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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Estimation of causal treatment effects has attracted a great deal of interest in many areas including social, biological and health science, and for this, instrumental variable (IV) has become a commonly used tool in the presence of unmeasured confounding. In particular, many IV methods have been developed for right-censored time-to-event outcomes. In this paper, we consider a much more complicated situation where one faces interval-censored time-to-event outcomes, which are ubiquitously present in studies with, for example, intermittent follow-up but are challenging to handle in terms of both theory and computation. A sieve maximum likelihood estimation procedure is proposed for estimating complier causal treatment effects under the additive hazards model, 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. It is applied to a breast cancer screening study. [ABSTRACT FROM AUTHOR]

Estimation of compiler causal treatment effects has been discussed by many authors under different situations but only limited literature exists for interval-censored failure time data, which often occur in many areas such as longitudinal or periodical follow-up studies. Particularly it does not seem to exist a method that can deal with informative interval censoring, which can happen naturally and make the analysis much more challenging. Also, it has been shown that when the informative censoring exists, the analysis without taking it into account would yield biased or misleading results. To address this, we propose an estimated sieve maximum likelihood approach with the use of instrumental variables. The asymptotic properties of the resulting estimators of regression parameters are established, and a simulation study is performed and suggests that it works well. Finally, it is applied to a set of real data that motivated this study. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Semi-parametric transformation models provide a general and flexible class of models for regression analysis of failure time data and many methods have been developed for their estimation. In particular, they include the proportional hazards and proportional odds models as special cases. In this paper, we discuss the situation where one observes left-truncated and interval-censored data, for which it does not seem to exist an established method. For the problem, in contrast to the commonly used conditional approach that may not be efficient, a pairwise pseudo-likelihood method is proposed to recover some missing information in the conditional method. The proposed estimators are proved to be consistent and asymptotically efficient and normal. A simulation study is conducted to assess the empirical performance of the method and suggests that it works well in practical situations. This method is illustrated by using a set of real data arising from an HIV/AIDS cohort study. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Summary: Variable selection for interval‐censored failure time data has recently attracted a great deal of attention along with the analysis of interval‐censored data in both method developments and practical applications. Interval‐censored data are a general type of time‐to‐event or failure time data where the failure time of interest is known or observed only to lie in an interval instead of being observed exactly. They often occur in different forms and in many fields, including demographical studies, epidemiological studies, medical or public health researches and social sciences. This paper will discuss and review the existing methods for variable selection based on interval‐censored data, a relatively new but important topic, along with some directions or issues that need more research. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The case-cohort design is widely used as a means of reducing the cost in large cohort studies, especially when the disease rate is low and covariate measurements may be expensive, and has been discussed by many authors. In this paper, we discuss regression analysis of case-cohort studies that produce interval-censored failure time with dependent censoring, a situation for which there does not seem to exist an established approach. For inference, a sieve inverse probability weighting estimation procedure is developed with the use of Bernstein polynomials to approximate the unknown baseline cumulative hazard functions. The proposed estimators are shown to be consistent and the asymptotic normality of the resulting regression parameter estimators is established. A simulation study is conducted to assess the finite sample properties of the proposed approach and indicates that it works well in practical situations. The proposed method is applied to an HIV/AIDS case-cohort study that motivated this investigation. [ABSTRACT FROM AUTHOR]

This article discusses regression analysis of multivariate doubly censored data with a wide class of flexible semiparametric transformation frailty models. The proposed models include many commonly used regression models as special cases such as the proportional hazards and proportional odds frailty models. For inference, we propose a nonparametric maximum likelihood estimation method and develop a new expectation–maximization algorithm for its implementation. The proposed estimators of the finite-dimensional parameters are shown to be consistent, asymptotically normal and semiparametrically efficient. We also conduct a simulation study to assess the finite sample performance of the developed estimation method, and the proposed methodology is applied to a set of real data arising from an AIDS study. [ABSTRACT FROM AUTHOR]

Stratified regression models are commonly employed when study subjects may come from possibly different strata such as different medical centers, and for the situation, one common question of interest is to test the existence of the stratum effect. To address this, there exists some literature on the testing of the stratum effects under the framework of the proportional hazards model when one observes right-censored data or interval-censored data. In this paper, we consider the situation under the additive hazards model when one faces current status data, for which there does not seem to exist an established test procedure. The asymptotic distributions of the proposed test procedure are provided. Also a simulation study is performed to evaluate the performance of the proposed method and indicates that it works well for practical situations. The approach is applied to a set of real current status data from a tumorigenicity study. [ABSTRACT FROM AUTHOR]

Variable selection or feature extraction is fundamental to identify important risk factors from a large number of covariates and has applications in many fields. In particular, its applications in failure time data analysis have been recognized and many methods have been proposed for right-censored data. However, developing relevant methods for variable selection becomes more challenging when one confronts interval censoring that often occurs in practice. In this article, motivated by an Alzheimer's disease study, we develop a variable selection method for interval-censored data with a general class of semiparametric transformation models. Specifically, a novel penalized expectation-maximization algorithm is developed to maximize the complex penalized likelihood function, which is shown to perform well in the finite-sample situation through a simulation study. The proposed methodology is then applied to the interval-censored data arising from the Alzheimer's disease study mentioned above. [ABSTRACT FROM AUTHOR]

Doubly censored failure time data occur when the failure time of interest represents the elapsed time between two events, an initial event and a subsequent event, and the observations on both events may suffer censoring. A well-known example of such data is given by the acquired immune deficiency syndrome (AIDS) cohort study in which the two events are HIV infection and AIDS diagnosis, and several inference methods have been developed in the literature for their regression analysis. However, all of them only apply to limited situations or focus on a single model. In this paper, we propose a marginal likelihood approach based on a general class of semiparametric transformation models, which can be applied to much more general situations. For the implementation, we develop a two-step procedure that makes use of both the multiple imputation technique and a novel EM algorithm. The asymptotic properties of the resulting estimators are established by using the modern empirical process theory, and the simulation study conducted suggests that the method works well in practical situations. An application is also provided. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Many methods have been developed in the literature for regression analysis of current status data with noninformative censoring and also some approaches have been proposed for semiparametric regression analysis of current status data with informative censoring. However, the existing approaches for the latter situation are mainly on specific models such as the proportional hazards model and the additive hazard model. Corresponding to this, in this paper, we consider a general class of semiparametric linear transformation models and develop a sieve maximum likelihood estimation approach for the inference. In the method, the copula model is employed to describe the informative censoring or relationship between the failure time of interest and the censoring time, and Bernstein polynomials are used to approximate the nonparametric functions involved. The asymptotic consistency and normality of the proposed estimators are established, and an extensive simulation study is conducted and indicates that the proposed approach works well for practical situations. In addition, an illustrative example is provided. [ABSTRACT FROM AUTHOR]

The testing of the stratum effects in the Cox model is an important and commonly asked question in medical research as well as in many other fields. In this paper, we will discuss the problem where one observes interval-censored failure time data and generalize the procedure given in Sun and Yang (2000) for right-censored data. The asymptotic distribution of the new test statistic is established and the simulation study conducted for the evaluation of the finite sample properties of the method suggests that the generalized procedure seems to work well for practical situations. An application is provided. [ABSTRACT FROM AUTHOR]

Failure time data occur in many areas and in various censoring forms and many models have been proposed for their regression analysis such as the proportional hazards model and the proportional odds model. Another choice that has been discussed in the literature is a general class of semiparmetric transformation models, which include the two models above and many others as special cases. In this paper, we consider this class of models when one faces a general type of censored data, case K informatively interval-censored data, for which there does not seem to exist an established inference procedure. For the problem, we present a two-step estimation procedure that is quite flexible and can be easily implemented, and the consistency and asymptotic normality of the proposed estimators of regression parameters are established. In addition, an extensive simulation study is conducted and suggests that the proposed procedure works well for practical situations. An application is also provided. [ABSTRACT FROM AUTHOR]

This paper discusses regression analysis of clustered interval-censored failure time data, which often occur in medical follow-up studies among other areas. For such data, sometimes the failure time may be related to the cluster size, the number of subjects within each cluster or we have informative cluster sizes. For the problem, we present a within-cluster resampling method for the situation where the failure time of interest can be described by a class of linear transformation models. In addition to the establishment of the asymptotic properties of the proposed estimators of regression parameters, an extensive simulation study is conducted for the assessment of the finite sample properties of the proposed method and suggests that it works well in practical situations. An application to the example that motivated this study is also provided. [ABSTRACT FROM AUTHOR]

This paper discusses regression analysis of doubly censored failure time data when there may exist a cured subgroup. By doubly censored data, we mean that the failure time of interest denotes the elapsed time between two related events and the observations on both event times can suffer censoring (Sun in The statistical analysis of interval-censored failure time data. Springer, New York, 2006). One typical example of such data is given by an acquired immune deficiency syndrome cohort study. Although many methods have been developed for their analysis (De Gruttola and Lagakos in Biometrics 45:1-12, 1989; Sun et al. in Biometrics 55:909-914, 1999; 60:637-643, 2004; Pan in Biometrics 57:1245-1250, 2001), it does not seem to exist an established method for the situation with a cured subgroup. This paper discusses this later problem and presents a sieve approximation maximum likelihood approach. In addition, the asymptotic properties of the resulting estimators are established and an extensive simulation study indicates that the method seems to work well for practical situations. An application is also provided. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Longitudinal data occur in many fields such as the medical follow-up studies that involve repeated measurements. For their analysis, most existing approaches assume that the observation or follow-up times are independent of the response process either completely or given some covariates. In practice, it is apparent that this may not be true. In this paper, we present a joint analysis approach that allows the possible mutual correlations that can be characterized by time-dependent random effects. Estimating equations are developed for the parameter estimation and the resulted estimators are shown to be consistent and asymptotically normal. The finite sample performance of the proposed estimators is assessed through a simulation study and an illustrative example from a skin cancer study is provided. [ABSTRACT FROM AUTHOR]

This paper discusses regression analysis of current status failure time data arising from the additive hazards model in the presence of informative censoring. Many methods have been developed for regression analysis of current status data under various regression models if the censoring is noninformative, and also there exists a large literature on parametric analysis of informative current status data in the context of tumorgenicity experiments. In this paper, a semiparametric maximum likelihood estimation procedure is presented and in the method, the copula model is employed to describe the relationship between the failure time of interest and the censoring time. Furthermore, I-splines are used to approximate the nonparametric functions involved and the asymptotic consistency and normality of the proposed estimators are established. A simulation study is conducted and indicates that the proposed approach works well for practical situations. An illustrative example is also provided. [ABSTRACT FROM AUTHOR]

This paper discusses regression analysis of current status or case I interval-censored failure time data arising from the additive hazards model. In this situation, some covariates could be missing because of various reasons, but there may exist some auxiliary information about the missing covariates. To address the problem, we propose an estimated partial likelihood approach for estimation of regression parameters, which makes use of the available auxiliary information. The method can be easily implemented, and the asymptotic properties of the resulting estimates are established. To assess the finite sample performance of the proposed method, an extensive simulation study is conducted and indicates that the method works well. [ABSTRACT FROM AUTHOR]