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Bayesian credible intervals for binomial proportions in a single patient trial
Journal article   Open access   Peer reviewed

Bayesian credible intervals for binomial proportions in a single patient trial

Jacob J Oleson
Statistical methods in medical research, Vol.19(6), pp.559-574
12/2010
DOI: 10.1177/0962280209349008
PMCID: PMC3307549
PMID: 20181779
url
https://www.ncbi.nlm.nih.gov/pmc/articles/3307549View
Open Access

Abstract

Practitioners are often asking if the treatment successfully improved performance. Many times this question is directed towards the outcome of a single individual. In this article, we develop a method to assess the improvement of a single individual who is administered a test of percent correct at pre-treatment and post-treatment. A Bayesian approach is taken where the number correct is modelled as a binomial random variable and the percent correct is set to a beta prior distribution. The first model assumes percent correct at pre-test is equal to the percent correct at post-test and the posterior predictive distribution is used to evaluate the change in the number correct. We subsequently model the proportions correct at pre-test and post-test as unequal. The second model then assumes independent proportions and the third assumes correlated beta distributions for the two proportions. 95% credible intervals are calculated for the various methods for number of correct at post-test given a particular level at pre-test. An example using data from a cochlear implant clinical trial is presented where clinicians recorded percent correct in a consonant-nucleus-consonant test.
 Biostatistics Binomial Distribution Clinical Trials as Topic - statistics & numerical data Humans Bayes Theorem Treatment Outcome Models, Statistical Cochlear Implants - statistics & numerical data

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