## 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,

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

Types of nonlinear PK

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

To show

» 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

- \(\beta <1\)

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.

- \(\beta >1\)

This happens if metabolizing enzymes get saturated or a drug is an autoinhibitor.

*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*?—

Helmut Schütz

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*Dif-tor heh smusma*🖖Helmut Schütz

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### Complete thread:

- Linear and Non-linear pharmacokinetics Sridhar.E 2020-10-08 12:23 [PK / PD]
- Linear and Non-linear pharmacokinetics ElMaestro 2020-10-08 13:13
- Linear and Non-linear pharmacokinetics Sridhar.E 2020-10-08 13:23

- Linear and Non-linear pharmacokineticsHelmut 2020-10-08 13:44
- Linear and Non-linear pharmacokinetics martin 2020-10-16 08:34
- OT: The Wild Bunch Helmut 2020-10-16 15:38

- Linear and Non-linear pharmacokinetics ElMaestro 2020-10-08 13:13