Lianming Wang

Fast Bayesian Inference in Dirichlet Process Mixture Models.

There has been increasing interest in applying Bayesian nonparametric methods in large samples and high dimensions. As Markov chain Monte Carlo (MCMC) algorithms are often infeasible, there is a pressing need for much faster algorithms. This article proposes a fast approach for inference in Dirichlet process mixture (DPM) models. Viewing the partitioning of subjects into clusters as a model selection problem, we propose a sequential greedy search algorithm for selecting the partition. Then, when conjugate priors are chosen, the resulting posterior conditionally on the selected partition is available in closed form. This approach allows testing of parametric models versus nonparametric alternatives based on Bayes factors. We evaluate the approach using simulation studies and compare it with four other fast nonparametric methods in the literature. We apply the proposed approach to three datasets including one from a large epidemiologic study. Matlab codes for the simulation and data analyses using the proposed approach are available online in the supplemental materials.

Bayesian proportional hazards model for current status data with monotone splines

The proportional hazards model is widely used to deal with time to event data in many fields. However, its popularity is limited to right-censored data, for which the partial likelihood is available and the partial likelihood method allows one to estimate the regression coefficients directly without estimating the baseline hazard function. In this paper, we focus on current status data and propose an efficient and easy-to-implement Bayesian approach under the proportional hazards model. Specifically, we model the baseline cumulative hazard function with monotone splines leading to only a finite number of parameters to estimate while maintaining great modeling flexibility. An efficient Gibbs sampler is proposed for posterior computation relying on a data augmentation through Poisson latent variables. The proposed method is evaluated and compared to a constrained maximum likelihood method and three other existing approaches in a simulation study. Uterine fibroid data from an epidemiological study are analyzed as an illustration.

Regression analysis for current status data using the EM algorithm

We propose new expectation-maximization algorithms to analyze current status data under two popular semiparametric regression models: the proportional hazards (PH) model and the proportional odds (PO) model. Monotone splines are used to model the baseline cumulative hazard function in the PH model and the baseline odds function in the PO model. The proposed algorithms are derived by exploiting a data augmentation based on Poisson latent variables. Unlike previous regression work with current status data, our PH and PO model fitting methods are fast, flexible, easy to implement, and provide variance estimates in closed form. These techniques are evaluated using simulation and are illustrated using uterine fibroid data from a prospective cohort study on early pregnancy.

A semiparametric probit model for case 2 interval-censored failure time data.

Interval-censored data occur naturally in many fields and the main feature is that the failure time of interest is not observed exactly, but is known to fall within some interval. In this paper, we propose a semiparametric probit model for analyzing case 2 interval-censored data as an alternative to the existing semiparametric models in the literature. Specifically, we propose to approximate the unknown nonparametric nondecreasing function in the probit model with a linear combination of monotone splines, leading to only a finite number of parameters to estimate. Both the maximum likelihood and the Bayesian estimation methods are proposed. For each method, regression parameters and the baseline survival function are estimated jointly. The proposed methods make no assumptions about the observation process and can be applicable to any interval-censored data with easy implementation. The methods are evaluated by simulation studies and are illustrated by two real-life interval-censored data applications.

A flexible, computationally efficient method for fitting the proportional hazards model to interval-censored data

The proportional hazards model (PH) is currently the most popular regression model for analyzing time-to-event data. Despite its popularity, the analysis of interval-censored data under the PH model can be challenging using many available techniques. This article presents a new method for analyzing interval-censored data under the PH model. The proposed approach uses a monotone spline representation to approximate the unknown nondecreasing cumulative baseline hazard function. Formulating the PH model in this fashion results in a finite number of parameters to estimate while maintaining substantial modeling flexibility. A novel expectation-maximization (EM) algorithm is developed for finding the maximum likelihood estimates of the parameters. The derivation of the EM algorithm relies on a two-stage data augmentation involving latent Poisson random variables. The resulting algorithm is easy to implement, robust to initialization, enjoys quick convergence, and provides closed-form variance estimates. The performance of the proposed regression methodology is evaluated through a simulation study, and is further illustrated using data from a large population-based randomized trial designed and sponsored by the United States National Cancer Institute.

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

Current status data commonly arise in many fields such as epidemiological studies and cross-sectional tumorigenicity studies. In this article, we propose a semiparametric Bayesian approach for analyzing current status data with the proportional odds model. The use of monotone splines for the baseline odds function and a novel data augmentation with Poisson latent variables enable simple updating all of the parameters in the posterior computation. The proposed approach shows good performance and is compared with the approach in Wang and Dunson (2010) in a simulation study. We also generalize the proposed approach to analyze clustered and multivariate current status data under the frailty proportional odds models.

Regression analysis of bivariate current status data under the Gamma-frailty proportional hazards model using the EM algorithm

The Gamma-frailty proportional hazards (PH) model is commonly used to analyze correlated survival data. Despite this models popularity, the analysis of correlated current status data under the Gamma-frailty PH model can prove to be challenging using traditional techniques. Consequently, in this paper we develop a novel expectation-maximization (EM) algorithm under the Gamma-frailty PH model to study bivariate current status data. Our method uses a monotone spline representation to approximate the unknown conditional cumulative baseline hazard functions. Proceeding in this fashion leads to the estimation of a finite number of parameters while simultaneously allowing for modeling flexibility. The derivation of the proposed EM algorithm relies on a three-stage data augmentation involving Poisson latent variables. The resulting algorithm is easy to implement, robust to initialization, and enjoys quick convergence. Simulation results suggest that the proposed method works well and is robust to the misspecification of the frailty distribution. Our methodology is used to analyze chlamydia and gonorrhea data collected by the Nebraska Public Health Laboratory as a part of the Infertility Prevention Project.

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.

Bayesian semiparametric model for spatially correlated interval-censored survival data

Interval-censored survival data are often recorded in medical practice. Although some methods have been developed for analyzing such data, issues still remain in terms of efficiency and accuracy in estimation. In addition, interval-censored data with spatial correlation are not unusual but less studied. In this paper, we propose an efficient Bayesian approach under a proportional hazards frailty model to analyze interval-censored survival data with spatial correlation. Specifically, a linear combination of monotonic splines is used to model the unknown baseline cumulative hazard function, leading to a finite number of parameters to estimate while maintaining adequate modeling flexibility. A conditional autoregressive distribution is employed to model the spatial dependency. A two-step data augmentation through Poisson latent variables is used to facilitate the computation of posterior distributions that are essential in the proposed MCMC algorithm. Simulation studies are conducted to evaluate the performance of the proposed method. The approach is illustrated through geographically referenced smoking cessation data in southeastern Minnesota where time to relapse is modeled and spatial structure is examined.

Semiparametric Bayes Multiple Testing: Applications to Tumor Data

In National Toxicology Program (NTP) studies, investigators want to assess whether a test agent is carcinogenic overall and specific to certain tumor types, while estimating the dose-response profiles. Because there are potentially correlations among the tumors, a joint inference is preferred to separate univariate analyses for each tumor type. In this regard, we propose a random effect logistic model with a matrix of coefficients representing log-odds ratios for the adjacent dose groups for tumors at different sites. We propose appropriate nonparametric priors for these coefficients to characterize the correlations and to allow borrowing of information across different dose groups and tumor types. Global and local hypotheses can be easily evaluated by summarizing the output of a single Monte Carlo Markov chain (MCMC). Two multiple testing procedures are applied for testing local hypotheses based on the posterior probabilities of local alternatives. Simulation studies are conducted and an NTP tumor data set is analyzed illustrating the proposed approach.