  Dynamic treatment regimes (DTRs) aim to formalize personalized medicine by
tailoring treatment decisions to individual patient characteristics.
G-estimation for DTR identification targets the parameters of a structural
nested mean model known as the blip function from which the optimal DTR is
derived. Despite considerable work deriving such estimation methods, there has
been little focus on extending G-estimation to the case of non-additive
effects, non-continuous outcomes or on model selection. We demonstrate how
G-estimation can be more widely applied through the use of
iteratively-reweighted least squares procedures, and illustrate this for
log-linear models. We then derive a quasi-likelihood function for G-estimation
within the DTR framework, and show how it can be used to form an information
criterion for blip model selection. These developments are demonstrated through
application to a variety of simulation studies as well as data from the
Sequenced Treatment Alternatives to Relieve Depression study.
