If you assume there’s an FDA that makes yes/no decision about which drugs to approve and you hate the p values that they use currently, what do you think should be the alternative statistical FDA standard?
Do you have a specific way they should do Bayesianism in mind?
A specific method? No, obviously. That depends on the problem. What I would love to see is:
“H0, H1 and H2 are our prior hypothesis. We assume them to be mutually exclusive and complete. H0, based on these empirical assesments, has probability P0. H1, base on those other considerations, has probability P1. H2 intercepts all the other possible explanations and has probability 1 - P0 - P1. We are going to use this method to analyze the data. These are the data. Based on the calculations, the revised probabilities for the three hypothesis are P0′, P1′ and P2′.”
How do you get the explicitly stated priors?
How about: we only know the mean of the effect, so we suppose an exponential prior distribution. Or: we value error quadratically, so we apply a normal distribution? Or: we know that the effect stays the same at every time scale, so we are going to start from a Poisson distribution?
When it comes to a test problem, what about an antidepression drug?
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Who’s that in case of a FDA approval process? The person who wants his drug approved or the FDA? If it’s the person who wants his drug approved, why don’t they just go into it with strong priors?
When it comes to a test problem, what about an antidepression drug?
You’ll need to be a lot more specific if you want a specific answer.
Who’s that in case of a FDA approval process? The person who wants his drug approved or the FDA?
It’s whomever is doing the trial.
If it’s the person who wants his drug approved, why don’t they just go into it with strong priors?
They will surely go with strong prior. However, it’s already like this even with frequentist methods (it just takes a different form): math cannot force honesty out of anyone. The advantage of the Bayesian approach is that priors are explicit, and others can judge them more easily.
The basic idea of how the FDA process works is that it’s extremely predefined and doesn’t allow the person who wants the approval to cherry pick statistics.
It seems like your approach is to provide more flexibility. Did I get the wrong impression?
I have no idea how the FDA approval process work, so if you tell me that it doesn’t allow any statistics variation then sure, I can only agree and say that the Bayesian method outlined (which not ‘mine’ for any stretch of the word) is more flexible.
If you assume there’s an FDA that makes yes/no decision about which drugs to approve and you hate the p values that they use currently, what do you think should be the alternative statistical FDA standard?
Clearly pre-committed methodology and explicitly stated priors. Double blinds whenever possible. Bayesian model analysis. Posterior distributions, not conclusions.
Do you have a specific way they should do Bayesianism in mind? How do you get the explicitly stated priors?
A specific method? No, obviously. That depends on the problem. What I would love to see is:
“H0, H1 and H2 are our prior hypothesis. We assume them to be mutually exclusive and complete. H0, based on these empirical assesments, has probability P0. H1, base on those other considerations, has probability P1. H2 intercepts all the other possible explanations and has probability 1 - P0 - P1.
We are going to use this method to analyze the data.
These are the data.
Based on the calculations, the revised probabilities for the three hypothesis are P0′, P1′ and P2′.”
How about: we only know the mean of the effect, so we suppose an exponential prior distribution. Or: we value error quadratically, so we apply a normal distribution? Or: we know that the effect stays the same at every time scale, so we are going to start from a Poisson distribution?
When it comes to a test problem, what about an antidepression drug?
Who’s that in case of a FDA approval process? The person who wants his drug approved or the FDA? If it’s the person who wants his drug approved, why don’t they just go into it with strong priors?
You’ll need to be a lot more specific if you want a specific answer.
It’s whomever is doing the trial.
They will surely go with strong prior. However, it’s already like this even with frequentist methods (it just takes a different form): math cannot force honesty out of anyone. The advantage of the Bayesian approach is that priors are explicit, and others can judge them more easily.
The basic idea of how the FDA process works is that it’s extremely predefined and doesn’t allow the person who wants the approval to cherry pick statistics.
It seems like your approach is to provide more flexibility. Did I get the wrong impression?
I have no idea how the FDA approval process work, so if you tell me that it doesn’t allow any statistics variation then sure, I can only agree and say that the Bayesian method outlined (which not ‘mine’ for any stretch of the word) is more flexible.