Dear all,
I have studied pharmacoeconomics for a while. I would like to calculate alpha and beta of beta distribution data for probabilistic sensitivity analysis. Is it possible from 95% CI to calculate alpha and beta?
Thank you.
Naoto
Yes, that is possible.
See e.g.: https://en.wikipedia.org/wiki/Beta_distribution
You may even want to consider that a published CI may have assumed a normal distribution so that the CI is not or differently skewed than with a beta distribution.
Hi, Robert,
Thank you so much for your information.
I would like to ask you one more thing. According to the site, for example,
when a probability of a side effect is 4.4% and population size is 610, alpha = 0.044 * (610+2) = 26.9 and beta = (1-0.044) * 612 = 585. Is this acceptable?
Naoto
Yes, that is acceptable.
I tend to not add 2 to the number of observations, which would give parameters: 26.84 and 583.16 but it would be better to use the actually observed numbers, which were probably 27 and 583. This is practically the same in this example. With a smaller number of observations the difference would be larger. But it goes wrong when you have only 1 observation.
Maybe this section in Wikipedia helps explain:
https://en.wikipedia.org/wiki/Beta_distribution#Bayesian_inference
But for practical modeling, not really something to worry about.
It seems more important to consider: Do you really only have information concerning this probably from those 610 observations and nothing else? But most in this field of modeling prefer to include only information that can be directly converted into a parameter value and not consider that we probably already knew something about this before the 610 observations were made. Anyway, probably more then you wanted to consider; you can also just consider the first sentence here. :-)
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