## RE: "SHOULD META-ANALYSES OF INTERVENTIONS INCLUDE OBSERVATIONAL STUDIES IN ADDITION TO RANDOMIZED CONTROLLED TRIALS? A CRITICAL EXAMINATION OF UNDERLYING PRINCIPLES"

We have shown that if one decides to use probabilities to replace confidences, the construction of the intervals is completely different than the usual method

C. Pereira

2009

#### Scholarcy highlights

• American Journal of Epidemiology a The Author 2009
• Shrier et al considered a 95% confidence interval as being one with a 95% probability that a population parameter is included in the interval and a 5% probability that it will lie outside the interval
• Let p be the population proportion of possible patients who would not respond to the treatment. p is the parameter of interest; its true unknown value is the quantity to be estimated
• We calculate an exact interval with 90% confidence that happens to be nonsymmetric around 6/20:. This may be the smallest 90% confidence interval for the observation ‘‘6 out of 20.’’ The correct interpretation of the information that p is in this interval with 90% confidence is as follows: If we could repeat this procedure over a large number of samples of size 20, the true unknown value of p would be contained in 90% of the intervals; we are confident that our particular interval,, contains the true value of p
• To build Bayesian credible intervals, consider a uniform prior in. This corresponds to normalizing the likelihood function, producing a beta posterior with, for example, a 1⁄4 7 and b 1⁄4 15
• Rather than providing 95% confidence that the true value of the population parameter lies within the interval, the correct interpretation is that with the performance of equivalent studies, 95% of the observed confidence intervals would cover the true value of the parameter—a subtle but important difference, since population parameters are not random quantities and probability statements should not be attached to them
• In the Bayesian framework, which was not considered by Shrier et al, are parameters treated as random variables

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