Advantages of Bayesian Approaches to Designing and Analyzing Clinical Trials

Frank E. Harrell, Jr.

October 8, 1998

ABSTRACT

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 × 2 frequency tables, α–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).

From the Division of Biostatistics and Epidemiology, Dept. of Health Evaluation Sciences, University of Virginia School of Medicine, Charlottesville

Address for correspondence and reprint requests:

Frank E Harrell Jr, PhD

Box 600

Health Sciences Center

University of Virginia

Charlottesville VA 22908 USA

E-mail: fharrell@virginia.edu

\underline{Key words}: P –values, prior and posterior probabilities, multiplicity, sequential monitoring, multiple endpoints, hypothesis testing, confidence intervals