  Individualized treatment rules (ITRs) are deterministic decision rules that
recommend treatments to individuals based on their characteristics. Though
ubiquitous in medicine, ITRs are hardly ever evaluated in randomized controlled
trials. To evaluate ITRs from observational data, we introduce a new
probabilistic model and distinguish two situations: i) the situation of a newly
developed ITR, where data are from a population where no patient implements the
ITR, and ii) the situation of a partially implemented ITR, where data are from
a population where the ITR is implemented in some unidentified patients. In the
former situation, we propose a procedure to explore the impact of an ITR under
various implementation schemes. In the latter situation, on top of the
fundamental problem of causal inference, we need to handle an additional latent
variable denoting implementation. To evaluate ITRs in this situation, we
propose an estimation procedure that relies on an expectation-maximization
algorithm. In Monte Carlo simulations our estimators appear unbiased with
confidence intervals achieving nominal coverage. We illustrate our approach on
the MIMIC-III database, focusing on ITRs for dialysis initiation in patients
with acute kidney injury.
