Adaptive treatment and robust control

Abstract

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 so as 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 modelling and inference per se. We propose that modelling and estimation be based on standard statistical techniques but subsequent treatment policy 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.

[Regular Paper] Model Predictive and Proportional Integral Control of Blood Clotting Speed Using Warfarin when Data are Missing

“…Hence, our overarching aim is to combine ideas from well established approaches in control with the statistical theory of ODT regimes. Progress has been made towards this by using robust control theory in ODT selection [23].…”

Robustness evaluation and robust design for proportional-integral-plus control

“…However, despite providing a closely related but more general alternative to PID control, no equivalent design methods currently exist for PIP control. The NMSS/PIP approach has been extended, or constrained, and used to mimic exactly a number of other design methods including, for example, minimal linear quadratic (LQ) and generalised predictive control (Taylor, Chotai, & Young, 2000), other forms of model-predictive control (Exadaktylos & Taylor, 2010;Wang & Young, 2006), and statistical regret-regression (Clairon, Wilson, Henderson, & Taylor, 2017). Taylor, Young, and Chotai (1996) and Taylor et al (2013) utilise linear-exponential-of-quadratic cost functions (Whittle, 1981) to link PIP design to H ∞ concepts but subsequently rely entirely on Monte-Carlo simulation to investigate robustness.…”

[Regular Paper] Stochastic Non-minimal State Space Control with Application to Automated Drug Delivery

“…Such PIP controllers have been utilised in a range of application areas e.g. [8], [9], [10], [11] and they also show promise for biomedical control applications [12]. In the discrete-time case, the non-minimal state vector consists of the present and past sampled values of the output, past sampled values of the input and, commonly, an integral-of-error term.…”