The following examples are intended to show the advantages of Bayesian reporting of treatment efficacy analysis, as well as to provide examples contrasting with frequentist reporting. As detailed here, there are many problems with p-values, and some of those problems will be apparent in the examples below. Many of the advantages of Bayes are summarized here. As seen below, Bayesian posterior probabilities prevent one from concluding equivalence of two treatments on an outcome when the data do not support that (i.
Professor of Biostatistics
Vanderbilt University School of Medicine
Professor of Psychiatry and, by courtesy, of Medicine (Cardiovascular Medicine) and of Biomedical Data Science
Stanford University School of Medicine
Revised July 17, 2017 It is often said that randomized clinical trials (RCTs) are the gold standard for learning about therapeutic effectiveness. This is because the treatment is assigned at random so no variables, measured or unmeasured, will be truly related to treatment assignment.
Type I error for smoke detector: probability of alarm given no fire=0.05
Bayesian: probability of fire given current air data
Frequentist smoke alarm designed as most research is done:
Set the alarm trigger so as to have a 0.8 chance of detecting an inferno
Advantage of actionable evidence quantification:
Set the alarm to trigger when the posterior probability of a fire exceeds 0.02 while at home and at 0.
Randomized clinical trials (RCT) have long been held as the gold standard for generating evidence about the effectiveness of medical and surgical treatments, and for good reason. But I commonly hear clinicians lament that the results of RCTs are not generalizable to medical practice, primarily for two reasons:
Patients in clinical practice are different from those enrolled in RCTs Drug adherence in clinical practice is likely to be lower than that achieved in RCTs, resulting in lower efficacy.