"Frankly, it didn't have a discernable impact agai

"Frankly, it didn't have a discernable impact against the entire trial. If it was really good against a certain portion, that means it must have been worse against another portion."

First, thank you for your thorough analysis. But I have to argue that your statement may sound intuitively correct, but it actually is very wrong. When the effectiveness for 2 groups is equal, but each sub portion in one group can have a drastic improvement over corresponding sub portion in another group. The caveat is in makeup proportion of sub portions.

To illustrate this idea, let's look the following imaginary case. Assume we have a drug that can save 50% patients with certain desease in any sub portion of patients. Assume 2/10 of severe sub portion die with placebo, 10/10 of critical sub portion die with placebo. Then 1/10 of severe sub portion die with treatment, 5/10 of critical sub portion die with treatment.

Assume placebo arm has 40 patients, 30 severe, 10 critical, death=2/10x30+10/10x10 = 6+10 = 16

Treatment arm has 40 patients, 10 severe, 30 critical, death=1/10x10+5/10x30=1+15 = 16

In this imaginary case, both placebo arm and treatment has 16/40=40% mortality, but the drug actually save half of the patients.

The lesson learned from this costly trial is that, you should identify the most important subgroup of patients when designing trial, use stratification in the randomization process to reduce their impact. Hopefully we learn from it in CD16, be conservative and give us enough margin for error.