Joint Modeling of a Time-to-Event and Partially Observed Biomarker Using Lévy Processes

• Activity Number: 280 - New Methodology Developments in Analyzing Complex Survival Data
• Type: Contributed
• Date/Time: Tuesday, August 9, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Lifetime Data Science Section
• Author(s): Theresa Devasia* and Alexander Tsodikov
• Companies: Surveillance Research Program, National Cancer Institute and University of Michigan
• Keywords: stochastic process; Lévy process; Gamma process; marked survival; joint model

Abstract

In clinical studies, the outcome of interest is often a time-to-event. In addition, longitudinal biomarker data representing a partially-observed latent biological process may be collected. To capture the dependence between failure and the biomarker process, a joint model is needed. In this joint model, the cumulative hazard of failure can be modeled as a Lévy process with a continuous time transformation representing the accumulated risk of failure. We derive the survival and hazard functions of failure under the assumption of a Gamma process cumulative hazard and different observation mechanisms for the biomarker. We focus on the case of marked survival wherein the marker and event are observed simultaneously. We apply our method to SEER prostate cancer incidence data, where men diagnosed with prostate cancer have prostate specific antigen (PSA) collected at diagnosis.