## Linear and Non-linear pharmacokinetics [PK / PD]

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 AUC0–τ ≈ single dose AUC0–∞). 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?

Dif-tor heh smusma 🖖
Helmut Schütz

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