Frank Harrell PhD
Mario Peruggia PhD
Div. of Biostatistics and Epidemiology
Dept. of Health Evaluation Sciences
School of Medicine
fharrell@virginia.edu
8 February, 2000
Outline of the Bayesian Approach to Randomized Clinical Trials
Background : Traditional (Frequentist) Approach to
Fixed Sample Size Trials

Sample size estimation is often a game to allow one to launch a
study within a fixed budget no matter what is really required to
detect a clinically relevant difference and no matter what precision
is required for estimates of treatment effect

Studies are often sized to detect a more than clinically
relevant difference
 We often underestimate the variance of the response, which also
results in sample sizes that are too small
 The choices for a and b are arbitrary
 The most common outcome of a clinical trial is `we don't know
the treatment effect with any precision.' Thus all too often
subjects who agree to participate in trials do not end up providing
useful scientific information about the response variable.
 Studies may be shortened sometimes; the answer may be known
before the target sample size is reached.
 Fixed sample size designs are inflexible, e.g., if the final
P=0.06 we may not know what to conclude; often a definitive result
may be obtained by extending a study somewhat
 aadjustment in the context of flexible sequential study
designs is complex and there are many different methods for
preserving typeI error
 Pvalues are very frequently misinterpreted

Small Pvalues may not mean important treatment effects when n
is large (i.e., statistical significance does not translate into
clinical significance)
 Large Pvalues mean nothing when n is small
 Pvalues can provide evidence against a hypothesis but can never
provide evidence in support of a hypothesis
 There are good reasons to emphasize estimation instead of
hypothesis testing; confidence intervals solve some of the problems of
Pvalues
Bayesian Design before the Trial Begins

Choose patient response(s), randomization scheme, etc.
 Choose a statistical model for the response(s): parametric
(e.g., normal distribution) or rankbased
 Describe state of prior knowledge about the effect of treatment
on each response. Do this by choosing a prior probability
distribution; this may be a flat distribution if there is no prior
knowledge about the treatment effect. Some investigators choose a
skeptical prior distribution that works against what they are trying
to demonstrate; this will result in a study that is more convincing
to skeptics.
 Choose clinically relevant differences for secondary analyses of
`clinical significance'
 In a `noninferiority' trial (e.g., equivalence trial,
similarity trial) choose the lowest allowable treatment difference,
e.g., we may want to compute the likelihood that a new drug is no
more than 10% worse than the approved drug
 If sufficient information is available, estimate minimum,
average, and maximum sample sizes
As the Trial Proceeds
As often as desired update the state of prior knowledge using data
collected to date to obtain a ``current'' or ``posterior'' probability
distribution

Probability of efficacy, e.g., Prob[d < 0]; stop
when > 0.95
 Probability of clinically important efficacy, e.g., Prob[ratio
> 0.9]; stop when > 0.9
 Probability of similarity, e.g., Prob[.2 < d
< .2]; stop when < 0.8
 Can also stop when run out of money; latest current
probabilities are still valid
 Futility analysis ¾ predict how acquiring more data would change
the result
 Can optionally modify treatment allocation ratio as results unfold
Bayesian Design of ProtonPump Inhibitor Laryngitis Study

Twogroup parallel design, minimum sample size 15 patients/group
 Response variable is the maximum of four symptom analog scale values
(0100)
 Assume a normal distribution for the response
 Let d denote the difference in population mean response (proton
pump minus placebo)
 Prior probability distribution for d: normal with mean zero
and variance such that the probability that d > 50 or
< 50 is only 0.05
 As data accrue compute Prob[d < 0]; stop when
> 0.95
 Also compute Prob[15 < d < 15]; stop when
> .8
For a detailed handout see
http://hesweb1.med.virginia.edu/biostat under
Teaching Materials then Bayesian Methods for Clinicians
Disclaimer: Currently the majority of biostatisticians rely on
frequentist methods with fixed sample sizes.