Modelling associations between time-to-event responses in pilot cancer clinical trials using a Plackett-Dale model

This work was motivated by the need to find surrogate endpoints for survival of patients in oncology studies. The goal of this article is to determine associations between five time-to-event outcomes coming from three clinical trials for non-small cell lung cancer. To this end, we propose to use the multivariate Dale model for time-to-event data introduced by Tibaldi et al. (Stat. Med. 2003). We fit the model to these data, using a pseudo-likelihood approach to estimate the model parameters. We evaluate and compare the performance of different dimensional models and we relate the Dale model association parameter, i.e. the odds ratio, to well-known quantities such as Kendall's tau and Spearman's rho. Finally, the results are discussed with a perspective on surrogate marker validation. Some suggestions are made regarding further studies in this field.