In this paper two problems of computer-aided diagnosis with 'independence Bayes' were investigated: selection of variables and monotonicity in performance as the number of measurements is increased. Using prospective data from patients with upper gastrointestinal bleeding, the stepwise forward selection approach maximizing the apparent diagnostic accuracy was analysed with respect to different kinds of bias in estimation of the true diagnostic accuracy and to the stability of the number and type of variables selected. The results of this study suggest first that the selection of variables should be evaluated against the estimated true diagnostic accuracy obtained using all variables, and secondly that the results of a single selected sequence may be severely biased.