Hi Patrick,
For clarification, the text that you quote from my prior comments was in the context of providing for an estimate of the required sample size to achieve a desired precision (half width) for 95% confidence intervals for discrete observed data in isolation, not for the estimated precision of predictions from a potentially complex multivariable model as part of model development and validation.
On the latter subject, at least initially, I would refer you to, first, the second edition of Frank’s book, “Regression Modeling Strategies”, where in the index, there are several references to estimating sample sizes for various models that you can review, along with associated validation methods and other relevant content.
I would also refer you to Ewout Steyerberg’s book, “Clinical Prediction Models: A Practical Approach to Development, Validation, and Updating”, where there are references to relevant topics on sample sizes in chapter 19 of his book, and as with Frank’s book, other relevant content throughout as well.
I do not use Stata, but do use R, and Frank has a number of relevant functions in his “rms” and “Hmisc” packages for engaging in model development and validation processes.
There is also a discussion thread here that you might find of interest:
My recommendation, given some of your comments, would be to seek local statistical expertise to aid you in this endeavor. You will likely want to take advantage of that expertise in a collaborative environment, taking into account relevant prior work, and how that may reasonably influence what you do moving forward, not only with respect to the overall sample size that may be apropos, but also any considerations for the characteristics of that sample, and the implications of the intended decision making that should be part of the overall process.