Archimedean copula model selection under dependent truncation

Abstract

One-sided truncated survival data arise when a pair of time-to-event variables (X, Y) is observed only when X<Y. Existing methods of analysis rely on the assumption of quasi-independence between X and Y. Recently, Lakhal-Chaieb et al. (Biometrika 2006; 93:655-669) modeled potential dependency between these random variables via a semi-survival Archimedean copula. In this paper, we present a model selection procedure to rank a set of semi-survival Archimedean copula families according to their ability to fit a given data set subject to dependent truncation. The proposed procedure is based on a truncated version of Kendall's tau (J. Multivariate Anal. 1996; 56:60-74). The performance of the proposal is illustrated through simulations and three real data sets.