betaMod function

Beta model

The beta model is defined as [REMOVE_ME]$f(d,\theta)=E_0+E_{max}B(\delta_1,\delta_2)(d/scal)^{\delta_1}(1-d/scal)^{\delta_2}f(d,theta)=E0+Emax B(delta1,delta2)(d/scal)^delta1(1-d/scal)^delta2 [REMOVE_ME_2]$

where [REMOVE_ME]$B(\delta_1,\delta_2)=(\delta_1+\delta_2)^{\delta_1+\delta_2}/(\delta_1^{\delta_1} \delta_2^{\delta_2})B(delta1,delta2)=(delta1+delta2)^(delta1+delta2)/(delta1^delta1 delta2^delta2). [REMOVE_ME_2]$

Description

The beta model is defined as

where

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)

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.

Returns

Response value

See Also

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