DoseFinding (version 0.1-3)

betaMod: Beta model

Description

The beta model is defined as $$f(d,\theta)=E_0+E_{max}B(\delta_1,\delta_2)(d/scal)^{\delta_1}(1-d/scal)^{\delta_2}$$ where $$B(\delta_1,\delta_2)=(\delta_1+\delta_2)^{\delta_1+\delta_2}/(\delta_1^{\delta_1} \delta_2^{\delta_2})$$

Usage

betaMod(dose, e0, eMax, delta1, delta2, scal)

Arguments

dose

Dose variable

e0

Placebo effect

eMax

Maximum effect

delta1

delta1 parameter

delta2

delta2 parameter

scal

Scale parameter (not estimated in the code)

Value

• Response value

Details

The beta model is intended to capture non-monotone dose-response relationships and is more flexible than the quadratic model. The kernel of the beta model function consists of the kernel of the density function of a beta distribution on the interval [0,scal]. The parameter scal is not estimated but needs to be set to a value larger than the maximum dose via the argument scal.

See Also

logistic, sigEmax, linlog, linear, quadratic, emax, exponential

Examples

## some example shapes
betaModList <- list(betaMod = rbind(c(1,1), c(1.5,0.75), c(0.8,2.5), c(0.4,0.9)))
plotModels(betaModList, c(0,1), base = 0, maxEff = 1, scal = 1.2)