MDC Connects: Principles and Modelling of PK and PD Relationships
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This document discusses principles of pharmacokinetic (PK) and pharmacodynamic (PD) modeling. It notes that while all models are imperfect, some can still be useful. Simple models require fewer assumptions but more data, while complex models replace assumptions with data. The aim is the simplest useful model. Example models show how PK data can predict exposure from different doses and how PK-PD models integrate exposure over time with drug effects. Direct PK-PD models have effects directly linked to concentrations, while indirect models have time delays between exposure and response. Indirect models may allow less frequent dosing. The document stresses designing PK-PD studies based on all available knowledge to test hypotheses and obtain informative data on concentration-effect and time relationships
MDC Connects: Principles and Modelling of PK and PD Relationships
- 1. Principles and Modelling of Pharmacokinetic and Pharmacodynamic Relationships Graham Trevitt (CSO, XenoGesis)
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- 3. • “All models are wrong, but some are useful” • George Box (statistician) • “Perfect is the enemy of the good” • Voltaire • Models are based on data and assumptions - if either are wrong then the model will likely fail to be useful • A simple model often has more assumption but needs less data • Replacing assumptions with data can often be challenging/$$$ • A general aim is to have the simplest useful model with minimal data/cost • “Useful” can change with time • A model that is useful in the discovery phase may be inadequate for clinical development 3
- 4. Example of a useful model • Useful models describe what we already know to allow us to predict what we don’t • e.g. I know the plasma exposure from a single 10mg/kg dose, what do I expect trough concentrations to be from a 30mg/kg dose twice a day (BID)? • We can use models to generate hypotheses that challenge the model • 30mg/kg BID is predicted to give unbound exposure in excess of my in vitro EC90 – let’s see if that translates to efficacy in our pharmacology model 4 10mg/kg Data Model Simulation Predicted concentration >EC90 from Day 3 @ 30mg/kg
- 5. Conc EffectPercent TIME Conc Pharmacokinetics, Pharmacodynamics and PK-PD Pharmacodynamics (PD) • What the drug does to the body • Effect versus concentration 5 Pharmacokinetics (PK) • What the body does to the drug • Concentration versus time PK-PD • Effect versus time • Integrated relationship between plasma exposure versus time (PK) and effect versus concentration (PD) for a given dose and route of administration If PK-PD is well understood, then changing the PK side of the model allows us to predict response (e.g. repeat dose or from mouse to human) TIMEEffectPercent
- 6. Basic PK model – Single compartment IV • Amount of drug (A1) dosed into a single compartment of volume V • Clearance (volume of compartment from which drug is removed per unit time) = Cl • Rate of elimination = Cl/V • Units of 1/time • Rate of change of amount of drug = amount of drug * Cl/V • Differential equation • d(A1)/dt = -Cl/V*A1 • Concentration of drug, C = Amount of drug/V 6
- 7. Modelling observed data • 2 parameters describe the model: Cl and V • If we have observed data at a range of time-points (CObs, red circles) for a given initial dose (A1) we can fit the data to estimate Cl and V • What values best fit the observed data? 7
- 8. What if the data doesn’t fit? • New data set isn’t a good fit to a single compartment model • A more complex model is needed • Adding an additional compartment with volume V2 and clearance between this compartment and the central compartment (Cl2) allows us to capture the observed data 8
- 9. Adding an oral compartment • Drug now starts in dose compartment (amount Aa) and is absorbed at a rate Ka into the central compartment • The rest of the model is a two compartment model we used previously 9
- 10. Adding a PD Effect • We can now add parameters that combine observed effect (EObs) to plasma (C) • Example shown relates effect (E) to plasma concentration (C) using an Emax model • E=Emax*C/(C+EC50) • This is an example of a direct PK-PD relationship 10
- 11. TIME Conc Direct Direct PK-PD models • Simplest PK-PD scenario • At all time-points, concentration in plasma is directly related to effect • Diagnostic observations: • Maximum effect at maximum concentration (occurs at Tmax) • A plot of effect versus concentration can be described by (for example) Emax and EC50 • E=Conc*Emax/(Conc+EC50) • Classical, sigmoidal response curve on semi-log plot • In the example shown, EC50 = 10nM and maximum effect is at Tmax (1h) 11 Effect and concentration versus time Effect versus concentration
- 12. Indirect PK-PD • Time delay in response due to signalling pathways, cell- cycle, protein re-synthesis etc. results in delay in effect relative to concentration • Example shown is same PK/dose as previous slide, but PK-PD is indirect • Diagnostic observations • Maximum effect occurs later than plasma Cmax (9h v 1h in the example shown) • Effect versus concentration shows “hysteresis” - same effect at two different concentrations (e.g. 50% at 79nM and 0.7nM) • Time delay can be described empirically (e.g. through an effect compartment) but can be more mechanistic • e.g. tumour growth as a function of biomarker/pathway inhibition • More complex models = more data 12 Effect and concentration versus time Effect versus concentration TIME Conc Indirect Conc Indirect
- 13. Impact of indirect v direct PK-PD • When PK-PD is indirect, the duration of effect may be significantly greater than the duration of exposure • Less frequent dosing may be needed than for direct PK-PD • Plots show same underlying PK and EC50 • Direct PK-PD needs BID dosing for >70% effect • Indirect PK-PD achieves >80% from QD dose 13 Direct PK-PD: BID Dose schedule Indirect PD-PD: QD dose schedule Modelling the single dose PK-PD would allow for the optimal design of the repeat dose study
- 14. Interpretation and design of PK-PD studies • PK-PD experiments should be designed • Integrate all available knowledge (PK, in vitro pharmacology and biology) and design studies to test a hypothesis • Select dose levels and sample times to investigate concentration-effect and time dependence • Avoid simple dose-effect interpretation • Exposure drives efficacy, dose is simply a means to achieve exposure • Efficacy where the only dose was 100mg/kg doesn’t tell us much other than 100mg/kg does something… • Obtain exposure-time and effect-time data where possible 14 Integrate modelling and simulation into PK-PD design to maximise value of studies
- 15. Summary • Models integrate knowledge of a drug and can help support decision making throughout the drug discovery process • A model doesn’t have to perfect to be useful (but it does need to be useful) • Refine models as the project progresses to make them more useful – replace assumptions with data • PK models should be combined with biological knowledge/hypotheses to design PK-PD studies for maximal value • A sound understanding of PK-PD (including the limitations of the PD model itself) is fundamental to the prediction of human dose • Want to know more? Look out for the DMDG PK-PD modelling course (info@dmdg.org) 15
- 16. Questions? Contact info@xenogesis.com for support 16