Adaptive Treatment and Robust Control

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.

The investigators have a track record of successful impact generation. For example Taylor's MATLAB-compatible CAPTAIN Toolbox has been downloaded approximately 50 times per month since 2008 and has been used extensively by government departments and industrial licence-holders. Henderson's work with British Nuclear Fuels (now Sellafield Sites) and National Nuclear Laboratories underpin a Newcastle University impact case study submitted to REF2014.

Task 15 of the proposal is to develop free-to-use software for implementation of the new methodology. In addition we have five specific application areas that are included as a route to immediate impact. In all cases we have letters of support from our partners.

Horse heart rate. The project team will build on an existing engineering/biosciences collaboration with colleagues in M3--BIORES at KU Leuven to analyse data-sets on the dynamic responses of living organisms, in order to monitor and control their well-being, health and performance. These data include athletic horse heart rate, an example that has potential application as a basis for training improvement. Here, the output is the heart rate measured every 20 seconds, whilst the input is a running speed, as generated by the decision rule and communicated to the rider. There is a high noise to signal ratio, and the data are limited to relatively few horses and riders, hence are apposite for statistical analysis as under ODT.

Targeted growth curves. Representing a second link with M3-BIORES, growth control in chickens has been proven to be an efficient method to ensure broiler yield, and to lessen health problems. In this example, an MPC algorithm has previously been used to calculate the feed supply to the broilers with the intention of following a target growth trajectory. Practical tests by our collaborators have considered experiments under 'ideal' laboratory conditions and, less successfully to date, a working broiler farm on a larger scale. We will work toward the larger scale implementation of control and ODT methodology.

Leukaemia control. We have continuing collaboration with colleagues in Copenhagen who are partners in a long-term study into treatment of childhood leukaemia. The output is white blood cell count and the input is the type and dose of chemotherapy. Children are scheduled to be monitored weekly but in practice clinic visits are sometimes missed. Our approach under Theme 2 on missing data is required for the efficient analysis of data of this form, aimed at recommending optimal treatments.

Anticoagulation control. ODT methods have been previously been tested on warfarin anticoagulation data. We will work with Newcastle colleagues on the development of ODT for anticoagulant control, using observational data collected from 45,00 patients over 10 years. Output is blood clotting speed and input is anticoagulant dose. Challenges include high between and within patient variability together with random clinic scheduling. With over 2 million people on long-term antocoagulation in Europe alone, there is potential in this application for massive non-academic impact.

Forced ventilation. New results into thermal control of the environmental test chamber, under Themes 2 and 3, will contribute to agricultural engineering applications. We have already set up a link for industry exploitation of such research with NP Structures Ltd and other collaborating partners in the UK, for a related project on reducing the operational costs and energy consumption of closed-environment growing systems. With the ability to control crop delivery date and flavour by regulation of the lighting and micro-climatic systems, such grow-cells are presently stimulating much industrial and academic interest.