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

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 pairwise pseudo-likelihood approach for regression analysis of left-truncated failure time data with various types of censoring

BACKGROUND

Failure time data frequently occur in many medical studies and often accompany with various types of censoring. In some applications, left truncation may occur and can induce biased sampling, which makes the practical data analysis become more complicated. The existing analysis methods for left-truncated data have some limitations in that they either focus only on a special type of censored data or fail to flexibly utilize the distribution information of the truncation times for inference. Therefore, it is essential to develop a reliable and efficient method for the analysis of left-truncated failure time data with various types of censoring.

METHOD

This paper concerns regression analysis of left-truncated failure time data with the proportional hazards model under various types of censoring mechanisms, including right censoring, interval censoring and a mixture of them. The proposed pairwise pseudo-likelihood estimation method is essentially built on a combination of the conditional likelihood and the pairwise likelihood that eliminates the nuisance truncation distribution function or avoids its estimation. To implement the presented method, a flexible EM algorithm is developed by utilizing the idea of self-consistent estimating equation. A main feature of the algorithm is that it involves closed-form estimators of the large-dimensional nuisance parameters and is thus computationally stable and reliable. In addition, an R package LTsurv is developed.

RESULTS

The numerical results obtained from extensive simulation studies suggest that the proposed pairwise pseudo-likelihood method performs reasonably well in practical situations and is obviously more efficient than the conditional likelihood approach as expected. The analysis results of the MHCPS data with the proposed pairwise pseudo-likelihood method indicate that males have significantly higher risk of losing active life than females. In contrast, the conditional likelihood method recognizes this effect as non-significant, which is because the conditional likelihood method often loses some estimation efficiency compared with the proposed method.

CONCLUSIONS

The proposed method provides a general and helpful tool to conduct the Cox's regression analysis of left-truncated failure time data under various types of censoring.

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

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

A new approach to estimation of the proportional hazards model based on interval-censored data with missing covariates

This paper discusses the fitting of the proportional hazards model to interval-censored failure time data with missing covariates. Many authors have discussed the problem when complete covariate information is available or the missing is completely at random. In contrast to this, we will focus on the situation where the missing is at random. For the problem, a sieve maximum likelihood estimation approach is proposed with the use of I-spline functions to approximate the unknown cumulative baseline hazard function in the model. For the implementation of the proposed method, we develop an EM algorithm based on a two-stage data augmentation. Furthermore, we show that the proposed estimators of regression parameters are consistent and asymptotically normal. The proposed approach is then applied to a set of the data concerning Alzheimer Disease that motivated this study.

A simulation-extrapolation approach for regression analysis of misclassified current status data with the additive hazards model

Current status data arise when each subject is observed only once and the failure time of interest is only known to be either smaller or larger than the observation time rather than observed exactly. For the situation, due to the use of imperfect diagnostic tests, the failure status could often suffer misclassification or one observes misclassified data, which may result in severely biased estimation if not taken into account. In this article, we discuss regression analysis of such misclassified current status data arising from the additive hazards model, and a simulation-extrapolation (SIMEX) approach is developed for the estimation. Furthermore, the asymptotic properties of the proposed estimators are established, and a simulation study is conducted to assess the empirical performance of the method, which indicates that the proposed procedure performs well. In particular, it can correct the estimation bias given by the naive method that ignores the existence of misclassification. An application to a medical study on gonorrhea is also provided.

New methods for the additive hazards model with the informatively interval-censored failure time data

The additive hazards model is one of the most commonly used models for regression analysis of failure time data and many inference procedures have been developed for it under various situations. In particular, Wang et al. (2018a, Computational Statistics and Data Analysis, 125, 1-9) discussed the situation where one observes informatively interval-censored data and proposed a likelihood estimation approach. However , it involves estimation of the unknown baseline cumulative hazard function and thus may be time-consuming . Corresponding to this, we propose two new procedures, an estimating equation-based one and an empirical likelihood-based one, and both do not need estimation of the cumulative hazard function and can be easily implemented. The asymptotic properties of the proposed methods are established and an extensive simulation study suggests that they work well in practical situations. An application is also provided.

An additive hazards cure model with informative interval censoring

The existence of a cured subgroup happens quite often in survival studies and many authors considered this under various situations (Farewell in Biometrics 38:1041-1046, 1982; Kuk and Chen in Biometrika 79:531-541, 1992; Lam and Xue in Biometrika 92:573-586, 2005; Zhou et al. in J Comput Graph Stat 27:48-58, 2018). In this paper, we discuss the situation where only interval-censored data are available and furthermore, the censoring may be informative, for which there does not seem to exist an established estimation procedure. For the analysis, we present a three component model consisting of a logistic model for describing the cure rate, an additive hazards model for the failure time of interest and a nonhomogeneous Poisson model for the observation process. For estimation, we propose a sieve maximum likelihood estimation procedure and the asymptotic properties of the resulting estimators are established. Furthermore, an EM algorithm is developed for the implementation of the proposed estimation approach, and extensive simulation studies are conducted and suggest that the proposed method works well for practical situations. Also the approach is applied to a cardiac allograft vasculopathy study that motivated this investigation.

Nonparametric tests for stratified additive hazards model based on current status data

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.

Semiparametric regression analysis of multivariate doubly censored data

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.