Clinical Trials

Abstract

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 …