Interval-censored Failure Time Data Research Articles

Weighted rank estimation of nonparametric transformation models with case-1 and case-2 interval-censored failure time data

Case-1 and case-2 interval-censored failure time data commonly occur in medical research as well as other fields and many methods have been developed for their analysis under different frameworks. In this paper, we consider regression analysis of such data and present a general class of nonparametric transformation models. One major advantage of these models is their flexibility and generality as they include the linear transformation model as a special case. For estimation of regression parameters, we propose a weighted rank (WR) estimation procedure and establish the consistency and asymptotic normality of the resulting estimator. Furthermore, to estimate the asymptotic covariance matrix of the proposed estimator, a resampling technique, which does not involve nonparametric density estimation or numerical derivatives, is developed. A numerical study is also conducted and suggests that the proposed methodology works well in practice. Finally an application is provided.

Semiparametric regression analysis of case-cohort studies with multiple interval-censored disease outcomes.

Interval-censored failure time data commonly arise in epidemiological and biomedical studies where the occurrence of an event or a disease is determined via periodic examinations. Subject to interval-censoring, available information on the failure time can be quite limited. Cost-effective sampling designs are desirable to enhance the study power, especially when the disease rate is low and the covariates are expensive to obtain. In this work, we formulate the case-cohort design with multiple interval-censored disease outcomes and also generalize it to nonrare diseases where only a portion of diseased subjects are sampled. We develop a marginal sieve weighted likelihood approach, which assumes that the failure times marginally follow the proportional hazards model. We consider two types of weights to account for the sampling bias, and adopt a sieve method with Bernstein polynomials to handle the unknown baseline functions. We employ a weighted bootstrap procedure to obtain a variance estimate that is robust to the dependence structure between failure times. The proposed method is examined via simulation studies and illustrated with a dataset on incident diabetes and hypertension from the Atherosclerosis Risk in Communities study.

Semiparametric analysis of case K interval-censored failure time data in the presence of a cured subgroup and informative censoring

Interval censoring and the existence of a cured subgroup occur quite often in survival studies and many procedures have been developed for dealing with each of the two issues individually or them together. In this paper, we discuss the situation where both issues exist and furthermore, interval censoring may be informative, for which there exists relatively much less literature. For the problem, we present a frailty-based joint model approach in which a frailty term is employed to describe the correlation between the failure time of interest and the censoring mechanism. For inference, a two-step estimation procedure is developed and in particular, the sieve maximum-likelihood estimation approach is used for estimation of the unknown function. The proposed estimators of regression parameters are shown to be consistent and asymptotically normal, and an extensive simulation study conducted suggests that the proposed procedure works well for practical situations. In addition, an application is provided.

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

Clustered interval-censored failure time data occur in many areas and many methods have been proposed for their analysis. In practice, in addition to the clustering and interval censoring, such data may also present two other issues, cure fraction and informative cluster size, and it does not seem to exist an approach that can deal with all of these issues together. To address this, we present a within-cluster resampling method and in the approach, the multiple imputation procedure is applied for estimation of unknown parameters. To assess the performance of the proposed method, a simulation study is conducted and suggests that it works well in practical situations. Also the method is applied to a set of real data that motivated this study.

Robust Regression Analysis for Clustered Interval-Censored Failure Time Data

Clustered interval-censored failure time data often occur in a wide variety of research and application fields such as cancer and AIDS studies. For such data, the failure times of interest are interval-censored and may be correlated for subjects coming from the same cluster. This paper presents a robust semiparametric transformation mixed effect models to analyze such data and use a U-statistic based on rank correlation to estimate the unknown parameters. The large sample properties of the estimator are also established. In addition, the authors illustrate the performance of the proposed estimate with extensive simulations and two real data examples.

Simultaneous variable selection and estimation for joint models of longitudinal and failure time data with interval censoring.

This paper discusses variable selection in the context of joint analysis of longitudinal data and failure time data. A large literature has been developed for either variable selection or the joint analysis but there exists only limited literature for variable selection in the context of the joint analysis when failure time data are right censored. Corresponding to this, we will consider the situation where instead of right-censored data, one observes interval-censored failure time data, a more general and commonly occurring form of failure time data. For the problem, a class of penalized likelihood-based procedures will be developed for simultaneous variable selection and estimation of relevant covariate effects for both longitudinal and failure time variables of interest. In particular, a Monte Carlo EM (MCEM) algorithm is presented for the implementation of the proposed approach. The proposed method allows for the number of covariates to be diverging with the sample size and is shown to have the oracle property. An extensive simulation study is conducted to assess the finite sample performance of the proposed approach and indicates that it works well in practical situations. An application is alsoprovided.

Variable selection for generalized odds rate mixture cure models with interval-censored failure time data

Variable selection for failure time data with a cured fraction has been discussed by many authors but most of existing methods apply only to right-censored failure time data. In this paper, we consider variable selection when one faces interval-censored failure time data arising from a general class of generalized odds rate mixture cure models, and we propose a penalized variable selection method by maximizing a derived penalized likelihood function. In the method, the sieve approach is employed to approximate the unknown function, and it is implemented using a novel penalized expectation–maximization (EM) algorithm. Also the asymptotic properties of the proposed estimators of regression parameters, including the oracle property, are obtained. Furthermore, a simulation study is conducted to assess the finite sample performance of the proposed method, and the results indicate that it works well in practice. Finally, the approach is applied to a set of real data on childhood mortality taken from the Nigeria Demographic and Health Survey.

EM algorithm for the additive risk mixture cure model with interval-censored data.

Interval-censored failure time data arise in a number of fields and many authors have recently paid more attention to their analysis. However, regression analysis of interval-censored data under the additive risk model can be challenging in maximizing the complex likelihood, especially when there exists a non-ignorable cure fraction in the population. For the problem, we develop a sieve maximum likelihood estimation approach based on Bernstein polynomials. To relieve the computational burden, an expectation-maximization algorithm by exploiting a Poisson data augmentation is proposed. Under some mild conditions, the asymptotic properties of the proposed estimator are established. The finite sample performance of the proposed method is evaluated by extensive simulations, and is further illustrated through a real data set from the smoking cessation study.

Nonparametric screening and feature selection for ultrahigh-dimensional Case II interval-censored failure time data.

For the analysis of ultrahigh-dimensional data, the first step is often to perform screening and feature selection to effectively reduce the dimensionality while retaining all the active or relevant variables with high probability. For this, many methods have been developed under various frameworks but most of them only apply to complete data. In this paper, we consider an incomplete data situation, case II interval-censored failure time data, for which there seems to be no screening procedure. Basing on the idea of cumulative residual, a model-free or nonparametric method is developed and shown to have the sure independent screening property. In particular, the approach is shown to tend to rank the active variables above the inactive ones in terms of their association with the failure time of interest. A simulation study is conducted to demonstrate the usefulness of the proposed method and, in particular, indicates that it works well with general survival models and is capable of capturing the nonlinear covariates with interactions. Also the approach is applied to a childhood cancer survivor study that motivated thisinvestigation.

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.

A gamma-frailty model for interval-censored data with dependent examination times: a computationally efficient approach

Interval-censored survival data arise naturally in many fields such as medical follow-up studies, in which the event or failure is not observed exactly but only known to occur within a time interval. Most existing approaches for analyzing interval-censored failure time data assume that the examination times and the failure time are independent or conditionally independent given covariates. While this assumption offers considerable simplification, it is not plausible in some situations, e.g., the visiting rate can be positively or negatively correlated with the risk of failure due to unobservable health status even after adjusting for observable covariates. In this article, we consider dependent interval-censored data, where there exists dependence between the failure time and the entire visiting process. A shared frailty is used to characterize the dependence of hazard function of failure time and intensity function of visiting process. Moreover, the joint model could describe the possible none, positive or negative association between failure time and visiting process. We propose the semiparametric maximum likelihood estimators and develop an EM algorithm based on a Poisson data augmentation. The performance of the proposed method is examined through extensive simulation studies and an application to a bladder cancer dataset is presented.

Joint analysis of longitudinal and interval-censored failure time data

Methods for joint analysis of longitudinal measures and right-censored survival outcomes have received much attention in the literature. However, in clinic and epidemiology research, the event of interest is only examined at the inspection time, resulting in the interval-censored failure time data. In this article, we construct a joint model for the longitudinal outcomes and the failure time, which is subject to interval censoring. We account for the dependence between the longitudinal measures and failure time through the incorporation of random effects. The semiparametric regression model with random effects and the Cox frailty model is used for the longitudinal outcome and the failure time, respectively. Spline functions are applied to approximate the infinite-dimensional baseline mean function and baseline cumulative hazard function in the joint model. The EM algorithm is used to find the maximum likelihood estimators and the estimated standard deviations are computed from the log observed-data likelihood. Extensive simulation studies are conducted to assess the performance of the proposed estimators. Simulation results show that the proposed method performs quite well. Finally, we illustrate the proposed approach by analyzing the chronic kidney disease.

Analysis of Interval Censored Competing Risk Data via Nonparametric Multiple Imputation

In many clinical studies, the time to event of interest may involve several causes of failure. Furthermore, when the failure times are not completely observed, and instead are only known to lie somewhere between two observation times, interval censored competing risk data occur. For estimating regression coefficient with right censored competing risk data, Fine and Gray introduced the concept of censoring complete data and derived an estimating equation using an inverse probability censoring weight technique to reflect the probability being censored. As an alternative to achieve censoring complete data, Ruan and Gray considered to directly impute a potential censoring time for the subject who experienced the competing event. In this work, we extend Ruan and Gray’s approach to interval censored competing risk data by applying a multiple imputation technique. The suggested method has an advantage to be easily implemented by using several R functions developed for analyzing interval censored failure time data without competing risks. Simulation studies are conducted under diverse schemes to evaluate sizes and powers and to estimate regression coefficients. A dataset from an AIDS cohort study is analyzed as a real data example.

A Mixture Model for Bivariate Interval-Censored Failure Times with Dependent Susceptibility

Interval-censored failure times arise when the status with respect to an event of interest is only determined at intermittent examination times. In settings where there exists a sub-population of individuals who are not susceptible to the event of interest, latent variable models accommodating a mixture of susceptible and nonsusceptible individuals are useful. We consider such models for the analysis of bivariate interval-censored failure time data with a model for bivariate binary susceptibility indicators and a copula model for correlated failure times given joint susceptibility. We develop likelihood, composite likelihood, and estimating function methods for model fitting and inference, and assess asymptotic-relative efficiency and finite sample performance. Extensions dealing with higher-dimensional responses and current status data are also described.

Estimation of the additive hazards model with case [formula omitted] interval-censored failure time data in the presence of informative censoring

The additive hazards model is one of the most commonly used model in regression analysis of failure time data and many estimation procedures have been developed for its inference under various situations (Kalbfleisch and Prentice (2002); Lin and Ying (1994); Sun (2006)). In this paper, we consider a situation, case K interval-censored data with informative interval censoring, that often occurs in practice such as medical follow-up studies but has not been discussed much in the literature due to the difficulties involved. For the problem, a joint model is proposed to describe the correlation between the failure time of interest and the underlying censoring or observation process and a sieve maximum likelihood approach is developed. In particular, an EM algorithm is presented for the implementation of the proposed estimation procedure and the asymptotic properties of the resulting estimators are established. A simulation study is conducted to assess the finite sample performance of the proposed method and suggests that it works well for practical situations. Also the method is applied to an AIDS study that motivated this study.

Regression analysis of interval-censored failure time data with time-dependent covariates

Interval-censored failure time data often occur in many areas and their analysis has recently attracted a great deal of attention. On the other hand, most of the existing literature for them can only deal with time-independent covariates. Sometimes one may face time dependent covariates and furthermore the covariates could also suffer measurement errors. For the situation, one approach is to conduct a joint analysis for which many methods have been developed in the literature under various framework. One drawback of these methods is that they usually assume that there are no more measurements on the covariates after the failure time and it is apparent that this may not be true. In this paper, a new joint analysis approach is proposed that can take into account the extra observations. In particular, for estimation, a MCEM algorithm is developed that is much more stable and converges much faster than the existing algorithms. To assess the finite sample performance of the proposed method, an extensive simulation study is conducted and suggests that it works well for practical situations. Also the method is applied to an AIDS study that motivated this investigation.

Regression analysis of informatively interval-censored failure time data with semiparametric linear transformation model

ABSTRACT Regression analysis of interval-censored failure time data with noninformative censoring has been widely investigated and many methods have been proposed. Sometimes the mechanism behind the interval censoring may be informative and several approaches have also been developed for this latter situation. However, all of these existing methods are for single models and it is well known that in many situations, one may prefer more flexible models. Corresponding to this, the linear transformation model is considered and a maximum likelihood estimation method is established. In the proposed method, the association between the failure time of interest and the censoring time is modelled by the copula model, and the involved nonparametric functions are approximated by spline functions. The large sample properties of the proposed estimators are derived. Numerical results show that the proposed method performs well in practical application. Besides, a real data example is presented for the illustration.

Semiparametric inference for a two-stage outcome-dependent sampling design with interval-censored failure time data.

We propose a two-stage outcome-dependent sampling design and inference procedure for studies that concern interval-censored failure time outcomes. This design enhances the study efficiency by allowing the selection probabilities of the second-stage sample, for which the expensive exposure variable is ascertained, to depend on the first-stage observed interval-censored failure time outcomes. In particular, the second-stage sample is enriched by selectively including subjects who are known or observed to experience the failure at an early or late time. We develop a sieve semiparametric maximum pseudo likelihood procedure that makes use of all available data from the proposed two-stage design. The resulting regression parameter estimator is shown to be consistent and asymptotically normal, and a consistent estimator for its asymptotic variance is derived. Simulation results demonstrate that the proposed design and inference procedure performs well in practical situations and is more efficient than the existing designs and methods. An application to a phase 3 HIV vaccine trial is provided.

Regression analysis of interval-censored failure time data with cured subgroup and mismeasured covariates

Failure time data occur in many areas and also in various forms and in particular, many authors have discussed regression analysis of failure time data in the presence of interval censoring, a cured subgroup or mismeasured covariates. However, it does not seem to exist an established procedure that can deal with all three issues together. Corresponding to this, we propose a sieve maximum likelihood estimation procedure that takes into account all three issues with the use of the SIMEX algorithm. The asymptotic properties of the proposed estimators are established, and an extensive simulation study is also conducted and suggests that the proposed method works well for practical situations.

A class of semiparametric transformation cure models for interval-censored failure time data

This paper discusses regression analysis of interval-censored failure time data with a cured subgroup under a general class of semiparametric transformation cure models. For inference, a novel and stable expectation maximization (EM) algorithm with the use of Poisson variables is developed to overcome the difficulty in maximizing the observed data likelihood function with complex form. The asymptotic properties of the resulting estimators are established and in particular, the estimators of regression parameters are shown to be semiparametrically efficient. The numerical results obtained from a simulation study indicate that the proposed approach works well for practical situations. An application to a set of data on children’s mortality is also provided.