DoseFinding (version 0.1-3)

emax: Emax model

Description

The model function for the Emax model is defined as $$f(d,\theta)=E_0+E_{max}\frac{d}{ED_{50}+d}$$

Usage

emax(dose, e0, eMax, ed50)

Arguments

dose

Dose variable

e0

Placebo effect

eMax

Asymptotic maximum change from placebo effect

ed50

Dose giving half of the asymptotic maximum effect

Value

• Response value

Details

The emax model is used to represent monotone, concave dose-response shapes. To distinguish it from the more general sigmoid emax model it is sometimes also called hyperbolic emax model.

References

MacDougall, J. (2006). Analysis of dose-response studies - Emax model,in N. Ting (ed.), Dose Finding in Drug Development, Springer, New York, pp. 127--145 Pinheiro, J. C., Bretz, F. and Branson, M. (2006). Analysis of dose-response studies - modeling approaches, in N. Ting (ed.). Dose Finding in Drug Development, Springer, New York, pp. 146--171

See Also

sigEmax, logistic, betaMod, linlog, linear, quadratic, exponential

Examples

## some emax example shapes
emaxModList <- list(emax = c(0.02,0.1,0.5,1))
plotModels(emaxModList, c(0,1), base = 0, maxEff = 1)