We propose model selection procedures for bivariate survival models for cen
sored data generated by the Archimedean copula Family. In route to construc
ting the selection methodology, we develop estimates of some time-dependent
association measures, including estimates of the local and global Kendall'
s tau, local odds ratio, and other measures defined throughout the literatu
re. We propose a goodness-of-fit-base model selection methodology as well a
s a graphical approach. We show that the proposed methods have desirable as
ymptotic properties and perform well in finite samples.