# DualEndpointBeta-class: Dual endpoint model with beta function for dose-biomarker... In crmPack: Object-Oriented Implementation of CRM Designs

## Description

This class extends the `DualEndpoint` class. Here the dose-biomarker relationship f(x) is modelled by a parametric, rescaled beta density function:

## Details

f(x) = E_{0} + (E_{max} - E_{0}) * Beta(δ_{1}, δ_{2}) * (x/x^{*})^{δ_{1}} * (1 - x/x^{*})^{δ_{2}}

where x^{*} is the maximum dose (end of the dose range to be considered), δ_{1} and δ_{2} are the two beta parameters, and E_{0} and E_{max} are the minimum and maximum levels, respectively. For ease of interpretation, we parametrize with δ_{1} and the mode of the curve instead, where

mode = δ_{1} / (δ_{1} + δ_{2}),

and multiplying this with x^{*} gives the mode on the dose grid.

All parameters can currently be assigned uniform distributions or be fixed in advance. Note that `E0` and `Emax` can have negative values or uniform distributions reaching into negative range, while `delta1` and `mode` must be positive or have uniform distributions in the positive range.

## Slots

`E0`

either a fixed number or the two uniform distribution parameters

`Emax`

either a fixed number or the two uniform distribution parameters

`delta1`

either a fixed number or the two uniform distribution parameters

`mode`

either a fixed number or the two uniform distribution parameters

`refDoseBeta`

the reference dose x^{*} (note that this is different from the `refDose` in the inherited `DualEndpoint` model)

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```model <- DualEndpointBeta(E0 = c(0, 100), Emax = c(0, 500), delta1 = c(0, 5), mode = c(1, 15), refDose=10, useLogDose=TRUE, refDoseBeta = 1000, mu = c(0, 1), Sigma = matrix(c(1, 0, 0, 1), nrow=2), sigma2W = c(a=0.1, b=0.1), rho = c(a=1, b=1)) ```

crmPack documentation built on June 13, 2019, 9:02 a.m.