The NCCTG randomized controlled clinical trial for the treatment of advanced colorectal carcinoma is a wonderful case study of the dynamic interplay between scientific learning and statistical inference. Ethical concerns for minimizing the number of patients assigned to an inferior treatment and interest in identifying subsets of patients for whom a treatment is most likely efficacious pose challenging problems for the practice of statistics. In the first part of this paper, I comment on the applications of Bayesian methods to these problems in the NCCTG trial as presented by Freedman and Spieglehalter and Dixon and Simon, respectively. In the second part of this paper, I discuss and illustrate a Bayesian approach to model sensitivity analysis with a particular focus on model specification and criticism. The Bayesian approach provides a formal methodology to assess the sensitivity of inferences to the inputs into an analysis so that it is possible to investigate the consequences of the specification of the model. I apply these methods to the specification and criticism of a class of survival models for the analysis of survival times in the NCCTG trial.