You are right that once you have a prediction for risk if untreated, and a prediction risk if treated, you just need a cost/benefit analysis. However, you won’t get to that stage without a paradigm for extrapolation, whether implicit or explicit. I prefer making that paradigm explicit.
If you want to plug in raw experimental data, you are going to need data from people who are exactly like the patient in every way. Then, you will be relying on a paradigm for extrapolation which claims that the conditional counterfactual risks (rather than the magnitude of the effect) can be extrapolated from the study to the patient. It is a different paradigm, and one that can only be justified if the conditioning set includes every cause of the outcome.
In my view, this is completely unrealistic. I prefer a paradigm for extrapolation that aims to extrapolate the scale-specific magnitude of the effect. If this is the goal, our conditioning set only needs to include those covariates that predict the magnitude of the effect of treatment, which is a small subset of all covariates that cause the outcome.
On this specific point, my view is consistent with almost all thinking in medical statistics, with the exception of some very recent work in causal modeling (who prefer the approach based on counterfactual risks). My disagreement with this work in causal modeling is at the core of my last discussion about this on Less Wrong. See for example “Effect Heterogeneity and External Validity in Medicine” and the European Journal of Epidemiology paper that it links to
I very emphatically disagree with this.
You are right that once you have a prediction for risk if untreated, and a prediction risk if treated, you just need a cost/benefit analysis. However, you won’t get to that stage without a paradigm for extrapolation, whether implicit or explicit. I prefer making that paradigm explicit.
If you want to plug in raw experimental data, you are going to need data from people who are exactly like the patient in every way. Then, you will be relying on a paradigm for extrapolation which claims that the conditional counterfactual risks (rather than the magnitude of the effect) can be extrapolated from the study to the patient. It is a different paradigm, and one that can only be justified if the conditioning set includes every cause of the outcome.
In my view, this is completely unrealistic. I prefer a paradigm for extrapolation that aims to extrapolate the scale-specific magnitude of the effect. If this is the goal, our conditioning set only needs to include those covariates that predict the magnitude of the effect of treatment, which is a small subset of all covariates that cause the outcome.
On this specific point, my view is consistent with almost all thinking in medical statistics, with the exception of some very recent work in causal modeling (who prefer the approach based on counterfactual risks). My disagreement with this work in causal modeling is at the core of my last discussion about this on Less Wrong. See for example “Effect Heterogeneity and External Validity in Medicine” and the European Journal of Epidemiology paper that it links to