@DocMcstuffins,
"
Similar to an N of 12 it is virtually meaningless."
This is the statement that I was originally responding to. The results from our N of 12 are not virtually meaningless. Otherwise, why would the results even be offered to support our request for Fast Track Designation? Seems the FDA agrees they indicate that there MAY be some benefit from Remestemcel-L in the treatment of ARDS.
But, of course, you need that larger, RCT to "prove" it has some benefit.
"
Now the chance of our coins flipping heads 10/12was 1.93%, what about 9/12? What about 8/12? Just one different result make a huge difference in the likelihood of the results being due to chance rather than treatment."
What you are saying is that 12 is an awfully small number for a clinical trial. If the treatment was only of marginal benefit, then you would probably need a very large N to reveal that marginal benefit with any reasonable level of statistical significance. So no, I would not design a trial with such a small N.
But the question at hand is: can we infer anything from the data that we actually have, which at the moment is a sample size of 12?
I used the coin flip example because it was something simple that most people without any background in statistics could wrap their brains around. If 10 out of 12 patients survived, is it reasonable to conclude that, for some reason, these people were "weighted coins"? Meaning, is it reasonable to conclude that their actual chance at survival was better than 50 percent? The coin flip calculation tells us that there is only a 1.93 percent probability that their odds were 50/50. There is a 98 percent chance that their odds were in fact better than 50 percent.
So then the question is, what is it about these patients that gave them a greater than 50 percent chance of survival? Is it because all patients in similar circumstances have a greater than 50 percent chance of survival? That might make sense looking at current standard of care, for all ventilated patients.
But these patients were selected at a time and place where they were seeing roughly 80 percent mortality among ventilated patients. And as OP has pointed out, we didn't randomly select the 12, we actually selected the sickest of the sick. If anything, given the time and place, you would expect their chance of survival to be less than 20 percent.
Yet the results tell us that their odds were better than 50 percent. What is so special about our 12 patients? Maybe they appeared to be the sickest of the sick, but were actually superb physical specimens with inherent ARDS fighting capabilities. Or is it, perhaps, the fact that they were treated with Remestemcel-L?
I strongly suspect the latter, and look forward to trial results to confirm.
Those college and graduate school statistics courses were several decades ago, and I have forgotten most of what I learned. But I remember enough to realize that the actual results of our tiny sample size are compelling, and I have enough common sense to think that the explanation for those compelling results might be that Remestemcel-L actually improves chances of survival.
I do enjoy the lessons taught by our resident statistical experts, such as
@kervio. But I won't be signing up for any of your classes anytime soon.
(20min delay)