Analysis Of Current Status Data Research Articles

Deep partially linear cox model for current status data.

Deep learning has continuously attained huge success in diverse fields, while its application to survival data analysis remains limited and deserves further exploration. For the analysis of current status data, a deep partially linear Cox model is proposed to circumvent the curse of dimensionality. Modeling flexibility is attained by using deep neural networks (DNNs) to accommodate nonlinear covariate effects and monotone splines to approximate the baseline cumulative hazard function. We establish the convergence rate of the proposed maximum likelihood estimators. Moreover, we derive that the finite-dimensional estimator for treatment covariate effects is $\sqrt{n}$-consistent, asymptotically normal, and attains semiparametric efficiency. Finally, we demonstrate the performance of our procedures through extensive simulation studies and application to real-world data on news popularity.

Regression Analysis of Dependent Current Status Data with Left Truncation

Current status data are encountered in a wide range of applications, including tumorigenic experiments and demographic studies. In this case, each subject has one observation, and the only information obtained is whether the event of interest happened at the moment of observation. In addition to censoring, truncating is also very common in practice. This paper examines the regression analysis of current status data with informative censoring times, considering the presence of left truncation. In addition, we propose an inference approach based on sieve maximum likelihood estimation (SMLE). A copula-based approach is used to describe the relationship between the failure time of interest and the censoring time. The spline function is employed to approximate the unknown nonparametric function. We have established the asymptotic properties of the proposed estimator. Simulation studies suggest that the developed procedure works well in practice. We also applied the developed method to a real dataset derived from an AIDS cohort research.

Empirical analysis of current status data for additive hazards model with auxiliary covariates

Empirical analysis of current status data for additive hazards model with auxiliary covariates

Regression analysis of current status data with latent variables.

Current status data occur in many fields including demographical, epidemiological, financial, medical, and sociological studies. We consider the regression analysis of current status data with latent variables. The proposed model consists of a factor analytic model for characterizing latent variables through their multiple surrogates and an additive hazard model for examining potential covariate effects on the hazards of interest in the presence of current status data. We develop a borrow-strength estimation procedure that incorporates the expectation-maximization algorithm and correlated estimating equations. The consistency and asymptotic normality of the proposed estimators are established. A simulation study is conducted to evaluate the finite sample performance of the proposed method. A real-life study on the chronic kidney disease of type 2 diabetic patients is presented.

Marginal analysis of current status data with informative cluster size using a class of semiparametric transformation cure models.

This research is motivated by a periodontal disease dataset that possesses certain special features. The dataset consists of clustered current status time-to-event observations with large and varying cluster sizes, where the cluster size is associated with the disease outcome. Also, heavy censoring is present in the data even with long follow-up time, suggesting the presence of a cured subpopulation. In this paper, we propose a computationally efficient marginal approach, namely the cluster-weighted generalized estimating equation approach, to analyze the data based on a class of semiparametric transformation cure models. The parametric and nonparametric components of the model are estimated using a Bernstein-polynomial based sieve maximum pseudo-likelihood approach. The asymptotic properties of the proposed estimators are studied. Simulation studies are conducted to evaluate the performance of the proposed estimators in scenarios with different degree of informative clustering and within-cluster dependence. The proposed method is applied to the motivating periodontal disease data for illustration.

Current status data with two competing risks and missing failure types: a parametric approach

ABSTRACT Missing cause of failure is a common problem in competing risks data. Here we consider a general missing pattern in which one observes a set of possible causes containing the true cause. In this work, we focus on the parametric analysis of current status data with two competing risks and the above-mentioned missing pattern. We make some simpler assumptions on the conditional probability of observing a set of possible causes of failure given the true cause and carry out maximum-likelihood estimation of the model parameters. Asymptotic properties of the maximum-likelihood estimators are also discussed. Simulation studies are performed to study the finite sample properties of the estimators and also to investigate the role of the monitoring time distribution. Finally, the method is illustrated through the analysis of a real data set.

Regression analysis of dependent current status data with the accelerated failure time model

In this article, we discuss the regression analysis of dependent current status data under the accelerated failure time model. There exist many literatures discussing the regression analysis of current status data under different models, but few literature discussing the regression problem of dependent current status data under the AFT model. Corresponding to this, we propose a sieve maximum likelihood approach for estimation of covariate effects. In the approach, we model the correlation between the interested survival time and the observation time by the copula function. Simulation study is conducted in order to assess the finite sample behavior of the method. A real data example is provided to illustrate the application of the proposed method.

Efficient estimation for the non-mixture cure model with current status data

Medical advances including the neoadjuvant anti-PD-1 immunotherapy play a role in promoting clinical outcomes such as improved overall and progression-free survival probabilities. This paper considers the regression analysis of current status data with a cured subgroup in the population using a semiparametric non-mixture cure model. We propose a sieve maximum likelihood estimation for the model with the Bernstein polynomials. Moreover, an expectation–maximization (EM) algorithm is developed under the non-mixture cure model to calculate the estimators for both parametric and non-parametric components. Under some mild conditions, the asymptotic properties of the estimators are established, including the strong consistency, the convergence rate and the asymptotic normality. Simulation studies are conducted to investigate the finite sample performance of the proposed estimators. A real dataset from the tumorigenicity experiment is analysed for illustration.

Regression analysis of informative current status data with the semiparametric linear transformation model

ABSTRACTMany 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.

Regression analysis of current status data in the presence of dependent censoring with applications to tumorigenicity experiments

Current status data frequently occur in many fields including demographic studies and tumorigenicity experiments. In these cases, the censoring or observation time may be correlated to the failure time of interest, the situation that is often referred to as dependent or informative censoring. Although several semiparametric methods have been developed in the literature for the situation, they either only apply to limited situations or may be computationally unstable. To address these, a frailty model-based maximum likelihood approach is proposed with the use of monotone splines to approximate the unknown baseline cumulative hazard function of the failure time. Also a novel EM algorithm, which is based on a three-stage data augmentation and can be easily implemented, is presented. The proposed estimators are proved to be consistent and asymptotically normally distributed. An extensive simulation study is performed to assess the finite sample performance of the proposed approach and suggests that it works well for practical situations. An application to a tumorigenicity study is provided.

Regression analysis of current status data with auxiliary covariates and informative observation times.

This paper discusses regression analysis of current status failure time data with information observations and continuous auxiliary covariates. Under the additive hazards model, we employ a frailty model to describe the relationship between the failure time of interest and censoring time through some latent variables and propose an estimated partial likelihood estimator of regression parameters that makes use of the available auxiliary information. Asymptotic properties of the resulting estimators are established. To assess the finite sample performance of the proposed method, an extensive simulation study is conducted, and the results indicate that the proposed method works well. An illustrative example is also provided.

Regression analysis of current status data in the presence of a cured subgroup and dependent censoring.

This paper discusses regression analysis of current status data, a type of failure time data where each study subject is observed only once, in the presence of dependent censoring. Furthermore, there may exist a cured subgroup, meaning that a proportion of study subjects are not susceptible to the failure event of interest. For the problem, we develop a sieve maximum likelihood estimation approach with the use of latent variables and Bernstein polynomials. For the determination of the proposed estimators, an EM algorithm is developed and the asymptotic properties of the estimators are established. Extensive simulation studies are conducted and indicate that the proposed method works well for practical situations. A motivating application from a tumorigenicity experiment is also provided.

Regression Analysis of Current Status Data Under the Additive Hazards Model with Auxiliary Covariates

AbstractThis 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.

Assessing age‐at‐onset risk factors with incomplete covariate current status data under proportional odds models

Motivated by an epidemiological survey of fracture in elderly women, we develop a semiparametric regression analysis of current status data with incompletely observed covariate under the proportional odds model. To accommodate both the interval-censored nature of current status failure time data and the incompletely observed covariate data, we propose an analysis based on the validation likelihood (VL), which is derived from likelihood pertaining to the validation sample, namely the subset of the sample where the data are completely observed. The missing data mechanism is assumed to be missing at random and is explicitly modeled and estimated in the VL approach. We propose implementing the VL method by integrating self-consistency and Newton-Raphson algorithms. Asymptotic normality and standard error estimation for the proposed estimator of the regression parameter are guaranteed. Simulation results reveal good performance of the VL estimator. The VL method has some gain in efficiency compared with the naive complete case method. But the VL method leads to unbiased estimators, whereas the complete case method does not when missing covariates are not missing completely at random. Application of the VL approach to the fracture data confirms that osteoporosis (low bone density) is a strong risk factor for the age at onset of fracture in elderly women.

On efficient estimation in additive hazards regression with current status data

The additive hazard regression (AHR) model is known for its convenience in interpretation, as hazard is modeled as a linear function of covariates. One outstanding issue in the application of such a model in the analysis of current status data is that there lacks an efficient and computationally simple approach for parameter estimation. In the current literature, Lin et al.’s (1998) method enjoys the computational ease but it is not semi-parametrically efficient, whereas Martinussen and Scheike’s (2002) method is semi-parametrically efficient but difficult to compute. In this paper, we propose a new estimation approach in the context of Lin et al.’s AHR models where the monitor time process follows a proportional hazard model. We show that not only the proposed estimator achieves semi-parametric information bound, but also its implementation can be done easily using existing statistical software. We evaluate this new method via simulation studies. Also, we illustrate the proposed method through an analysis of renal function recovery data.

Analysis of Current Status Data with Missing Covariates

Statistical inference based on right-censored data for the proportional hazards (PH) model with missing covariates has received considerable attention, but interval-censored or current status data with missing covariates has not yet been investigated. Our study is partly motivated by the analysis of fracture data from the 2005 National Health Interview Survey Original Database in Taiwan, where the occurrence of fractures was interval censored and the covariate osteoporosis was not reported for all residents. We assume that the data are realized from a PH model. A semiparametric maximum likelihood estimate implemented by a hybrid algorithm is proposed to analyze current status data with missing covariates. A comparison of the performance of our method with full-cohort analysis, complete-case analysis, and surrogate analysis is made via simulation with moderate sample sizes. The fracture data are then analyzed.

A Multiple Imputation Approach to the Analysis of Current Status Data with the Additive Hazards Model

This article discusses regression analysis of current status data, which occur in many fields including cross-sectional studies, demographical investigations, and tumorigenicity experiments (Keiding, 1991; Sun 2006). For the problem, we focus on the situation where the survival time of interest can be described by the additive hazards model and a multiple imputation approach is presented for inference. A major advantage of the approach is its simplicity and it can be easily implemented by using the existing software packages for right-censored failure time data. Extensive simulation studies are conducted and indicate that the approach performs well for practical situations and is comparable to the existing methods. The methodology is applied to a set of current status data arising from a tumorigenicity experiment and the model checking is discussed.

A model with long-term survivors for the analysis of current-status nuptiality data

The model proposed in this paper combines a logistic regression model and a Weibull regression model for the analysis of current-status data. This joint model allows a simultaneous estimation of two sets of effects on the covariates: one on the probability that the event occurs (also known as quantum) and the other on the timing of the event. Thus, the model can be seen either as an extension of a survival-analysis model for use with current-status data where a survival fraction is added in order explicitly to take into account the possibility that the event may never occur, or as an extension of survival analysis with long-term survivors to the analysis of current-status data. As an illustrative application we apply our model to a study of nuptiality in seventeenth-century Italy.

A semiparametric regression cure model with current status data

This paper considers the analysis of current status data with a cured proportion in the population using a mixture model that combines a logistic regression formulation for the probability of cure with a semiparametric regression model for the time to occurrence of the event. The semiparametric regression model belongs to the flexible class of partly linear models that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies were carried out to investigate the performance of the proposed method and the model is fitted to a dataset from a study of calcification of the hydrogel intraocular lenses, a complication of cataract treatment.

Statistical analysis of current status data with informative observation times

Current status data arise when each study subject is observed only once and the survival time of interest is known only to be either less or greater than the observation time. Such data often occur in, for example, cross-sectional studies, demographical investigations and tumorigenicity experiments and several semi-parametric and non-parametric methods for their analysis have been proposed. However, most of these methods deal only with the situation where observation time is independent of the underlying survival time completely or given covariates. This paper discusses regression analysis of current status data when the observation time may be related to the underlying survival time and inference procedures are presented for estimation of regression parameters under the additive hazards regression model. The procedures can be easily implemented and are applied to two motivating examples.