Survival Likelihood Intervals with Censored Data

• Activity Number: 413
• Type: Contributed
• Date/Time: Thursday, August 12, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Alain C. Vandal*+ and Robert Gentleman and Xuecheng Liu
• Companies: McGill University/SMBD Jewish General Hospital and Harvard School of Public Health and McGill University
• Keywords: empirical likelihood ; vertex-exchange method ; interval-censored data ; nonparametric estimation ; EM algorithm ; current status data

Abstract

The determination of a likelihood-ratio-based confidence interval for a survival function given any type of censored data can be boiled down to a constrained optimization problem. We characterize the constraint as it applies to the cumulative distribution function's (CDF) nonparametric maximum likelihood estimator (NPMLE); special care must be taken in doing so since the CDF NPMLE is defined only up to an equivalence class for every possible constraint. We represent the estimand as a discrete probability vector. Various algorithms can then be specialized to solve the constrained problem; we propose two. The constrained EM works by rescaling at every iteration. The constrained VEM applies the constraint once on subsimplices of the probability vector simplex and essentially runs an unconstrained VEM in each of them. The constrained VEM is efficient enough to compute empirical likelihood ratio curves rapidly and can be used in practice to produce likelihood intervals for the CDF NPMLE. Asymptotic coverage probabilities for these intervals is known for some cases including current status data. We illustrate the technique on a current status dataset of muscle necrosis after injury.