Constructing dynamic treatment regimes over indefinite time horizons

Existing methods for estimating optimal dynamic treatment regimes are limited to cases where a utility function is optimized over a fixed time period. We develop an estimation procedure for the optimal dynamic treatment regime over an indefinite time period and derive associated largesample results. The proposed method can be used to estimate the optimal dynamic treatment regime in chronic disease settings. We illustrate this by simulating a dataset corresponding to a cohort of patients with diabetes that mimics the third wave of the National Health and Nutrition Examination Survey, and examining the performance of the proposed method in controlling the level of haemoglobin A1c.