ABSTRACT
Based on the formal statistical framework, definition of feasible sets of treatment options, and assumptions introduced in Chapter 6, a rigorous exposition of optimal multiple decision treatment regimes for a given specification of feasible sets is presented. A precise, careful characterization of an optimal regime in terms of potential outcomes is given using the principle of backward induction, and that a regime following from this characterization satisfies the definition of an optimal regime is demonstrated explicitly. It is then shown that an optimal regime can be expressed equivalently in terms of the observed data. Formulation of an optimal regime for treating patients who present subsequent to the first decision point is discussed. Detailed accounts of methods for estimation of an optimal regime for a given specification of feasible sets are presented, including for Q-learning, A-learning, methods based on inverse and augmented inverse probability weighting and their implementation through backward iterative estimation and an analogy to a series of weighted classification problems, methods based on restricting the class of regimes to those whose rules are in the form of decision lists, and methods based on marginal structural models. Additional approaches in the literature are reviewed.
