A structural transformation model for a latent, quasi-independent truncation time as a function of the observed dependent truncation time and the event time, and an unknown dependence parameter. The dependence parameter is chosen to minimize the conditional Kendall's tau (Martin and Betensky, 2005) <doi:10.1198/016214504000001538>. The marginal distribution for the truncation time and the event time are completely left unspecified.