Nonparametric Hazard Rate Estimation of Left-Truncated and Right-Censored Data with Application to Breast Cancer Data

• Activity Number: 74
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jufen Chu* and Sam Efromovich
• Companies: The University of Texas at Dallas and The University of Texas at Dallas
• Keywords: Survival analysis ; Breast cancer ; Longevity ; Data-driven estimation ; Nonparametric ; MISE

Abstract

The method and theory of sharp minimax nonparametric estimation of the hazard rate with left truncated and right censored data are developed. For the first time in the literature it is shown how left truncation and right censoring affect the MISE convergence. The proposed data-driven estimator adapts to smoothness of an underlying hazard rate and distributions of the truncating and censoring random variables. Monte Carlo simulations also show that the proposed estimator outperforms known estimators for small sample sizes. The proposed estimator is used for analysis of breast cancer data in the WHEL study. It is shown how carotenoid concentration affects the risk of the breast cancer recurrence. Nonparametric estimates are complemented by hypotheses testing and confidence bands.