Bayesian Survival Analysis Based on Imperfect Diagnostic Tests

• Activity Number: 225
• Type: Contributed
• Date/Time: Tuesday, August 9, 2005 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Peng Zhang*+ and Stephen W. Lagakos
• Companies: Harvard University and Harvard University
• Keywords: Panel data ; Interval censored data ; Bayesian survival analysis ; Gamma process

Abstract

We consider estimation of a survival distribution in settings where the event-determining failure is silent, but whose occurrence can be assessed periodically using a diagnostic test. If the diagnostic test were perfect, this would become an interval-censored survival problem. However, when the diagnostic test is imperfect, it cannot be determined when the event has occurred due to false positives and false negatives. The problem is further complicated by the nonconcave likelihood function from a set of observations of this type. We adopt a Bayesian approach for this problem that models the cumulative hazard function as a Gamma process and uses a data-augmentation scheme and Gibbs sampler to generate sample paths from the posterior survival function. The Bayesian approach overcomes the difficulty that can arise using standard likelihood methods. In addition to the posterior distribution of survival, the approach can be used to obtain the posterior distribution of the true survival status of individuals. This distribution can be a useful tool for the medical management of patients being sequentially followed for the onset of a seminal event such as HIV infection.