Suggestion: Change-in-estimate projection

In epidemiology we are concerned with the selection of confounders. One way to select confounders for an exposure is to fit a full model (reference model) with all potential confounders and then remove potential confounders in such a way that the effect estimate for the exposure(s) is as similar to the estimate for the full model as possible, while keeping the model as small as possible. Typically only the point estimate is considered which throws away information.

I wonder whether the projection could be adjusted to work towards this goal, instead of selecting the minimal submodel that keeps the same predictive performance. Maybe something to look into?

The issue proposes changing projection predictive variable selection to preserve exposure effect estimates for confounder selection rather than only predictive performance. No files, tests, or entry points are identified; first define the statistical objective and acceptance criteria, then locate the projection and variable-selection implementation. Done requires an agreed method and validation that it selects the intended submodels.