Adaptive treatment and robust control.

A control theory perspective on determination of optimal dynamic treatment regimes is considered. The aim is to adapt statistical methodology that has been developed for medical or other biostatistical applications to incorporate powerful control techniques that have been designed for engineering or other technological problems. Data tend to be sparse and noisy in the biostatistical area and interest has tended to be in statistical inference for treatment effects. In engineering fields, experimental data can be more easily obtained and reproduced and interest is more often in performance and stability of proposed controllers rather than modeling and inference per se. We propose that modeling and estimation should be based on standard statistical techniques but subsequent treatment policy should be obtained from robust control. To bring focus, we concentrate on A-learning methodology as developed in the biostatistical literature and H∞ -synthesis from control theory. Simulations and two applications demonstrate robustness of the H∞ strategy compared to standard A-learning in the presence of model misspecification or measurement error.