Confidence intervals for a binomial parameter based on binary data subject to false-positive misclassification

2006 ◽  
Vol 50 (12) ◽  
pp. 3369-3385 ◽  
Author(s):  
Doyle H. Boese ◽  
Dean M. Young ◽  
James D. Stamey
Keyword(s):  
Confidence Intervals ◽  
False Positive ◽  
Binary Data ◽  
Binomial Parameter ◽  
Data Subject

scholarly journals True and false positive rates for different criteria of evaluating statistical evidence from clinical trials

2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Don van Ravenzwaaij ◽  
John P. A. Ioannidis
Keyword(s):  
Clinical Trials ◽  
Confidence Intervals ◽  
False Positive ◽  
Evaluation Criteria ◽  
Small Sample ◽  
Statistical Evidence ◽  
Bayes Factors ◽  
True Positive ◽  
Small Sample Sizes ◽  
Meta Analyses

Abstract Background Until recently a typical rule that has often been used for the endorsement of new medications by the Food and Drug Administration has been the existence of at least two statistically significant clinical trials favoring the new medication. This rule has consequences for the true positive (endorsement of an effective treatment) and false positive rates (endorsement of an ineffective treatment). Methods In this paper, we compare true positive and false positive rates for different evaluation criteria through simulations that rely on (1) conventional p-values; (2) confidence intervals based on meta-analyses assuming fixed or random effects; and (3) Bayes factors. We varied threshold levels for statistical evidence, thresholds for what constitutes a clinically meaningful treatment effect, and number of trials conducted. Results Our results show that Bayes factors, meta-analytic confidence intervals, and p-values often have similar performance. Bayes factors may perform better when the number of trials conducted is high and when trials have small sample sizes and clinically meaningful effects are not small, particularly in fields where the number of non-zero effects is relatively large. Conclusions Thinking about realistic effect sizes in conjunction with desirable levels of statistical evidence, as well as quantifying statistical evidence with Bayes factors may help improve decision-making in some circumstances.

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