| Abstract |
In medical research, an adaptive treatment strategy (or adaptive intervention) is a set of rules for choosing effective treatments for individual patients. The treatment choices made for a particular patient are based on that individual's characteristics and history, with the goal of optimizing his or her long-term clinical outcome. In the statistical literature, research in the area of optimal dynamic treatment (ODT) regimes has developed rapidly in the past 10 years. The essential problem is causal inference in the presence of time-varying confounders and the specific task is to derive adaptive decision rules for medical treatments or other interventions based on subject-specific characteristics and individual biomarker trajectories. In many applications there are few decision times, a low number of possible treatments and a finite follow-up period. However, the methods have begun to be used for adaptive treatment of chronic conditions, for dose selection and under infinite horizons. These methods are linked to machine learning and control theory in engineering and computer science. However, there have been no attempts to date to make use of control methodology in optimal dynamic treatment selection. Control theory is concerned with the mathematical analysis of causal dynamical systems. The goal is to design a control law in order to achieve engineering specifications and to optimise some objective function. The main concern is to ensure that controllers behave well in the presence of modelling uncertainty, external disturbances and sensor noise, considerations that have close parallels in ODT regimes. In this project we shall combine the ideas from two well-established approaches to control with the statistical theory of ODT regimes. These are receding-horizon methods (such as model predictive control, MPC) and H-infinity control. In medical applications the input will often be a treatment, the output will be a measure of health, data will be available in the form of short sequences of observations on many subjects, and there will be no feasible opportunity to collect repeat data. By contrast, in engineering applications, usually a single subject is under study but it is closely monitored, with frequent observations. In the case of an aircraft, for example, the control inputs will lead to movement of the ailerons, elevators and fin, in order to manipulate the attitude of the aircraft during its flight mission. Recently there has been growing interest in the use of control in biomedical applications, which typically have greater stochastic uncertainty and weaker repeatability than found in classical engineering application areas. Although control theory has been connected to biological systems for decades, developments in sensor technology mean that it is now possible to measure variables such as the heart rate of animals on-line. Examples include the real-time control of physiological variables such as heart rate and growth. Thus there is need and scope for use of modern statistical estimation and inference methodology alongside modern control methods. To address these issues, the present project involves a three-way collaboration between researchers in statistics, in control engineering, and in mathematical analysis. The aim is to solve an array of problems in the general area of adaptive intervention through the integration of techniques and approaches that have been developed in distinct ways in the three fields. The problems are focused around the cross-disciplinary themes of irregular sampling and robustness. |