  Dynamic treatment regimes (DTRs) consist of a sequence of decision rules, one
per stage of intervention, that finds effective treatments for individual
patients according to patient information history. DTRs can be estimated from
models which include the interaction between treatment and a small number of
covariates which are often chosen a priori. However, with increasingly large
and complex data being collected, it is difficult to know which prognostic
factors might be relevant in the treatment rule. Therefore, a more data-driven
approach of selecting these covariates might improve the estimated decision
rules and simplify models to make them easier to interpret. We propose a
variable selection method for DTR estimation using penalized dynamic weighted
least squares. Our method has the strong heredity property, that is, an
interaction term can be included in the model only if the corresponding main
terms have also been selected. Through simulations, we show our method has both
the double robustness property and the oracle property, and the newly proposed
methods compare favorably with other variable selection approaches.
