Is the Bayesian Approach Ready for Prime Time? Yes!
The defining characteristic of any statistical approach is how it deals with uncertainty. In the Bayesian approach, all uncertainty is measured by probability. Anything unknown has a probability, including future results in a clinical trial (based on current results). Frequentists also use probabilities, but in a restricted sense.
Bayesian conclusions depend on results actually observed. Because their use of probability is limited, frequentists go through contortions to draw conclusions. In particular, conclusions depend on more than just observed results. For example, frequentist p-values include probabilities of results more extreme than observed, in which probability calculations depend on the trial’s design. Both aspects are scientifically questionable. “More extreme results” were not observed and should not matter at all. Small p-values are taken to be evidence against the null hypothesis, so one may reject a hypothesis because it assigns little probability to unobserved results, and—for the same data—accept one because it assigns greater probability to unobserved results. The other questionable aspect is the strong dependence of conclusions on design. Because the same data but different intentions of the investigator had something happened that did not happen,1 the p-value may be any number from 0 to 1. And calculating a p-value is not possible unless the design is followed exactly. One implication is that keeping an experiment running to collect additional data is not an option. That seems unscientific.
In contrast, the Bayesian paradigm is tailored to the learning process. As information becomes available, one updates what one knows. This gives the Bayesian approach its flexibility and makes it ideal for clinical research. Bayesian probabilities can be calculated at any time and on the basis of whatever information is available. One consequence is the ability to calculate probabilities of future results. At any time, one can assess where a trial is going, the probability that it will be a success, etc.
An example is the Acute Stroke Therapy by Inhibition of Neutrophils (ASTIN) trial.2,3⇓ The dose assigned to the next patient was chosen to maximize information about the dose–response relationship. Doses proving to be uninteresting are little used. Informative doses garner more observations. And predictive probabilities allow for addressing whether one wants to make the next observation at all.
The Bayesian approach is also tailored to making decisions. Designing a clinical trial is a decision problem. The ASTIN trial was a major research advance because it used Bayesian updating, but even it did not fully exploit the Bayesian potential. For example, it carried artificial constraints. One was the timing of decisions to stop accrual. The algorithm would have recommended stopping well before it was given its first opportunity to do so. Another aspect of the design was dictated apart from Bayesian considerations: accrual rate. This is an important part of a trial’s design. A Bayesian decision analysis can address whether tempering accrual is wise (on the basis of a drug’s patent life, potential profits, costs associated with the trial, etc). It can also address changing accrual rate in an adaptive fashion, depending on the accumulating data. Had an accrual governor been available in the ASTIN trial, it would have been applied when the data were suggesting that no dose of the agent was effective.
A design’s false-positive rate is a traditional frequentist notion that is also important in a Bayesian approach. False-positive rate and statistical power can be calculated for any prospective Bayesian design and serve to relate the new with the old.
“Is the Bayesian approach ready for prime time?” suggests that the Bayesian approach has not been ready until now. Although I do not like this implication, there is an aspect of today’s world that makes the Bayesian approach more “ready” now: computational facility and speed. Adaptive Bayesian designs tend to be complex. For example, they look forward frequently during the trial and they steer the trial based on updated predictive probabilities. Predicting future results can be computationally intensive. Performing the necessary calculations during an actual trial is usually possible with 25-year-old computers. But calculating false-positive rate and power requires simulating the trial many thousands of times. The computer programs have loops within loops within loops. Computations are onerous and may require a supercomputer or a high-level cluster that were not available 25 years ago.
Why the question in the title? In view of the benefits described here, why is there not a long Bayesian tradition in clinical research? The answers lie in the 20th century history of statistics in which the Bayesian approach was usually dismissed as being subjective. Learning based on a trial’s results implies the existence of knowledge before the trial. Using Bayesian terminology, having a posterior probability implies the need for a prior probability. So the Bayesian approach requires specifying probabilities before the trial. This is a great virtue because it enables using historical and concurrent information.4 It also means there is an inevitably subjective aspect of prior probabilities and, therefore, of all probabilities.
Subjectivity in science is regarded by some as being bad. I think it is essential.1 For example, the choice of statistical model is subjective—there is no universal model. And the model chosen can easily have a greater impact on conclusions than does one’s prior probabilities. Moreover, if one wishes, one can use what is called noninformative or flat prior distributions5 in which the observed results dominate the final probability distribution. This emulates the frequentist attitude of ignoring historical information, but it preserves the Bayesian ability to learn and adapt.
The Bayesian approach provides tools for designing trials that treat participants more effectively and that identify better drugs and appropriate doses more efficiently and faster.
- Received January 21, 2005.
- Accepted January 21, 2005.
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Krams M, Lees KR, Hacke W, Grieve AP, Orgogozo JM, Ford GA. 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.
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