## Dose-proportionality versus dose-linearity [PK / PD]

Dear Ben,

Its a good idea looking at the definitions first and here is my understanding

On the premise of linear pharmacokinetics:

Taking the above points into consideration I think that linear PK does not imply dose-linearity.

Best regards

Martin

PS.: regarding an example for situation 2: you may think of a drug which is given far in excess of a receptor

PPS.: My understanding is that nearly all drugs are expected to exhibit nonlinear PK behavior when administered at "extremely" high doses (e.g. leading to saturable absorption or saturable metabolism which is studied in the field of toxicokinetics) which motivates formally assessing dose-proportionality only for the clinical relevant dose range.

Its a good idea looking at the definitions first and here is my understanding

*Linear pharmacokinetics:*All transport processes follow a first order kinetic (e.g. absorption, distribution and/or elimination) where*first order kinetic*means that the concentration is changed at a rate proportional to the concentration (in contrast to*non-linear kinetic*which means that one or more transport process(es) follow other than first order kinetic). Please note that this implies that an IV administration given as infusion modeled as zero-order absorption is per definition non-linear PK but typically regarded as a non-relevant deviation from linear PK in case that processes after end of infusion follow a first order kinetic and AUC during infusion time is small compared to the total AUC.*Dose-proportionality:*the relation between dose and exposure (e.g. AUC) is given as straight line passing through zero on the ordinate*Dose-linearity:*the relation between dose and exposure (e.g. AUC) is given as straight line starting on the ordinate at any value greater or smaller than zeroOn the premise of linear pharmacokinetics:

- PK metrics such as AUC, C
_{max}, C_{trough}increase proportional with dose (to be more general: on the premise of linear PK doubling of dose leads to doubling of any individual concentration at a given time point)

- PK metrics t
_{max}, t_{½}, CLs, Vss, MRT and F are independent of dose

- Concentrations after repeated dosing can be predicted from concentrations following a single dose (e.g. AUC
_{0–τ}at steady state = AUC_{0–∞}after a single dose)

- Linear pharmacokinetic implies dose proportionality and not necessarily vice versa

- Linear pharmacokinetic implies PK linearity after repeated administration (i.e. assessed if AUC
_{0–τ}at steady state equals AUC_{0–∞}after a single dose) and not necessarily vice versa

Taking the above points into consideration I think that linear PK does not imply dose-linearity.

Best regards

Martin

PS.: regarding an example for situation 2: you may think of a drug which is given far in excess of a receptor

PPS.: My understanding is that nearly all drugs are expected to exhibit nonlinear PK behavior when administered at "extremely" high doses (e.g. leading to saturable absorption or saturable metabolism which is studied in the field of toxicokinetics) which motivates formally assessing dose-proportionality only for the clinical relevant dose range.

### Complete thread:

- Dose-proportionality versus dose-linearity martin 2018-08-03 10:25 [PK / PD]
- Dose-proportionality versus dose-linearity ElMaestro 2018-08-03 11:21
- Dose-proportionality versus dose-linearity Ben 2018-08-06 19:39
- Dose-proportionality versus dose-linearitymartin 2018-08-07 13:04

- Dose-proportionality versus dose-linearity Ben 2018-08-06 19:39

- Dose-proportionality versus dose-linearity ElMaestro 2018-08-03 11:21