Well since you asked for it, I will provide a question.
Senn advocates adjustment for prognostic covariates, my question is, prognostic for what? It seems that the concept of a prognostic covariate cannot be separated from the enrollment gate. The answer depends on the population constructed by the gate. If the gate selects a coherent causal system, the prognostic model has a clear biological referent. If the gate constructs a cause-agnostic disease mixture, then the prognostic model pertains to that potentially non-reproducible mixture rather than to any individual disease represented within it.
So the first question the biology trained reader may have is; āI see the math works but is it biologically meaningful, indeed, is it a blind assumption-based mathematical technique when performed without connecting the math to the gate. Does the joint distribution being modeled correspond to a biological data-generating process for which the covariates are prognostic or are they prognostic for an artifactual mixture distribution induced by a cause-agnostic enrollment gate (S=1)ā.
In that case, the regression model estimates a property of the disease mixture-defined estimand (Eā), not of any individual disease-specific estimand (Eā).