Bounds of the survival functions with informative drop-outs using FGM copulas

The underpinning assumption of independence of failure time and drop-out time is not well supported in many clinical or epidemiological studies. As a consequence, the marginal survival functions are not identifiable. In such a situation, many authors have proposed bounds for the survival functions to check the sensitivity of the estimates to the independence assumption. In this paper, we propose an alternative methodology by adopting an underlying selection process to account for this dependency. We use the Farlie-Gumbel-Morgenstern (FGM) bivariate family for the joint distribution of failure time and the selection variable. Subsequently we derive the conditional distribution of the survival time, given that it is observed, and show how, given the association parameter, the survival functions can be estimated. We compare the proposed estimates with the Copula-Graphic estimator for a real home haemodialysis data and simulated datasets for various proportions of drop-outs.