There a difference between asking yourself: "Does this drug work better than other drugs?" and then deciding based on the answer to that question whether or not to approve the drug and asking "What's the probability that the drug works?" and making a decision based on it.
In practice the FDA does ask their statistical tools "Does this drug work better than other drugs?" and then decides on that basis whether to approve the drug.
Why is that a problem? Take an issue like developing new antibiotica. Antibiotica are an area where there a consensus that not enough money goes into developing new ones. The special needs comes out of the fact that bacteria can develop resistance to drugs.
A bayesian FDA could just change the utility factor that goes to calculate the value of approving a new antibiotica medicament. Skipping the whole "Does this drug work?"- question and instead of focusing on the question "What's the expected utility from approving the drug?"
The bayesian FDA could get a probability value that the drug works from the trial and another number to quantify the seriousness of sideeffects. Those numbers can go together into a utility function for making a decision.
Developing a good framework which the FDA could use to make such decisions would be theoretical work. The kind of work in which not enough intellectual effort goes because scientists rather want to play with fancy equipment.
If the FDA would publish utility values for the drugs that it approves that would also help insurance companies. A insurance company could sell you an insurance that pays for drugs that exceed a certain utility value for a cerain price.
You could simply factor the file drawer effect into such a model. If a company preregisters a trial and doesn't publish it the utility score of the drug goes down. Preregistered trials count more towards the utility of the drug than trials with aren't preregistered so you create an incentive for registration. You can do all sorts of thinks when you think about designing an utility function that goes beyond ("Does this drug work better than existing ones"(Yes/No") and "Is it safe?"(Yes/No)).
You can even ask whether the FDA should do approval at all. You can just allow all drugs but say that insurance only pays for drugs with a certain demonstrated utility score. Just pay the Big Pharma more for drugs that have high demonstrated utility.
There you have a model of an FDA that wouldn't do any Type I errors. I solved the basis of a theoretical problem that JoshuaZ considered insolveable in an afternoon.
*I would add that if you want to end the war on drugs, this propsal matters a lot. (Details left as exercise for the reader)
Consider Alice and Bob. Alice is a mainstream statistician, aka a frequentist. Bob is a Bayesian.
We take our clinical trial results and give them to both Alice and Bob.
Alice says: the p-value for the drug effectiveness is X. This means that there is X% probability that the results we see arose entirely by chance while the drug has no effect at all.
Bob says: my posterior probability for drug being useless is Y. This means Bob believes that there is (1-Y)% probability that drug is effective and Y% probability that is has no effect.
Given that both are compete...
For those who haven't heard, NIH and NSF are no longer processing grants, leading to many negative downstream effects.
I've been directing my attention elsewhere lately and don't have anything informative to say about this. However, my uninformed intuition is that people who care about effective altruism (research in general, infrastructure development, X-risk mitigation, life-extension...basically everything, actually) or have transhumanist leanings should be very concerned.
The consequences have already been pretty disastrous. To provide just one, immediate example, the article says that the Center for Disease Control and Prevention has shut down. I think that this is almost certain to directly cause a nontrivial number of deaths. Each additional day that this continues could have huge negative impact down the line, perhaps delaying some key future discoveries by years. This event *might* be a small window of opportunity to prevent a lot of harm very cheaply.
So the question is:
1) Can we do anything to remedy the situation?
2) If so, is it worth doing it? (Opportunity costs, etc)