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

Dear Ben,

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 zero

On the premise of linear pharmacokinetics:
1. PK metrics such as AUC, Cmax, Ctrough 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)
2. PK metrics tmax, t½, CLs, Vss, MRT and F are independent of dose
3. Concentrations after repeated dosing can be predicted from concentrations following a single dose (e.g. AUC0–τ at steady state = AUC0–∞ after a single dose)
For this reason,
1. Linear pharmacokinetic implies dose proportionality and not necessarily vice versa
2. Linear pharmacokinetic implies PK linearity after repeated administration (i.e. assessed if AUC0–τ at steady state equals AUC0–∞ 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.