Summary 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 paper 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.

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.

Multivariate failure time data frequently occur in medical studies and the dependence or association among survival variables is often of interest ("Biometrics", 51 , 1995, 1384; "Stat. Med.", 18 , 1999, 3101; "Biometrika", 87 , 2000, 879; "J. Roy. Statist. Soc. Ser. B", 65 , 2003, 257). We study the problem of estimating the association between two related survival variables when they follow a copula model and only bivariate interval-censored failure time data are available. For the problem, a two-stage estimation procedure is proposed and the asymptotic properties of the proposed estimator are established. Simulation studies are conducted to assess the finite sample properties of the presented estimate and the results suggest that the method works well for practical situations. An example from an acquired immunodeficiency syndrome clinical trial is discussed. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..

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.