Extending the Concordance Index to Left-Truncated Time-to-Event Data

• Activity Number: 168 - Risk analysis and related topics
• Type: Contributed
• Date/Time: Tuesday, August 10, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Risk Analysis
• Author(s): Nicholas Hartman* and Sehee Kim and Kevin He and John D. Kalbfleisch
• Companies: Department of Biostatistics, University of Michigan-Ann Arbor and Department of Clinical Epidemiology and Biostatistics, Asan Medical Center and University of Michigan and University of Michigan
• Keywords: C-Index; Left-Truncation; Risk Prediction; Time-to-Event Analysis

Abstract

In the context of time-to-event analysis, a primary objective is to model the risk of experiencing a particular event in relation to a set of observed predictors. The Concordance Index (C-Index) is a statistic frequently used in practice to estimate how well such models discriminate various risk levels in a population. However, the properties of conventional C-Index estimators when applied to left-truncated time-to-event data have not been well-studied, despite the fact that left-truncation is commonly encountered in observational studies. We show that the limiting values of conventional C-Index estimators depend on the underlying distribution of truncation times, which can result in a misleading interpretation of model performance. We also develop a new C-Index estimator based on Inverse Probability Weighting (IPW) that corrects for this limitation. The IPW estimator is highly robust to the underlying truncation distribution and often outperforms conventional methods in terms of bias, mean squared error, and coverage probability.