Model checking with residuals for g-estimation of optimal dynamic treatment regimes

In this paper, we discuss model checking with residual diagnostic plots for g-estimation of optimal dynamic treatment regimes. The g-estimation method requires three different model specifications at each treatment interval under consideration: (1) the blip model; (2) the expected counterfactual model; and (3) the propensity model. Of these, the expected counterfactual model is especially difficult to specify correctly in practice and so far there has been little guidance as to how to check for model misspecification. Residual plots are a useful and standard tool for model diagnostics in the classical regression setting; we have adapted this approach for g-estimation. We demonstrate the usefulness of our approach in a simulation study, and apply it to real data in the context of estimating the optimal time to stop breastfeeding.