Sample Size Requirements for Calibrated Approximate Credible Intervals for Proportions in Clinical Trials.

Publisher: MDPI Country of Publication: Switzerland NLM ID: 101238455 Publication Model: Electronic Cited Medium: Internet ISSN: 1660-4601 (Electronic) Linking ISSN: 16604601 NLM ISO Abbreviation: Int J Environ Res Public Health Subsets: MEDLINE

Original Publication: Basel : MDPI, c2004-

Sample Size*; Bayes Theorem ; Confidence Intervals ; Probability

In Bayesian analysis of clinical trials data, credible intervals are widely used for inference on unknown parameters of interest, such as treatment effects or differences in treatments effects. Highest Posterior Density (HPD) sets are often used because they guarantee the shortest length. In most of standard problems, closed-form expressions for exact HPD intervals do not exist, but they are available for intervals based on the normal approximation of the posterior distribution. For small sample sizes, approximate intervals may be not calibrated in terms of posterior probability, but for increasing sample sizes their posterior probability tends to the correct credible level and they become closer and closer to exact sets. The article proposes a predictive analysis to select appropriate sample sizes needed to have approximate intervals calibrated at a pre-specified level. Examples are given for interval estimation of proportions and log-odds.

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Keywords: bayesian inference; highest posterior density intervals; normal approximation; predictive analysis; sample size determination

Date Created: 20210115 Date Completed: 20210318 Latest Revision: 20210318

20221213

PMC7827664

10.3390/ijerph18020595

33445651