Multiplicity-calibrated Bayesian hypothesis tests.
When testing multiple hypotheses simultaneously, there is a need to adjust the levels of the individual tests to effect control of the family-wise error rate (FWER). Standard frequentist adjustments control the error rate but are typically both conservative and oblivious to prior information. We propose a Bayesian testing approach-multiplicity-calibrated Bayesian hypothesis testing-that sets individual critical values to reflect prior information while controlling the FWER via the Bonferroni inequality. If the prior information is specified correctly, in the sense that those null hypotheses considered most likely to be false in fact are false, the power of our method is substantially greater than that of standard frequentist approaches. We illustrate our method using data from a pharmacogenetic trial and a preclinical cancer study. We demonstrate its error rate control and power advantage by simulation.
Guo
Mengye
M
Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, Boston, MA 02446, USA. mengye@jimmy.harvard.edu
Heitjan
Daniel F
DF
D001499:Bayes Theorem; D016642:Bupropion / Q000627:therapeutic use; D002986:Clinical Trials as Topic / Q000379:methods*; D003198:Computer Simulation; D018765:Dopamine Uptake Inhibitors / Q000627:therapeutic use; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D020641:Polymorphism, Single Nucleotide / Q000235:genetics; D012107:Research Design; D016540:Smoking Cessation / Q000379:methods
D018765:Dopamine Uptake Inhibitors; D016642:Bupropion