Reviews: Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes

The authors propose a method of estimating treatment effectiveness T(x) from a vector of patient features x. Treatment effectiveness is defined as (health outcome with treatment Yw) - (health outcome without treatment Y(1-w)). Presumably a health outcome might be something like survival time. If a patient survives 27 months with the treatment and only 9 without then the effectiveness T(x) would be 18 months? The authors estimate models of "outcome with treatment" and "outcome without treatment" jointly using RKHS kernel approximations on the whole dataset (I think there is a shared kernel). For a specific patient the effectiveness is based on the actual outcome of the patient which will be based on their features and their treatment condition minus the population model for the features of the opposite or counterfactual treatment condition.