A critique of the false-positive report probability.
The false positive report probability (FPRP) was proposed as a Bayesian prophylactic against false reports of significant associations. Unfortunately, the derivation of the FPRP is unsound. A heuristic derivation fails to make its point, and a formal derivation reveals a probabilistic misrepresentation of an observation. As a result, the FPRP can yield serious inferential errors. In particular, the FPRP can use an observation that is many times more likely under the null hypothesis than under the alternative to infer that the null hypothesis is far less probable than the alternative. Contrary to its intended purpose, the FPRP can promote false positive results. It should not be used. A modified FPRP is derived, but it appears to have limited application and does not address the problem of false reports of significant associations. The conditional error probability is a possible replacement for the FPRP.
Lucke
Joseph F
JF
Center for Clinical Research and Evidence-based Medicine, University of Texas Medical School at Houston, Houston, Texas 77030, USA. Joseph.F.Lucke@uth.tmc.edu
D001499:Bayes Theorem; D005189:False Positive Reactions; D020022:Genetic Predisposition to Disease; D006801:Humans; D008957:Models, Genetic; D015233:Models, Statistical; D017720:Molecular Epidemiology / Q000706:statistics & numerical data*; D011336:Probability