In practice, frequentist clinical trial design methods are dominant. Many funding bodies in particular will request frequentist quantities such as power and alpha levels to be set. There remains however, a large quantity of literature investigating Bayesian design methods for clinical trials. As far back as 1988 Sylvester [148] explored a Bayesian method for the design of phase II clinical trials, and these methods have begun to be used in practice.
Most notable is the MD Anderson centre, which as of 2005 had 20% of all trials designed from a Bayesian perspective [149]. More recently, two further reviews of Bayesian methodology, one with regard to medicine [18] and another more specific to the pharmaceutical industry [19] have evaluated the development of Bayesian methods over the previous 25 years.
It is clear that the decision over whether to use a frequentist or Bayesian frame- work (or some mix of the two) in clinical trials is a topic of some debate and given the increasing literature with respect to Bayesian trial design, Statistics in Medicine presented two publications by Berry [150] and Whitehead [1] who argue the case for each framework respectively. Here in particular, Berry argues against the ‘rigidity’ of the frequentist framework and notes that interpretations of trial results under a fre- quentist design are less direct, do not make use of all available information and are valid only under the pre-specified design conditions. The point is further made that frequentist designs are typically dependent upon two quantities, ‘power’ and ‘clinically relevant difference’ which are both chosen arbitrarily and often manipulated to ‘...give a sample size acceptable to investigators and sponsors’. A point reinforced by Amri and Kordestani [2] who note that the observed true magnitude of a difference is ‘...nearly always less than what was predicted at the time the trial was designed’. It is further noted that as a Bayesian trial can be analysed independent of any design conditions, no formal design parameters are required to begin a trial. Whitehead by contrast argues that for phase III trials in particular, a Bayesian approach should be discouraged due the possibility for subjectivity to enter the interpretation of results and that when a specific question is required to be answered, the frequentist approach can provide ‘...one of the most powerful tools of clinical research.’
With the growing accessibility of Bayesian techniques the Statistics in Medicine journal presented four further papers prefaced by Herson [13] with the specific aim of investigating the Bayesian analysis of cancer clinical trials. Specifically Wieand and Cha [17] introduce a trial designed under a frequentist framework to compare five treatments against a control arm for the treatment of patients with colorectal cancer. To the trial data, Dixon and Simon [14] consider using a Bayesian subset analysis to analyse the trial, whereas Freedman and Spiegelhalter [15] use Bayesian sequential stopping rules with informative priors on the hazard ratios. Lastly, Greenhouse [16] provides a review of the methods applied and shows that the overall conclusions between the two frameworks are in agreement.
Despite the dominance of frequentist methodology, interest in the Bayesian ap- proach was clearly growing and to this end, Spiegelhalter et al. [151] provided a set of practical approaches for applying Bayesian techniques to clinical trials with Hughes [152] suggesting a set of guidelines for reporting of trials in a Bayesian framework. Following this, Spiegelhalter et al. published a book discussing the use of Bayesian methodology in medical research [21].
Still, practical uptake has been slow and consequently publications by Howard et al. [11], Gonen [10] and Moye [27] all encouraging the use of Bayesian methods. Fur- thermore, Berry [153, 3] argues for the use of Bayesian techniques in cancer research, citing the increased efficiency and making ethical arguments. Lastly both Perneger [5]
and Berry [4] argue that Bayesian methods are more readily interpretable by medical professionals.
The majority of the literature concerning Bayesian methodology for trial design focuses around Phase I and Phase II trials. Phase I trials concerned with dose esti- mation are explored by Gatsonis and Greenhouse [154] and Whitehead [155]. A trial that makes uses of an adaptive Bayesian approach to assess both efficacy and safety is considered by Berry et al. [156], whereas Fan et al. [157] consider Bayesian Phase I trials designed from a decision theoretic perspective. Chevret [158] considers Phase I trials using a continual reassessment method, a unique feature of Bayesian designs which allows for the trial to be assessed after each individual patient is evaluated.
For Bayesian techniques following on from phase I trials, Thall and Estey [159] con- sider an approach for screening treatments to determine which is the most appropriate to carry through to a Phase II trial. For Phase II designs, both Tan and Machin [160] and Lewis and Berry [161] consider group sequential designs. Both Bandyopadhyay et al. [162] and Zhao et al. [163] consider two stage designs with a survival endpoint. Johnson and Cook consider the continual reassessment method in a Phase II setting whereas Parmar et al. [164] consider the monitoring of clinical trials using ‘enthusiastic’ and ‘sceptical’ priors with applications. Resnic [165] focuses on Bayesian methodology to monitor trial safety.
Adaptive designs, whereby the trial design is altered based on accumulated results have been explored by Berry [166, 167] and Yin et al. [168]. The latter of these use a predictive probability approach whereby the predicted results of the trial are estimated and used to inform the randomisation procedure during the trials progress. These are further utilised by Inoue et al. [169] who propose a method for seamlessly expanding from Phase II to Phase III, by Lee and Liu [170] who show that a predictive probability approach can be more efficient than frequentist approaches and by Hong and Shi [171] who use the approach to aid the decision to progress to a Phase III trial.