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I'm not a statistician, but an oncologist with interest in statistics.

Some background to my question:
In oncology in recent years, immunotherapy have made a breakthrough with uses in several different cancers. The same drug is used in multiple trials. Sometimes (but not always) I have a feeling that pharmaceutical companies use a certain throw-everything-on-and-see-what-sticks method.
If I understand it correctly,  when you perform several trials (and have a cut-off for significance of p<0.05), that would mean on average 1 in 20 is significant only due to chance.

Now to my question/-s:
Is this last sentence true if the p-values in the clinical trials is much lower than 0.05? For example if 40 trials report a p-value of 0.001, are they all so unlikely that they all are "true"? Or is it only the cut-off of 0.05 that matters?

If I'm mistaken, feel free to correct me or ask follow up questions!
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This is an area where it really pays to think like a Bayesian. The fact is that these studies in different indications are really \*not\* independent experiments (results from the same drug are quite likely to be correlated as whether a drug is biologically active tends to be pretty close to binary across tumor types with similar oncogenetic drivers). In addition, multiple endpoints are tested in each trial.

As an example, we have seen the first KRAS g12c approved drugs in NSCLC in recent years. The fact that a drug works in NSCLC means that there is a greatly increased likelihood of activity in any other tumor type driven by KRAS g12c mutations. The drug working in NSCLC greatly increases the likelihood that it's pharmacokinetically active in the tumor micro-environment across the other solid tumors. The PD-1s and PD-L1s have a very similar development history. Everyone went after melanoma first because it was commonly known that it was a very attackable pathway in that indication and huge unmet need. But the fact that the mechanism of action worked in melanoma opened the flood gates to other tumor types once it was established that the mechanism of action worked.

In isolation, yes, if you ran 20 completely independent trials with a drug that confers no benefit in some endpoint of interest (such as overall survival) then you would on average expect to see 1 p-value < .05. If you saw the result of a singular trial with p=.04 for OS, no benefit for PFS, an objective response rate close to zero, and a slew of other trials which were failures, then you would correctly not be impressed by the clinical benefit of that drug (and nor would the FDA) and most likely conclude that result is spurious despite the OS "benefit" in that one trial.

Likewise if you see a new trial result with p=.001 in one indication and the drug is already approved in 10 other clinical indications, I'd argue that the actual likelihood of that result being due to chance is much lower than .001 (this is a Bayesian sort of thinking). The p=.001 is calculated in isolation from that data from that one single study. The body of evidence about a drug's activity that's already approved in multiple other indications is, in fact, much stronger than that singular p-value. So this all but guarantees that that result is not due to chance, even beyond what would be implied by a single p-value.

I would argue from the drug development side that nobody has the money or time to throw shit at the wall and see what sticks. It costs on average well in excess of $100,000 to recruit a patient for an oncology trial (e.g. a 100 patient trial on average costs much more than $10mil). Trials take too long and are too expensive to run. The indications and compounds that get chosen are the ones with highest probability of success.

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