Bayesian Proportional Odds Models for Analyzing Current Status Data: Univariate, Clustered, and Multivariate

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.

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

Partly interval-censored time-to-event data often occur in biomedical studies of diseases where periodic medical examinations for symptoms of interest are necessary. Recent decades have seen blooming methods and R packages for interval-censored data; however, the research effort for partly interval-censored data is limited. We propose an efficient and easy-to-implement Bayesian semiparametric method for analyzing partly interval-censored data under the proportional hazards model. Two simulation studies are conducted to compare the performance of the proposed method with two main Bayesian methods currently available in the literature and the classic Cox proportional hazards model. The proposed method is applied to a partly interval-censored progression-free survival data from a metastatic colorectal cancer trial.

A Gamma-frailty proportional hazards model for bivariate interval-censored data

Correlated survival data naturally arise from many clinical and epidemiological studies. For the analysis of such data, the Gamma-frailty proportional hazards (PH) model is a popular choice because the regression parameters have marginal interpretations and the statistical association between the failure times can be explicitly quantified via Kendall's tau. Despite their popularity, Gamma-frailty PH models for correlated interval-censored data have not received as much attention as analogous models for right-censored data. In this work, a Gamma-frailty PH model for bivariate interval-censored data is presented and an easy to implement expectation-maximization (EM) algorithm for model fitting is developed. The proposed model adopts a monotone spline representation for the purposes of approximating the unknown conditional cumulative baseline hazard functions, significantly reducing the number of unknown parameters while retaining modeling flexibility. The EM algorithm was derived from a data augmentation procedure involving latent Poisson random variables. Extensive numerical studies illustrate that the proposed method can provide reliable estimation and valid inference, and is moreover robust to the misspecification of the frailty distribution. To further illustrate its use, the proposed method is used to analyze data from an epidemiological study of sexually transmitted infections.

A Bayesian proportional hazards model for general interval-censored data

The proportional hazards (PH) model is the most widely used semiparametric regression model for analyzing right-censored survival data based on the partial likelihood method. However, the partial likelihood does not exist for interval-censored data due to the complexity of the data structure. In this paper, we focus on general interval-censored data, which is a mixture of left-, right-, and interval-censored observations. We propose an efficient and easy-to-implement Bayesian estimation approach for analyzing such data under the PH model. The proposed approach adopts monotone splines to model the baseline cumulative hazard function and allows to estimate the regression parameters and the baseline survival function simultaneously. A novel two-stage data augmentation with Poisson latent variables is developed for the efficient computation. The developed Gibbs sampler is easy to execute as it does not require imputing any unobserved failure times or contain any complicated Metropolis-Hastings steps. Our approach is evaluated through extensive simulation studies and illustrated with two real-life data sets.

Spatial extended hazard model with application to prostate cancer survival

This article develops a Bayesian semiparametric approach to the extended hazard model, with generalization to high-dimensional spatially grouped data. County-level spatial correlation is accommodated marginally through the normal transformation model of Li and Lin (2006, Journal of the American Statistical Association 101, 591-603), using a correlation structure implied by an intrinsic conditionally autoregressive prior. Efficient Markov chain Monte Carlo algorithms are developed, especially applicable to fitting very large, highly censored areal survival data sets. Per-variable tests for proportional hazards, accelerated failure time, and accelerated hazards are efficiently carried out with and without spatial correlation through Bayes factors. The resulting reduced, interpretable spatial models can fit significantly better than a standard additive Cox model with spatial frailties.

Global rates of convergence of the MLE for multivariate interval censoring

We establish global rates of convergence of the Maximum Likelihood Estimator (MLE) of a multivariate distribution function on ℝ d in the case of (one type of) "interval censored" data. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse than n-1/3(log n)γ for γ = (5d - 4)/6.