Choice of conditional models in bivariate survival

We consider bivariate survival problems in which interest is in the conditional distribution of one survival variable given an uncensored observation of the other. The work is motivated by an analysis of time to cancer diagnosis then subsequent survival amongst a group of organ transplant recipients. The effect of conditioning is illustrated for five standard bivariate models. The consequences of adopting a misspecified marginal approach in which the conditioning variable is considered to be a fixed covariate are investigated.