Estimating the Survival in the Presence of Dependent Truncation

• Activity Number: 292
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Jing Qian*+ and Rebecca A. Betensky
• Companies: Harvard School of Public Health and Harvard School of Public Health
• Keywords: Copula ; Kendall's tau ; Peterson bounds ; Product limit estimator ; Quasi-independence

Abstract

An increasing number of clinical trials and observational studies are assembled using complex sampling involving truncation. Ignoring the issue of truncation or incorrectly assuming quasi-independence can lead to bias and incorrect results. Currently available approaches for dependently truncated data are sparse and incomplete. In this paper, we propose a product limit estimator for survival under dependent truncation using a hazard ratio assumption linking the unobservable region to the observable region. We also derive nonparametric sharp bounds for the survival and bounds for survival which are based on reasonable assumptions on a hazard ratio function using the proposed product limit estimator. The properties of these bounds are discussed. The proposed method is applied to some real data examples.