Bioequivalence and Bioavailability Forum

Hi Sridhar.e,

❝ can any one explain difference between Linear and Non-linear pharmacokinetics.

In practice: If Cmax or AUC or Clearance scales linear with the ingested dose, then kinetics is linear. For example, if the Cmax is 50 ng/mL at a dose of 100 mg, and it is 100 ng/mL at a dose of 200 mg, then it would seem linear at least in that interval.
This mainly has bearings on the dose you might need to apply in your BE trial if you wish to apply for waivers of some strengths. The design used for a linear drug is not necessarily different from the design used for a non-linear drug.

If the drug displays a more-than-proportional trace of Cmax (or AUC or CL) versus dose, then a dose at the upper end may be more discriminative. And vice versa.

Don't get bogged down by the discussion of terminology; linearity vs proportionality. I believe it is not particularly difficult to find people who happily spend hours on it. Just let them.

Finding out if a drug is linear is sometimes tricky. Often such ADME behaviour can be looked up on SPC's or prescr. info but if you need to study the phenomenon yourself then this is a pretty troublesome affair.

Hi Sridhar,

❝ can any one explain difference between Linear and Non-linear pharmacokinetics.

Linear PK means that bioavailability is – strictly – proportional to the dose, e.g., if you double the dose, the AUC will double as well. The EMA accepts data from reliable sources (peer-reviewed journals, PARs, SmPCs). If the the ratio of dose-normalized AUCs is within 75–125%, fine.
If you have no data, perform a higher-order crossover study and fit the „power model”$$AUC=\alpha\cdot Dose^{\, \beta}\tag{1}$$Since \((1)\) requires software for nonlinear modelling, most people opt for the linearized alternative $$\log_{e}AUC=\log_{e}\alpha+ \beta \cdot \log_{e}Dose \tag{2}$$ and assess the confidence interval of \(\beta\). For some examples see the vignette of the package PowerTOST. Note that the acceptance range of the CI depends on the ratio of the highest/lowest dose. Hence, to demonstrate dose proportionality you will need a larger sample size for an increasing dose range.

Types of nonlinear PK

1. \(\beta <1\)
   Sooner or later any drug will show that. It might be that limited solubility chimes in. Another possibility is that a drug is an autoinducer at higher doses.
   
2. \(\beta >1\)
   This happens if metabolizing enzymes get saturated or a drug is an autoinhibitor.

That’s not the end of the story. Only in linear PK the superposition principle holds (steady state AUC_0–τ ≈ single dose AUC_0–∞). Esp. when you have substantial accumulation and suspect relevant metabolization, a multiple dose study is a must. If you have to deal with an autoinducer or -inhibitor it will take some time till the system is fully activated. See this presentation (slides 3–5).

❝ if drugs exist Non-linear pharmacokinetics which study design likely to choose.

To show what?

dear sridhar,

Some hopefully helpful thoughts on linear/non-linear PK are also given here Assessing goodness‐of‐fit for evaluation of dose‐proportionality which you may find of interest.

hope this helps

martin