B0186
Title: Estimation of the cure rate for distributions in the Gumbel maximum domain of attraction under insufficient follow-up
Authors: Ross Maller - Australian National University (Australia)
Ingrid Van Keilegom - KU Leuven (Belgium)
Muzhi Zhao - Australian National University (Australia)
Mikael Escobar-Bach - University of Angers (France) [presenting]
Abstract: Estimating the cured proportion from survival data which may include observations on cured subjects, that is, those who never experience the event of interest, is a critical task in practice. Any proposed estimator can only be expected to perform well when the follow-up period is sufficient, in some sense. We propose an adjustment that ameliorates the problem when follow-up is insufficient and under the assumption that the survival distribution of those susceptible to the event belongs to the Gumbel maximum domain of attraction, since many commonly used lifetime distributions have this property. We use extrapolation techniques from extreme value theory to derive a non-parametric estimator of the cure proportion, which is consistent and approximately normally distributed under certain assumptions, and performs well in simulation studies. We illustrate with an application to survival data where patients with different stages of breast cancer have varying degrees of follow-up.
