Continuous safety monitoring for randomized controlled clinical trials with blinded treatment information. Part 2: Statistical considerations.

If the primary objective of a trial is to learn about the ability of a new treatment to help future patients without sacrificing the safe and effective treatment of the current patients, then a Bayesian design with frequent assessments of the accumulating data should be considered. Unfortunately, Bayesian analyses typically do not have standard approaches, and because of the subjectivity of prior probabilities and the possibility for introducing bias, statisticians have developed other methods for statistical inference that only depend on deductive probabilities. However, these frequentist probabilities are just theories about how certain relative frequencies will develop over time. They have no real meaning in a single experiment. Designed to work well in the long run, p-values become hard to explain for individual experiments. Fortunately, the controversy surrounding Bayes' theorem comes, not from the representation of evidence, but from the use of probabilities to measure belief. A prior distribution is not necessary. The likelihood function contains all of the information in a trial relevant for making inferences about the parameters. Monitoring clinical trials is a dynamic process which requires flexibility to respond to unforeseen developments. Likelihood ratios allow the data to speak for themselves, without regard for the probability of observing weak or misleading evidence, and decisions to stop, or continue, a trial can be made at any time, with all of the available information. A likelihood based method is needed.