The Bayesian analysis of a logistic regression model is described using an example of predicting the need for a corneal transplant in keratoconus. Controversy over the use of subjective prior information in Bayesian methods is avoided by a formulation representing negligible prior information. Simple computational procedures are described, and it is argued that the results are more accurate, clearer and make fuller use of the information contained in the data. Analysis of more complex models is considered. In particular, it is argued that classical methods as implemented in the computer package GLIM can be used as approximations to Bayesian methods, particularly at the initial stage of model selection.