A Bayesian approach for analyzing partly interval-censored data under the proportional hazards model

A Bayesian proportional hazards mixture cure model for interval-censored data

The proportional hazards mixture cure model is a popular analysis method for survival data where a subgroup of patients are cured. When the data are interval-censored, the estimation of this model is challenging due to its complex data structure. In this article, we propose a computationally efficient semiparametric Bayesian approach, facilitated by spline approximation and Poisson data augmentation, for model estimation and inference with interval-censored data and a cure rate. The spline approximation and Poisson data augmentation greatly simplify the MCMC algorithm and enhance the convergence of the MCMC chains. The empirical properties of the proposed method are examined through extensive simulation studies and also compared with the R package "GORCure". The use of the proposed method is illustrated through analyzing a data set from the Aerobics Center Longitudinal Study.

Conditional modeling of panel count data with partly interval-censored failure event

In longitudinal follow-up studies, panel count data arise from discrete observations on recurrent events. We investigate a more general situation where a partly interval-censored failure event is informative to recurrent events. The existing methods for the informative failure event are based on the latent variable model, which provides indirect interpretation for the effect of failure event. To solve this problem, we propose a failure-time-dependent proportional mean model with panel count data through an unspecified link function. For estimation of model parameters, we consider a conditional expectation of least squares function to overcome the challenges from partly interval-censoring, and develop a two-stage estimation procedure by treating the distribution function of the failure time as a functional nuisance parameter and using the B-spline functions to approximate unknown baseline mean and link functions. Furthermore, we derive the overall convergence rate of the proposed estimators and establish the asymptotic normality of finite-dimensional estimator and functionals of infinite-dimensional estimator. The proposed estimation procedure is evaluated by extensive simulation studies, in which the finite-sample performances coincide with the theoretical results. We further illustrate our method with a longitudinal healthy longevity study and draw some insightful conclusions.

Analysis of length-biased and partly interval-censored survival data with mismeasured covariates

In this paper, we analyze the length-biased and partly interval-censored data, whose challenges primarily come from biased sampling and interfere induced by interval censoring. Unlike existing methods that focus on low-dimensional data and assume the covariates to be precisely measured, sometimes researchers may encounter high-dimensional data subject to measurement error, which are ubiquitous in applications and make estimation unreliable. To address those challenges, we explore a valid inference method for handling high-dimensional length-biased and interval-censored survival data with measurement error in covariates under the accelerated failure time model. We primarily employ the SIMEX method to correct for measurement error effects and propose the boosting procedure to do variable selection and estimation. The proposed method is able to handle the case that the dimension of covariates is larger than the sample size and enjoys appealing features that the distributions of the covariates are left unspecified.

Bayesian transformation model for spatial partly interval-censored data

The transformation model with partly interval-censored data offers a highly flexible modeling framework that can simultaneously support multiple common survival models and a wide variety of censored data types. However, the real data may contain unexplained heterogeneity that cannot be entirely explained by covariates and may be brought on by a variety of unmeasured regional characteristics. Due to this, we introduce the conditionally autoregressive prior into the transformation model with partly interval-censored data and take the spatial frailty into account. An efficient Markov chain Monte Carlo method is proposed to handle the posterior sampling and model inference. The approach is simple to use and does not include any challenging Metropolis steps owing to four-stage data augmentation. Through several simulations, the suggested method's empirical performance is assessed and then the method is used in a leukemia study.

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.

A flexible parametric approach for analyzing arbitrarily censored data that are potentially subject to left truncation under the proportional hazards model

The proportional hazards (PH) model is, arguably, the most popular model for the analysis of lifetime data arising from epidemiological studies, among many others. In such applications, analysts may be faced with censored outcomes and/or studies which institute enrollment criterion leading to left truncation. Censored outcomes arise when the event of interest is not observed but rather is known relevant to an observation time(s). Left truncated data occur in studies that exclude participants who have experienced the event prior to being enrolled in the study. If not accounted for, both of these features can lead to inaccurate inferences about the population under study. Thus, to overcome this challenge, herein we propose a novel unified PH model that can be used to accommodate both of these features. In particular, our approach can seamlessly analyze exactly observed failure times along with interval-censored observations, while aptly accounting for left truncation. To facilitate model fitting, an expectation-maximization algorithm is developed through the introduction of carefully structured latent random variables. To provide modeling flexibility, a monotone spline representation is used to approximate the cumulative baseline hazard function. The performance of our methodology is evaluated through a simulation study and is further illustrated through the analysis of two motivating data sets; one that involves child mortality in Nigeria and the other prostate cancer.

A Bayesian Model for Spatial Partly Interval-Censored Data

Partly interval-censored data often occur in cancer clinical trials and have been analyzed as right-censored data. Patients' geographic information sometimes is also available and can be useful in testing treatment effects and predicting survivorship. We propose a Bayesian semiparametric method for analyzing partly interval-censored data with areal spatial information under the proportional hazards model. A simulation study is conducted to compare the performance of the proposed method with the main method currently available in the literature and the traditional Cox proportional hazards model for right-censored data. The method is illustrated through a leukemia survival data set and a dental health data set. The proposed method will be especially useful for analyzing progression-free survival in multi-regional cancer clinical trials.

Bayesian transformation models with partly interval-censored data

In many scientific fields, partly interval-censored data, which consist of exactly observed and interval-censored observations on the failure time of interest, appear frequently. However, methodological developments in the analysis of partly interval-censored data are relatively limited and have mainly focused on additive or proportional hazards models. The general linear transformation model provides a highly flexible modeling framework that includes several familiar survival models as special cases. Despite such nice features, the inference procedure for this class of models has not been developed for partly interval-censored data. We propose a fully Bayesian approach coped with efficient Markov chain Monte Carlo methods to fill this gap. A four-stage data augmentation procedure is introduced to tackle the challenges presented by the complex model and data structure. The proposed method is easy to implement and computationally attractive. The empirical performance of the proposed method is evaluated through two simulation studies, and the model is then applied to a dental health study.

A semiparametric mixture model approach for regression analysis of partly interval-censored data with a cured subgroup

Failure time data with a cured subgroup are frequently confronted in various scientific fields and many methods have been proposed for their analysis under right or interval censoring. However, a cure model approach does not seem to exist in the analysis of partly interval-censored data, which consist of both exactly observed and interval-censored observations on the failure time of interest. In this article, we propose a two-component mixture cure model approach for analyzing such type of data. We employ a logistic model to describe the cured probability and a proportional hazards model to model the latent failure time distribution for uncured subjects. We consider maximum likelihood estimation and develop a new expectation-maximization algorithm for its implementation. The asymptotic properties of the resulting estimators are established and the finite sample performance of the proposed method is examined through simulation studies. An application to a set of real data on childhood mortality in Nigeria is provided.

Regression analysis of arbitrarily censored survival data under the proportional odds model

Arbitrarily censored data are referred to as the survival data that contain a mixture of exactly observed, left-censored, interval-censored, and right-censored observations. Existing research work on regression analysis on arbitrarily censored data is relatively sparse and mainly focused on the proportional hazards model and the accelerated failure time model. This article studies the proportional odds (PO) model and proposes a novel estimation approach through an expectation-maximization (EM) algorithm for analyzing such data. The proposed EM algorithm has many appealing properties such as being robust to initial values, easy to implement, converging fast, and providing the variance estimate of the regression parameter estimate in closed form. An informal diagnosis plot is developed for checking the PO model assumption. Our method has shown excellent performance in estimating the regression parameters as well as the baseline survival function in a simulation study. A real-life dataset about metastatic colorectal cancer is analyzed for illustration. An R package regPO has been created for practitioners to implement our method.