strategy for large cohort studies, where some covariates are expensive to measure or obtain. In this paper, we consider regression analysis under a case-cohort study with interval-censored failure time data, where the failure time is only known to fall within an interval instead of being exactly observed. A common approach to analyzing data from a case-cohort study is the inverse probability weighting approach, where only subjects in the case-cohort sample are used in estimation, and the subjects are weighted based on the probability of inclusion into the case-cohort sample. This approach, though consistent, is generally inefficient as it does not incorporate information outside the case-cohort sample. To improve efficiency, we first develop a sieve maximum weighted likelihood estimator under the Cox model based on the case-cohort sample and then propose a procedure to update this estimator by using information in the full cohort. We show that the update estimator is consistent, asymptotically normal, and at least as efficient asthe original estimator. The proposed method can flexibly incorporate auxiliary variables to improve estimation efficiency. A weighted bootstrap procedure is employed for variance estimation. Simulation results indicate that the proposed method works well in practical situations. An application to a Phase 3 HIV vaccine efficacy trial is provided for illustration.

Semiparametric varying-coefficient additive hazards model for informatively interval-censored failure time data

The analysis of interval-censored data with informative observation processes has recently attracted much attention and a few methods have been developed. However, all of the existing methods assume that covariate effects are constant and this may not be true sometimes in practice. To address this, in this paper, we propose a varying-coefficient additive hazards model and in the proposed method, frailty variables are used to describe the dependence between the failure time and the informative observation process. For inference, a Bernstein polynomials-based, two-step sieve maximum likelihood method is developed and the proposed method can be easily implemented. Furthermore, the resulting estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and suggests that the proposed approach works well for practical situations. The proposed method is applied to a cardiac allograft vasculopathy (CAV) study that motivated this investigation.

A Simulation-Extrapolation Approach to the Analysis of Interval-Censored Failure Time Data with Mis-Measured Covariates

A Simulation-Extrapolation Approach to the Analysis of Interval-Censored Failure Time Data with Mis-Measured Covariates

Factor-augmented transformation models for interval-censored failure time data.

Interval-censored failure time data frequently arise in various scientific studies where each subject experiences periodical examinations for the occurrence of the failure event of interest, and the failure time is only known to lie in a specific time interval. In addition, collected data may include multiple observed variables with a certain degree of correlation, leading to severe multicollinearity issues. This work proposes a factor-augmented transformation model to analyze interval-censored failure time data while reducing model dimensionality and avoiding multicollinearity elicited by multiple correlated covariates. We provide a joint modeling framework by comprising a factor analysis model to group multiple observed variables into a few latent factors and a class of semiparametric transformation models with the augmented factors to examine their and other covariate effects on the failure event. Furthermore, we propose a nonparametric maximum likelihood estimation approach and develop a computationally stable and reliable expectation-maximization algorithm for its implementation. We establish the asymptotic properties of the proposed estimators and conduct simulation studies to assess the empirical performance of the proposed method. An application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study is provided. An R package ICTransCFA is also available for practitioners. Data used in preparation of this article were obtained from the ADNI database.

A conditional approach for regression analysis of case K interval-censored failure time data with informative censoring

This paper discusses regression analysis of case K interval-censored failure time data, a general type of failure time data, in the presence of informative censoring with the focus on simultaneous variable selection and estimation. Although many authors have considered the challenging variable selection problem for interval-censored data, most of the existing methods assume independent or non-informative censoring. More importantly, the existing methods that allow for informative censoring are frailty model-based approaches and cannot directly assess the degree of informative censoring among other shortcomings. To address these, we propose a conditional approach and develop a penalized sieve maximum likelihood procedure for the simultaneous variable selection and estimation of covariate effects. Furthermore, we establish the oracle property of the proposed method and illustrate the appropriateness and usefulness of the approach using a simulation study. Finally we apply the proposed method to a set of real data on Alzheimer's disease and provide some new insights.

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.

A new and unified method for regression analysis of interval-censored failure time data under semiparametric transformation models with missing covariates.

This paper discusses regression analysis of interval-censored failure time data arising from semiparametric transformation models in the presence of missing covariates. Although some methods have been developed for the problem, they either apply only to limited situations or may have some computational issues. Corresponding to these, we propose a new and unified two-step inference procedure that can be easily implemented using the existing or standard software. The proposed method makes use of a set of working models to extract partial information from incomplete observations and yields a consistent estimator of regression parameters assuming missing at random. An extensive simulation study is conducted and indicates that it performs well in practical situations. Finally, we apply the proposed approach to an Alzheimer's Disease study that motivated this study.

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.