Chapter 4

Question 1

How many and What are the parameters to estimate in the one-compartment oral absorption model.

Answer 1

3 parameters
Ke (or Cl), Vd and Ka.

Question 2

Explain the difference between rich and sparse data

Answer 2

Rich data sets consist of many samples collected from each individual, often at many time points

it is characterised by frequent sampling, allowing for detailed time-course data, typically seen in clinical pharmacokinetic studies.

Sparse Datasets consist of limited sampling points, common in population pharmacokinetic studies, where the focus is on the variability between individuals rather than detailed time courses.

Question 3

State when Rich and data and Sparse data is more likely to be used:

Answer 3

Rich data: Clinical pharmacokinetic studies

Sparse data: population pharmacokinetic studies (PopPK)

Question 4

What are the analytical approaches to modelling data:

Answer 4

Naive pooled approach
Naive average approach
Two-stage approach

Question 5

Describe Naive pooled approach

Answer 5

Naive Pooled Approach: Assumes all individuals have the same concentration at any given time, pooling data without considering inter-individual variability.

It treats all the data as if it is from a single individual, pool it together and fit a model (naive pooled approach)

Question 6

Naive pooled approach disadvantages:

Answer 6

Overestimates variability.

Treating all the data as if it comes from one individual. Variability is dumped into a single residual error term (at the end of the equation)

It does not take into account inter-individual variability

Naive pooled approach does not accurately describe the time-concentration profile of an individual.

Question 7

Describe Naive average approach:

Answer 7

Naive Average Approach: Averages concentration data across all subjects at each time point, overlooking individual differences. Average the data at each time point and then fit a model (naive average approach)

Question 8

Explain fixed effects

Answer 8

Fixed effects in an experiment or trial are controlled, or the same, for each individual.

For example, drug dose and frequency of administration are usually fixed. They may also be variables where all possible values/levels are studied.

For example, if you want to study the effect of smoking on the kinetics of a drug, you would study the drug kinetics in smokers- and non-smokers. The ‘smoking’ effect in your model is a fixed-effect since all levels of this factor (categorical)-variable are studied.

Question 9

Explain random effects

Answer 9

Random effects in an experiment or trials that are less controlled and do not include all possible levels. For example, we take a sample of participants in a trial, but we really want to know/make inferences about the population from which they are sampled. Since we do not study every single subject from the population, the participants in the study are a random effect.

Question 10

Explain mixed-effects (models)

Answer 10

Mixed-effects: a model which contains fixed- and random-effects.

Question 11

State the Advantages non-linear mixed effects approach

Answer 11

Enables modelling of sparse data, this is useful in later phase studies
Allows more complex identification of covariate effects (for example organ function)

Alternative sampling and modelling may allow for populations to be studied that are not straightforward to study in traditional phase-0/1 design (for example children, or drugs in pregnancy)

Allows complex simulations which can inform subsequent study design

Question 12

State the disadvantages non-linear mixed effects approach

Answer 12

Feels more complex (This can make people anxious about undertaking or understanding the process)

Computationally expensive

Time consuming

Often requires time cleaning/organising data from multiple sources

Question 13

The structural model

Answer 13

The structural model is the underlying equation that describes the mean population trend. This is the compartmental model you have chosen to model the data with.

Question 14

The statistical model

Answer 14

The statistical model is how we have chosen to model the parameter- and residual- variability.

Question 15

What is parameter variability referred to as?

Answer 15

Parameter variability is referred to as 𝜂 terms

Question 16

What is theta (θ) used to denote?

Answer 16

A population central tendency in population pharmacokinetics.
θ typically represents the fixed effects parameters, which are the average or typical values of pharmacokinetic parameters for the population being studied.
These parameters are assumed to be the same for every individual in the population unless modified by covariates (e.g., body weight, age, organ function).

Question 17

eta 𝜂 (eta)

Answer 17

individual deviation from the central tendancy.
𝜂 (eta) is commonly used to denote the random effects.
For instance, in a pharmacokinetic model, 𝜂 would represent how an individual’s drug clearance rate deviates from the population mean.

Question 18

Fixed effects vs random effects

Answer 18

Fixed effects are features common to the entire population (e.g. Cl, Vd, Ka)

Random effects is the population variability and measurement uncertainties: Between subject variability,
Inter- occasion variability and residual unexplained variability

Question 19

What is meant by balanced pharmacokinetic data?

Answer 19

Same number of samples per participant in the data

Question 20

What is meant by the term ‘fixed-effects’ in relation to a non-linear mixed-effects model? In your answer provide an example of a fixed-effect. (2 marks)

Answer 20

Fixed effects in an experiment or trial are controlled, or the same, for each individual. An example might be dose

Question 21

What is meant by the term ‘random-effects’ in relation to a non-linear mixed-effects model? In your answer, provide an example of a random-effect. (2 marks)

Answer 21

Random effects in an experiment or trial are un- or partially- controlled or they do not include all possible levels of a variable. Participants in a trial are an example

Question 22

Explain what is meant by the ‘structural model’ in relation to non-linear mixed-effects modeling.

Answer 22

The structural model is the underlying equation that describes the mean population trend. This is the compartmental model you have chosen to model the data with.

Question 23

Give an example of a structural model in relation to a pharmacokinetic model

Answer 23

e.g. one-compartment or two-compartment etc).

Question 24

Explain what is meant by the ’statistical model’ in relation to non-linear mixed-effects modeling.

Answer 24

The statistical model is how we have chosen to model the parameter- and residual- variability. Parameter variability is referred to as 𝜂 terms

Question 25

Give an example of a statistical model in relation to a pharmacokinetic model

Answer 25

Cl = \theta_{cl\ \ }X\ e^{\eta cl} Where: \eta\ ~\ (0,\ \omega_{cl}^2)

Question 26

Explain what is meant by the ‘covariate model’ in relation to non-linear mixed-effects modeling.

Answer 26

In non-linear mixed-effects modeling, a covariate model describes how covariates (e.g., body weight, age, genetic factors) affect the parameters of the main model to explain inter-individual variability. This involves incorporating covariates into the model parameters through specific mathematical functions, typically linear, to quantify their impact on outcomes like drug clearance or response. The primary goal of a covariate model is to reduce unexplained variability and improve the predictive accuracy of the model, tailoring predictions to individual characteristics.

Question 27

Give an example of a continuous covariate and a categorical covariate that might be included in a pharmacokinetic model (Covariate model)

Answer 27

In a pharmacokinetic model, an example of a continuous covariate is body weight, which can influence drug clearance and volume of distribution. An example of a categorical covariate is gender, which might affect how a drug is metabolized or distributed within the body.

Question 28

Best models for sparse data and why

Answer 28

non-linear mixed-effects approach compared to the naive-pooled approach (preferred of the other modelling approaches to sparse data).

The non-linear mixed-effects approach provides a superior fit to both absorption and elimination phases compared to the naive-pooled fit.

it is close to the ‘true’ population value. Additionally, with the non-linear mixed-effects approach, we retain information on the inter-individual variability of model parameters.

Question 29

Non-linear mixed-effects modelling in R

Answer 29

first part of the function is to set the initial estimates for your model parameters, this is known as the ini() block.

we need to tell nlmixr initial values for each of these parameters as well as values for the random-effects (𝜔2) associate with each parameter.

The second part of the function defines the model. The model() block. Here you describe the relationship between the fixed- and random-effects.