Mathematical and Statistical Modelling to Optimise Paediatric Medicines Research

This project will improve the methods used in mathematical and statistical modelling to help us make best use of medicines in children. Mathematical modelling uses equations to describe observations made during an experiment. For example, suppose we measure the number of bacteria in the lung of a child with a chest infection at a few time points. A simple model is a straight line given by the equation: y = mx + c, where y is the number of bacteria for each value of x (the time that the measurement was taken), m is the slope of the line, and c is the number of bacteria when time is 0. In this case, m and c are model parameters and we estimate their values from our observations. With these values of m and c, we can use the model to predict what the number of bacteria would be at values of x (time points) that were not measured in our experiment. We can also look at the values of m and c to learn about the system, e.g. m tells us how quickly the number of bacteria decreases with time. If we collected information like this from children receiving different doses or types of antibiotics, then we could see what effect antibiotic dose and type has on the rate that bacterial numbers decrease.

Because each child is an individual, the value of m and c might be different in different children. Also our mathematical model is a simple representation of the system. For these reasons, we add a statistical part to the model. This explains the variability between individuals, and the unexplained variability from the model. By adding this statistical part, we can judge how much confidence we should have in the predictions from the model. The models used will be more complex than the example above, and the technique is called nonlinear mixed effects modelling.

The reason that mathematical and statistical modelling is important is that fewer patients are needed than for traditional controlled trials, which involve comparing outcomes amongst large groups of subjects. By intensively studying a small number of children, we can work out the optimum treatment regime more efficiently. The models that will be used will be a system of equations to link three things: the dose of a medicine administered, its concentration in the body, and the effect. Research over the last 10-15 years has meant we now understand what kinds of models to use to link dose and concentration in children. This project will seek to improve our methods for linking concentration with effect. This will be done by designing new types of laboratory experiment and using new statistical methods. Three different scenarios have been identified where improvements in modelling the link between concentration and effect are required:

1. Situations where the effect is difficult or impossible to measure. An example of this is in bacterial infections, where we know the child is ill, but it is very difficult to measure the bacterial count. This problem will be addressed by doing laboratory experiments to mimic the site of bacterial infection, and then using mathematical and statistical modelling to link the results of these experiments with dose-concentration results obtained in clinical studies of children.

2. The effect is measured as a score or number of different responses. An example of this is in intensive care where the level of sedation is measured by combining scores for things like breathing rate, alertness, and tension in the face. A statistical technique called Item Response Theory will be used to model these scores and link them to the dose and concentration of sedative drugs.

3. Medicines are affecting a marker that we can readily measure. An example of this is the concentration of immune cells in the blood after a transplant where children receive drugs called immunosuppressants. Mathematical models that have parameters relating to birth and death rates of these cells will be used to understand the optimum immunosuppressant dose and how these rates change with age

This project aims to improve methods for modelling drug effects in the following three scenarios: effect is difficult to observe directly; effect is measured by a disease score or composite measure; effect is a clear biomarker. The methods will be developed using example applications. Where effect is difficult to observe, the example scenario is bacterial infection where serial cultures are rarely available in patients. In vitro hollow fibre infection model data will be combined with clinical dose-concentration data and a joint model formulated. Where effect is a disease score, the example scenarios will be taken from measures of sedation and toxicity used in paediatric critical care. Item response theory will be used to allow for pooling of different types of information , and again estimated jointly with dose-concentration data. Where effect is a clear biomarker the example scenario will be in immune reconstitution following transplant and antiretroviral initiation. Mechanistic differential equation models will be used to gain insight into drug, age and disease-related effects at the model parameter level. Mathematical models will be non-linear and mixed effects will be used to account for parameter and between occasion variability modelling. Optimal design of in vitro experiments will also be undertaken, and final optimum therapeutic guidelines derived using decision theory-based minimisation of loss function type approaches. The software for parameter estimation will be NONMEM and optimal design PoPED or PFIM. Scientific opportunities will mainly be the development and implementation of these methods in a paediatric setting. Medical opportunities will be development of dosing guidelines for some antimicrobials in children, developing sedation dosing guidelines for paediatric critical care, and improved understanding of interventions affecting immune reconstitution.

The primary beneficiaries of this research will be paediatric patients requiring medicines, in particular antimicrobials. Due to the generic nature of much of the work, the study design and data analysis methods developed could be applied to benefit patients of any age. Secondly, it is a regulatory requirement for almost all new medicines to be studied in children, meaning any pharmaceutical company involved in drug development, those seeking to extend existing product licenses, or those wishing to update paediatric dosing guidelines (e.g. in the light of increasing antimicrobial resistance), will all be beneficiaries of this research. In the latter cases in particular, non-profit organisations such as the PENTA-ID network (http://www.penta-id.org/) will also be beneficiaries. Thirdly, the Association of British Pharmaceutical Industries (ABPI) has identified pharmacokinetic-pharmacodynamic modelling as an area of high priority for skills development in the UK. Fourthly, medicines regulatory agencies will benefit from knowledge of these methods through their role in both guiding industry as to the types of studies required (through provision of scientific advice), and in assessing industry submissions for product licensing. Finally, should the application of the methods proposed contribute to reduced morbidity and mortality, this will benefit NHS organisations and the wider public.

The major way in which children will directly benefit from the research is that optimal dosing and treatment duration guidelines will be developed for six of the most commonly prescribed penicillins. These guidelines will seek to optimise the probability of successful treatment, whilst minimising course duration and the risk of inducing antimicrobial resistance. Publication of these guidelines in the form of scientific papers will begin in year 3 of the fellowship. Implementation into local UK hospital guidelines will begin within the first 6 months of publication since I will disseminate the papers and recommendations through the UK paediatric antimicrobial pharmacist network of which I am a member (antimicrobial pharmacists are generally the main person responsible for updating local hospital antimicrobial policies). Since the penicillin studies are already registered as clinical trials of investigational medicinal products, any results that indicate the need for a change in dosing guidelines will be fed back to manufacturers to update the Summary of Product Characteristic documents. This in turn will lead to British National Formulary updates.

Pharmaceutical companies and non-profit research organisations such as the PENTA-ID collaboration will benefit from the knowledge of experimental design and analysis of the antimicrobial in vitro method once conference presentations and publications are generated starting in Years 2 to 3. It is expected that the legacy of this fellowship will be the establishment of a UCL-St George's collaboration in the optimal design, conduct, and analysis of in vitro hollow fibre methods for guiding antimicrobial dosing. Furthermore, the methods developed will be extended to other therapeutic areas such as tuberculosis. This expertise will be attractive to smaller pharmaceutical companies and non-profit organisations who may lack expertise in this area, and will be offered as a modular consultancy service whereby any or all aspects of the design, conduct and data analysis will be available. The UK pharmaceutical industry will start to benefit from the availability of more UK-trained doctoral-level modellers by Year 4, and should this fellowship lead to a permanent position at UCL then this benefit will be on-going. The impact on regulatory expertise will begin immediately since I will be attending and contributing to the European Medicines Agency expert group on Modelling and Simulation.