TABLE OF CONTENTS Until relatively recently, Bayesian statistics were little more than an intellectual curiousity; rich in conceptual insight but of little practical value when it came to actual data analysis. All this has changed in the most dramatic fashion, with Bayesian methods and applications now forming an area of the most intense activity. In many cases, Bayesian approaches lead to the same or similar conclusions as those using the routine procedures of the frequentist statistician. But differences do occur and there are proponents on each side with, for example, Berry (1993) presenting the case for greater use of Bayesian methods in clinical trials and Whitehead (1993) presenting the case for the ongoing dominance of the frequentist approach, at least in the context of definitive phase III trials. Most statisticians involved in trials are typically rather pragmatic, for the most part using the familiar and quick to apply frequentist methods, but nonetheless also applying Bayesian methods where these are convenient or have some conceptual advantage and are acceptable to the intended consumer. Much recent work proposing Bayesian methods in clinical trials has been concerned as much with establishing acceptability as with developing the methods.
Traditional frequentist analysis essentially treats each trial or experiment as if it were entirely novel and each trial is usually being considered as being individually potentially decisive. Scientific progress may occur outside the narrow focus of this trial, but the numerical procedures themselves are not formulated to reflect the process of progressive learning nor one in which...
