Sample size in prognostic factor research

dear elias, thank you for your thoughts, discussions, and elaborations on other topics. The nuance of my question is that it is about causal inference and associations irrespective of overall prediction. Explanatory/causal models (with the goal of investigating one specific prognostic factor) should be treated very different than prediction models, for instance you can not adjust for mediators. I asked Richard himself during his prediction model course, if the sample size calculations of prediction models (the ones you cited) can be used for these explanatory models, and he clearly answered it is not possible. The formulas I cited in the very beginning were also recommended to me by Richard, he also posted them on his website: https://www.prognosisresearch.com/guidance-prognostic-factors And these formulas certainly apply when planning a new study and how many patients to recruit. However, we already have a biobank with a certain number of patients established. I already believed retrospectively using these formulas does not make sense, as also JiagiLi stated. Frank suggested that then it is crucial to present confidence intervals.