Posting: # 18171
In BE we need to apply a parametric model, regardless of whether the residual of the linear model is normal or not. Even if we know the residual is decidedly not normal by all sorts of p-values and testing we apply the parametric model. It has been discussed ad nauseam throughout the years.
What has not been discussed a single time is how such an observation may affect the sample size calculations and planning. I have given it a bit of thought as of lately.
If the residual is not normal, then obviously any sample size calculation based on the parametric approach is out the window. It would seem such a pity to plan a trial for 90% power if it in reality only has 57% power due to the wrong assumption etc.
Only we don't quite know by how much the power/sample size calculation is off, because we might need to have a better alternative model for the actual distribution of the residual. And that is never known.
This is where the bootstrap comes in. If we have a pilot trial (yes, some geek did publish a paper demonstrating the shortcoming of pilot trials as development tools, but we can leave it out for now), we can bootstrap our way to 80% power or 90% or whatever. This makes no inference about distribution of data other than that the data be distributed as observed, while maintaining the mandatory parametric evaluation.
"But what if the data from a pilot trial is not indicative of the underlying or true distribution?", is the typical counter-question. Well, then we may be making a mistake that is no worse as compared to the situation where we trust the pilot data enough to plan sample size via parametric calculation which is decidedly wrong by an unknown amount on the premise of the question. In the existence of pilot trial data I therefore don't see the particular advantage of the parametric power calulcations other than they have been made conveniently easy to do now that software or packages like power.TOST and Fartssie exist.
I hope you can see what I mean? Otherwise, this remains a postulate and I wish I had an example of a drug with a known non-normal but still "parameterizable" distribution for the residual, so I could quantitatively illustrate it.
Thanks for reading.
"(...) targeted cancer therapies will benefit fewer than 2 percent of the cancer patients they’re aimed at. That reality is often lost on consumers, who are being fed a steady diet of winning anecdotes about miracle cures." New York Times (ed.), June 9, 2018.