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So this great study was published and, as always, everyone is confused about interpreting non-inferior design.
Can a simple Bayesian approach help?
@Michael_Harhay, @otavio_ranzani, @reverendofdoubt, others pls
correct me if I am wrong!

As with any Bayesian analysis, we should have a prior for the success rate of first attempt intubation. I am no expert on this, but in Brazil is it probably around 70%, but values of 60-80% are possible.
The prior can then be assumed to be a beta distribution. A B(65,20) seems to do the trick (picture). This distribution is a probability distribution we will consider as prior for this data playing.
An uniform prior could be used if we knew nothing about intubation success %, which is not the case, the probability for sure is neither 0 nor 100%. Anyway, as we'll see prior won't matter much here.
The beta binomial distribution has two parameters (alpha and beta). Confusing, I know. Statisticians ran out of Greek letters so they started repeating them. Don't get confused by that. It's their charm.
A cool thing about the beta distribution is that it can easily be updated by adding raw success and failures values to its parameters. Just add successes to the first parameter and failures to the second.
In the case of this study, we can add successes and failures for both groups and we will have two other betas, one for rocuronium and other for sux (picture). The resulting parameters are in the legend.
Note that the peak is reasonably centered in the % success for each drug. The large sample coupled with a "weak" prior means results are largely defined by data.
Also note that the parameter of the beta for rocuronium and sux are simply the prior parameters added to success (for alpha) and failure (for beta). They are on figure legend.
We can then sample these distributions and plot the resulting difference. We could also do this mathematically, but sampling is also OK. So let's sample the distributions for rocuronium and sux and take their difference and plot it. How does it look?
Looks like the large mass is below zero, that is, rocuronium results in an average 4.2% less successful intubation on first attempt. This is pretty close to the 4.8% the study reported.
We can also calculate the probability that difference is higher than 0, that is, that rocuronium is associated with greater success rates (around 3.2% in this simulation). Doesn't look good, does it?
What this means? Instead of using "not non-inferior", this approach can tell us that it is *very* unlikely that rocuronium is better provided our assumptions are true.
This is just a very silly example. The above simulation takes no more than 10 lines of #rstats code and provides, I hope, a more straightforward interpretation.
So before blaming the study for its non-inferiority margin, remember there are always cool ways to look at data!
Please, if I made some wrong statement or calculation in this thread, help me finding my error! @ADAlthousePhD.
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