Understanding Clinical Trial Design - Research Advocacy Network

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Bayesian Clinical Trial
Example
UNDERSTANDING CLINICAL TRIAL DESIGN: A TUTORIAL FOR RESEARCH ADVOCATES
Consider the hypothetical cancer of the big toe trial outlined on page 14.
Researchers hypothesized that the experimental intervention (i.e., caffeine) is
superior to the standard of care (i.e., water) in treating cancer of the big toe.
In the Bayesian framework a prior probability would be assigned to this
hypothesis. For example, based on previous experience (e.g., trials in thumb
cancer), they might assign a prior probability of .6 to this hypothesis (i.e., the
probability that caffeine is better than water is slightly better than even
chance).
After collecting data, the researchers would calculate a posterior probability
which becomes their new best guess about the hypothesis. In this example,
suppose patients who were treated with caffeine lived an average of 8.6
years following treatment, whereas those treated with water lived an average
of 7.8 years. This would provide confirming evidence for the hypothesis, and
the posterior probability would be higher than the prior probability, (e.g.,
perhaps .8). On the other hand, if patients in the control arm survived
longer than those on the experimental arm, the trial would cast doubt on the
hypothesis. In such cases the posterior probability would be lower than the
prior probability (e.g., perhaps .5 or even less).
In this way new beliefs about the hypothesis (i.e., posterior probabilities)
combine prior knowledge (i.e., prior probability) with trial data. The larger
the trial and the greater the difference between the experimental and control
arms, the greater the influence of the trial data on the new belief about the
hypothesis.
While the calculations used in the Bayesian approach are beyond the scope of the
current tutorial, the above examples should have provided the reader with a sense
of how existing knowledge can be incorporated into the inferential process, as well
as the naturalness of the approach. In everyday life as well as the clinical setting,
very surprising results are almost always discounted. This is consistent with the
Bayesian, but not the frequentist approach.
A major criticism of the Bayesian approach is the apparent subjectivity associated
with establishing prior probabilities. Who gets to decide which pre-existing data
to incorporate and how heavily to weigh them? While not trivial, there are ways
around these issues. First, non-informative prior probabilities could be used. A
non-informative prior probability would be equivalent to chance, for example, .5
in a two-arm trial. Second, the same decisions about a hypothesis are often
reached for a wide range of prior probabilities. Third, in large trials, new data
tend to overpower any influence of prior probabilities.
Other differences between frequentists and Bayesians, besides the use of prior
information, are summarized in Figure 13. On the one hand, Bayesians use
Bayes’ Theorem to address questions and draw conclusions that are framed as
probabilities associated with various hypotheses. Frequentists, on the other hand,
use statistical methods (i.e., sampling distributions of test statistics) that support
hypothesis testing and limit error rates.