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Pharmacokinetic (PK) studies aim to understand the time course of a drug in our body. PK studies are routinely used in the study of malaria, for example, to understand how different drugs act on the malaria parasite, and for how long, so that we can establish treatment protocols to effectively clear infection . Blood samples are taken from study participants at a number of times post-treatment to monitor the concentration of the drug within an individual.

The design of these experiments – e.g. when to take the blood samples – is often governed by logistical, financial and ethical constraints, coupled with prior knowledge of the drug concentration time profile. These factors are all important, but there is often no formal consideration of the often complex, underlying statistical model that is used to analyse the drug concentration data.

There exists a suite of tools within the field of “optimal experimental design” that have been developed for this purpose. They aim to answer the question: “What is the best way to allocate my limited resources, in order to learn the most about my system?”.

In the context of these PK-malaria studies, we are limited by: how many samples we can feasibly take from each individual, and how close together these samples can be taken (ethical); how many samples we can afford to analyse, and how long the trial can run (financial); and what time individuals can come into a clinic – in the locations where the malaria parasite is prevalent, this often requires considerable travel (logistical). Given these constraints, we wish to learn the most about the PK-profile (that is, the drug concentration over time). We describe the underlying statistical model, and the range of feasible PK-profiles that we think might be realistic – these can be highly informed by studies of volunteers or small studies of malaria patients, or we could know almost nothing. These optimal design tools can then tell us when we should sample, accounting for how much information we have, and what we can practically achieve.

Figure 1 below shows an average PK-profile (black line), and the amount of variation we think is reasonable (grey). In this example, individuals are treated at 0, 1 and 2 days (corresponding to the steep rise), after presenting at the clinic/hospital, and we can afford to take 4 blood samples from each individual. The horizontal red regions correspond to the recommended intervals in which each of four blood samples should be taken.

This example suggests that the first sample is taken early – in order to capture the rate at which the drug is absorbed into the body – the second sample is taken around 2-3 weeks post-treatment – to capture the clearance rate of the drug – and the final two samples are taken as late as possible (in this case, 40-42 days post-treatment) – in order to capture the elimination of the drug from the body.

These kind of optimal experimental design tools have immense potential to inform the collection of data, so as to subsequently enhance our understanding of a wide-variety of processes. The example here relates to optimal times to sample for a single group of patients, but they can also be used to answer a variety of other questions, such as: how to allocate individuals to different “sampling design” groups, how many different groups, and what (e.g.) dose to give each group, to name a few.

If you are interested in further information, please contact David Price.