The Bayesian Principle
Can We Adapt?
Most clinicians are more familiar with the traditional trial design, for trials of therapy in acute stroke, consisting of fixed sample sizes based on power calculations using preexisting data (the frequentist approach referred to by our protagonists).
The Bayesian approach is unique in that unlike the traditional design, an initial dependence on preexisting data are constantly adjusted using new data as they are accrued from the current trial. Its main advantage is that this allows potential reduction of sample size by continually updating the probability of success or futility. As argued by Berry, this flexibility of Bayesian design makes it ideal for clinical research.
Why the need for new trial designs such as this? There is no doubt that the large number of negative stroke trials using neuroprotection is the main driver.1 A reason for this may be trial design and suggests the potential for more sensitive and efficient testing of hypotheses using such approaches as adaptive designs (as used in the Acute Stroke Therapy by Inhibition of Neutrophils [ASTIN] trial2) and responder analyses (in which success is calibrated against the initial neurological severity) used in the Abciximab in Emergency Stroke Treatment Trial (AbESTT) trial.3 Other drivers for novel trial design include the escalating cost of trial conduct, an increasingly wary pharmaceutical industry, and the need to consider the ethics of use of experimental agents in large trials. The Bayesian approach allows the use of online determination of futility, an approach that is ethically sound.
In essence, Howard argues that Bayesian analysis is seductive and appealing but introduces unacceptable biases because of the difficulty in accruing high-quality, unbiased previous data. He argues that the frequentist approach avoids these problems by providing an independent confirmation of previous work. Conversely, Berry is of the view that this problem is outweighed by the flexibility and almost “online” prediction of the likelihood of success. We would also submit that although the use of previous information occurs early in the trial process when using the Bayesian approach, as the trial progresses, this is overwhelmed by the new data accrued. For example, in ASTIN, the natural history data from the Copenhagen study were used as the previous distribution as a baseline for the treatment effect.2 The probability of efficacy becomes progressively more dependent on new data being continually accrued.
A third approach is to adopt frequentist design with a minimal sample size planned at the outset of the trial but then to perform prespecified interim analyses.4 Minimal sample sizes are often mandated by institutional ethics committees. Interim analyses necessitate adjustment of P values, with re-estimation of minimal group size, because of the potentially increased risk of type 1 error.
Regardless of the pros and cons, we regard this as an extremely healthy debate because it is a manifestation of the drive to develop new approaches to trial design and analysis. Indeed, we may need an adaptive design based on success or failure of future stroke trials to make continual assessment of the benefits of these alternative approaches.
Bayesian analysis is the use of previous distributions (past data) to estimate posterior distributions (what is happening now).
Frequentist design is the conventional approach of estimating minimal sample size in advance of the trial, completing the trial, and then analyzing the outcome in terms of P values.
Adaptive design/sampling is the adjustment of estimate of minimal sample (group) size as the trial progresses.
- Received January 21, 2005.
- Accepted January 21, 2005.
Fisher M; Stroke Therapy Academic Industry Roundtable. Recommendations for advancing development of acute stroke therapies: Stroke Therapy Academic Industry Roundtable 3. Stroke. 2003; 34: 1539–1546.
Krams M, Lees KR, Hacke W, Grieve AP, Orgogozo JM, Ford GA; ASTIN Study Investigators. Acute Stroke Therapy by Inhibition of Neutrophils (ASTIN): an adaptive dose-response study of UK-279 276 in acute ischemic stroke. Stroke. 2003; 34: 2543–2548.
AbESTT Investigators. Effects of abciximab for acute ischemic stroke: final results of the Abciximab in Emergency Stroke Treatment Trial (AbESTT). Stroke. 2003; 34: 253. Abstract.