Introduction in PK analysis

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PK/PD and PB/PK

• Pharmacokinetics (PK): study of the kinetics (movement) of a substance through an organism
• Pharmacodynamics (PD): study of the effects of a substance on the body
• PK/PD: study the relations between PK and PD (e.g. concentration-effect relation)
• Physiology-based PK (PB/PK): start with a mathmetical model a priori to describe the processes of or within an orgasnism based on mechanistic insights from in vitro and ex vivo experiments

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ADME kinetics

ADME refers to the processes of Absoprtion, Distribution, Metabolism and Excretion. These processes occur at certain rates. Think of a drug moving from one area to another, like the gut to the plasma or transforms at a certain rate from the parent compund into metabolites. The primary focus of Pharmacokinetic (PK) analysis is studying these rates and 'movements' (kinetics).



k : rate constants (kinetic) --> movement from 'x' to 'y'

• Ka: absorption constant
• Vc: distribution compartment (central)
• Q: rate constant between Vc and Vp
• Vp: distribution compartment (periph.)
• CL: elimination constant (clearance)

Described by differential equations of change in compartment (A) over time (T): dA/dT

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Methods of PK analyses

Many methods are available for PK analyses. Common traditional methods are for example:

Naive pooled data analysis (NPD) [rich and scarce data]
- Combines all data as if it concerns a single patient

Standard two-stage approach (STS) [rich data]
- Step 1: Calculate PK parameters of each individual
- Step 2: Combine results (e.g. average of all individuals)

Iterative two-stage approach (IT2S) [rich data]
- Step 1 and 2 same as STS
- Iterative: repeat step 1 with results of step 2 until no further improvement occurs


Data pooling:
Combine data of multiple subjects to create a 'population' curve.
As subjects (e.g. 2 and 6 in the figure below) lack data for an individual curve.


However, the main issue is retaining information concerning the individual with pooled data including subjects with sparse data. Currently a popular method is non-linear mixed effects modelling approach. With this method sparse and dense sampling can be used while being able to provide information concerning individual subjects through the use of stochastic models.


Non-linear mixed effects approach [NLME] [rich and scarce data]
- Designed to fit non linear statistical regression-type models
- Simultanious determine fixed and random effects in a population

Mixed effects refer to the mix of fixed and random effects:
- Fixed effects: input data (dosis, concentration, patient characteristics etc.)
- Fixed effect parameters: population parameters of fixed effects (e.g pop CL)
- Random effects: variability within the popPK parameters (IIV/BSV, IOV, res variability)

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Structural model

A mathematical model which best describes the data
- Describe the relations between dose, concentration and time
- Compare the fit of different mathematical models on the data
- Minimize the discrepancy between observations and model predictions (without overfitting)
- A priori information (known relations, initial estimates)







What kind of 'shape' does the data show? What kind of data do we have?
- Absorption phase?
- 1-compartment?
- 2-compartments?
- Linear?
- Saturation?
- Metabolites?
- Protein binding?

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Stochastic model

Describe, explain, and predict the variability in observations (random effects)

1. Interindividual variability (IIV)
2. Interoccasion variability (IOV)
3. Residual variability

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