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Jan 31

Population PK (PopPK): The What, The How, and The Why

Population Pharmacokinetics (PopPK) is the gold standard method of understanding drug safety and efficacy, particularly as it provides a unique insight into the variation of drug behaviour from person to person.

While not a novel methodology—Sheiner, Rosenberg and Marathe first demonstrated the analysis in 1977—techniques and approaches in PopPK have undergone continual improvement in the years since its inception. It is perhaps no surprise, therefore, that PopPK is seeing increasing emphasis from regulators, particularly as computational resources have never been cheaper.

Pharamacokinetics and Pharmacodynamics

Let’s take a step back. There are two components to understanding the behaviour of any drug: what the drug does to the body, and what the body does to the drug.

The former, pharmacodynamics (PD, from the Greek meaning “drug power”), encapsulates the response of the body to the introduction of the drug. For example this could be a reduction of heart pressure or helping a patient fall asleep.

The latter, pharmacokinetics (PK, “drug motion”), describes how the drug moves through the body through absorption, distribution, metabolisation, and excretion. Together, these phases are referred to as ADME.

PK and PD form the field of pharmacology, and both are crucial to the safety and efficacy of a drug. A drug might theoretically be the silver bullet which cures cancer, but if it can’t be absorbed by the body then it might as well be a glass of orange juice. On the other hand, the sugar in that glass of fresh OJ might be readily absorbed, but nobody’s going to prescribe a sugar cube as much more than a placebo.

Testing both PK and PD is therefore intrinsic to licensing a new drug. They are typically examined together in PK/PD studies, which combine the ADME of the drug alongside its known effects into what is known as a dose-response model. This model is then used to determine, for example, safe dosing levels for the new drug.

PopPK: A diagram showing the principles of ADME
Pharamacokinetics encapsulates the Absorption, Distribution, Metabolism, and Excretion of a drug, together referred to as ADME. Image from https://toolbox.eupati.eu/glossary/pharmacokinetics/

Ok, but what’s this business with populations?

Traditional (often known as individual) PK/PD studies are performed by introducing a drug to a subject and measuring an array of endpoints—typically drug concentration and whatever the drug is designed to do—at a series of timepoints. This is used to create a concentration-time profile of the drug, and in turn a dose-response model.

The problem is that these models require rich data—a large amount of information about each patient at each timepoint. This often limits the number of patients which can be included in PK/PD studies, which, in turn, means there is often less information available about how PK/PD varies across populations.

This can be a big problem: should a dose of your new drug be the same for a 14 year old girl be the same as a 50 year old man? Possibly not. What should the difference in dosing be? Chances are there weren’t many 14 year old girls included in the study, so it can be very difficult to say.

This is where PopPK enters the picture. By explicitly taking into account patient covariates—age & weight, pre-existing conditions, etc—variations in this dose-response model across clinically relevant populations can be determined. This allows for more informed dosing decisions where these variations have clinically significant effects.

How does PopPK work?

There are, broadly, 5 components to a PopPK analysis:

1. Data

As mentioned previously, the data collected for a PopPK analysis can be sparse, with fewer datapoints collected per subject. This means that PopPK can be used in later-stage clinical trials, such as phase 2 and phase 3. As taking variability into account is a key part of PopPK, data from multiple studies can be pooled for a single PopPK analysis.

2. Structural models

These are akin to the “platonic ideal” of how we expect a drug to behave. Essentially, they act as the scaffolding around which we expect data to vary, with the ADME of a drug modelled using a mix of differential and (most commonly) exponential equations.

These models are typically compartmental, with the drug modelled as flowing in and out of a series of compartments to mimic its movement through the body. Compartments need not be spatially localised – for example, the bloodstream might be a compartment. This means the drug’s concentration at its target location can be more effectively determined.

3. Statistical models

As we only have limited data with which to build our models, we need to allow for—and therefore, model—variability in both our data and model parameters. This typically falls into two categories. Between Subject Variability (BSV) is the variability between the population values of a parameter and those of individual subjects.

The Residual Unexplained Variability (RUV) is the variability which is “left-over” after the BSV is accounted for. It’s the typical random scatter which would be expected in any limited sample.

A third type of variability, Between Occurrence Variability (BOV), can also sometimes be included when the drug is administered on multiple occasions to the same subject, but this is not always possible.

Our estimates of the various forms of parameter variability are inferred from data, and captured by the parameters of our models. These models feed into the covariate evaluations which form the heart of PopPK. They can then be used for predictions and simulations.

4. Covariate models

While statistical models encapsulate the degree of parameter variability across the subject population, covariate analysis helps tell us why that variability exists, at least for the explainable BSV. For example, it might reveal that the clearance rate of a drug decreases with age, or that the peak drug concentration increases with body weight. These relationships are then modelled statistically so their effect can be incorporated into the overall model.

The choice of which covariates to look at needs to be made carefully to prevent unnecessarily examining factors which are unlikely to influence drug performance. These decisions are often based on knowledge of the drug and physiology: for example, weight and liver enzymes would be likely covariates for a highly metabolised drug. A statistical screening step is often also included, using regression-based techniques to check whether a relationship is present before undergoing a full model fit.

PopPK: Models of plasma concentration
Models of plasma concentration of a drug with time. The differences between the models are due to taking into account covariates.

Once covariate selection is complete, a full covariate model is constructed. Not all covariates chosen will impact the model meaningfully, so a pruning step takes place which systematically removes individual covariates from the model and checks how the overall model fit changes.

If removing a covariate significantly affects the model fit, it suggests that it has a strong effect on drug performance which isn’t captured by any of the other covariates. If the removal has only a small effect, we can conclude that either its relationship with drug performance wasn’t strong, or is captured by another, correlated covariate.

5. Final model

Finally, the individual components are combined into an overall model which takes into account the expected theoretical behaviour, variability due to covariates, and natural randomness from the data. In a similar way to the covariate model, the overall model is tested for goodness-of-fit against the data to ensure it replicates the known behaviour of the drug.

Why bother with PopPK?

So, we have a PopPK model. It was a somewhat statistically involved process: there were three aspects to model before we got to the final answer! Why put in all that effort?

We’ve a major reason already. Since PopPK determines the effect of covariates on drug behaviour, such factors can be taken into account when making dosing decisions and recommendations. Using PopPK, the difference in optimal dose for a 14 year old girl and a 50 year old man is far easier to obtain. This not only increases the safety and efficacy of treatments but also increases the efficiency of resource use.

In addition, since we’re explicitly including variability between subjects in our modelling, we can perform a PopPK study using sparse data. This means it can be used when repeated sampling of subjects would be difficult or unethical, such as in stage 2 or 3 clinical trials or paediatric studies.

The benefits don’t stop there, since the statistical models generated by a PopPK study can be used to simulate clinical trial outcomes. This can be extremely useful for testing study designs and optimising dosing schedules, particularly for adaptive study designs. Further, if early trials are in non-human subjects, then PopPK can be used to inform dosing in First-in-Human trials by extrapolating PK behaviour across species.

From a regulatory perspective, the FDA finalised and published official industry guidance for the use of PopPK in early 2022. They outline some of the benefits they see in the methodology, stating “Adequate population PK data collection and analyses…have in some cases alleviated the need for postmarketing requirements or postmarketing commitments”. With advantages for drug safety and efficacy, for clinical trial design and operation, and for development, PopPK is definitely the direction of travel for pharmacokinetics.

Quantics are experienced in performing PopPK studies and can guide you through every stage of the process. For more information, check out our services page.

About The Author

Matt is writing up a PhD at the University of Edinburgh. At Quantics, he works as a statistician with a focus on NMA. He has experience with machine learning, data science and experiment design, with additional interests in Model Explainability, inference in graphs, and bayesian models of cognition.