Estimation of survival function in presence of dependent censoring

Details

Supervisors

Van Keilegom, Ingrid

Faculty

Faculté des sciences

Degree label

Master [120] en statistique, orientation générale, à finalité spécialisée

Abstract

This master thesis explores the estimation of the survival function under dependent censoring, a situation frequently encountered in survival analysis. Building on the methodologies proposed in Czado and Van Keilegom (2023) and Rivest and Wells (2001), we employ copulas to model the dependence without needing to specify the copula’s association parameter explicitly. The survival time distribution is estimated non-parametrically using the copula graphic estimator from Rivest and Wells (2001), while the censoring time distribution is approached parametrically. Our results demonstrate that our estimator generally outperforms the Kaplan-Meier estimator. Specifically, for minor dependencies (Kendall’s tau of 0.2), a larger sample size is required for our estimator to achieve lower mean absolute deviation. However, for more substantial dependencies (Kendall’s tau of 0.5 and 0.7), our estimator performs better than Kaplan-Meier across most small sample sizes, albeit with some exceptions. We also find that Kendall’s tau estimates can be numerically unstable, as evidenced in two out of five simulations. Additionally, accurate specification of margins proves critical for robust estimation.