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\title{Advantages of Bayesian Approaches to Designing and Analyzing
		Clinical Trials
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\footnotetext{ From the Division of Biostatistics and Epidemiology, 
Dept.\ of Health Evaluation Sciences, University of Virginia School of
Medicine, Charlottesville

%This work was supported by: 

Address for correspondence and reprint requests:
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~~~~~ \= Frank E Harrell Jr, PhD \\
\> Box 600 \\
\> Health Sciences Center \\
\> University of Virginia \\
\> Charlottesville VA 22908 USA\\
\> E-mail: \Co{fharrell@virginia.edu} \\
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\author{Frank E. Harrell, Jr.
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\noindent{\bf ABSTRACT}
\vspace{1ex} \\ 
Frequentist statistical methods attempt to provide objective
information about treatment effects through the use of easily computed
$P$--values.  However, much controversy surrounds the use of
$P$--values, including statistical vs.\ clinical significance,
artificiality of null hypotheses, 1--tailed vs. 2--tailed tests,
difficulty in interpreting confidence intervals, falsely interpreting
non--informative studies as ``negative'', arbitrariness in testing for
similarity of two treatments, trading off type I and type II error,
using $P$--values to quantify evidence, which statistical test should
be used for $2 \times 2$ frequency tables, $\alpha$--spending and
adjusting for multiple comparisons, whether to adjust final
$P$--values for the intention of terminating a trial early even though
it completed as planned, complexity of group sequential monitoring
procedures, and whether a promising but statistically insignificant
trial can be extended.  Bayesian methods allow calculation of
probabilities that are usually of more interest to investigators,
patients, and regulatory agencies, e.g.  the probability that
treatment $A$ is similar to treatment $B$ or the probability that
treatment $A$ is at least 5\% better than treatment $B$, and these
methods are simpler to use in monitoring ongoing trials.  Bayesian
methods are controversial in that they require the use of a prior
distribution for the treatment effect, and calculations are more
complex in spite of the concepts being simpler.  I discuss
difficulties with frequentist approaches, advantages of estimation
over hypothesis testing, basics of the Bayesian approach, approaches
to choosing the prior distribution, and advantages of Bayesian methods
for study design and analysis.  I present a simple example from a
reanalysis of GUSTO--I ($t$--PA vs. streptokinase for acute MI).

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\underline{Key words}: 
\= $P$--values, prior and posterior probabilities, multiplicity, \\
\> sequential monitoring, multiple endpoints, hypothesis testing, \\
\> confidence intervals, study design
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\section{Introduction}


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