evalBRAIDrsm {braidrm}

Calculate BRAID Surface Values

Description

Calculates the value of the Bivariate Response to Additive Interacting Doses (BRAID) surface model for the given concentration pairs.

Usage

evalBRAIDrsm(DA, DB, parv)

Arguments

DA

vector of concentrations of drug A

DB

vector of concentrations of drug B

parv

ten-element vector specifying the full set of parameters for the BRAID surface (see Details below)

Details

The full ten-parameter BRAID model, which we refer to as the extended BRAID or eBRAID model is defined as:

E(D_A,D_B) = E_0 + \frac{E_f-E_0}{1+{{\tilde{D}}_{AB}}^{-\delta\sqrt{n_a n_b}}}

{\tilde{D}}_{AB} = {{\tilde{D}}_A}^\frac{1}{\delta\sqrt{n_a n_b}}+{{\tilde{D}}_B}^\frac{1}{\delta\sqrt{n_a n_b}} +\kappa\sqrt{{{\tilde{D}}_A}^\frac{1}{\delta\sqrt{n_a n_b}} {{\tilde{D}}_B}^\frac{1}{\delta\sqrt{n_a n_b}}}

{\tilde{D}}_A = \frac{\left(\frac{E_{f,A}-E_0}{E_f-E_0}\right)\left(\frac{D_A}{{ID}_{M,A}}\right)^{n_a}} {1+\left(1-\frac{E_{f,A}-E_0}{E_f-E_0}\right)\left(\frac{D_A}{{ID}_{M,A}}\right)^{n_a}}

{\tilde{D}}_B = \frac{\left(\frac{E_{f,B}-E_0}{E_f-E_0}\right)\left(\frac{D_B}{{ID}_{M,B}}\right)^{n_b}} {1+\left(1-\frac{E_{f,B}-E_0}{E_f-E_0}\right)\left(\frac{D_B}{{ID}_{M,B}}\right)^{n_b}}

The parameters of this equation must satisfy n_a>0, n_b>0, \delta>0, \kappa> -2, sign(E_f-E_0)=sign(E_{f,A}-E_0)=sign(E_{f,B}-E_0), |E_f-E_0|\geq|E_{f,A}-E_0|, and |E_f-E_0|\geq|E_{f,B}-E_0|. With this definition, the ten-element parameter vector is [{ID}_{M,A}, {ID}_{M,B}, n_a, n_b, \delta, \kappa, E_0, E_{f,A}, E_{f,B}, E_f]. The simpler standard BRAID model, as described in Twarog et al. is obtained by setting \delta equal to 1 and setting E_f such that |E_f-E_0| is equal to the maximum of |E_{f,A}-E_0| and |E_{f,B}-E_0|. Assuming that this sets E_f equal to E_{f,A}, this causes the equation for {\tilde{D}}_A to simplify to

{\tilde{D}}_A = \left(\frac{D_A}{{ID}_{M,A}}\right)^{n_a}

Value

A vector of response values corresponding to the pairs of concentrations in DA and DB

Author(s)

Nathaniel R. Twarog

See Also

braidrm, invertBRAIDrsm

Examples

conc1 <- rep(seq(0,3*10^-6,length=50),each=50)
conc2 <- rep(seq(0,3*10^-6,length=50),times=50)

# Additive surface
act <- evalBRAIDrsm(conc1,conc2,parv=c(10^-6,10^-6,1.5,1.5,1,0,0,100,100,100))
# A BRAID additive surface is not a Loewe additive surface
act <- evalBRAIDrsm(conc1,conc2,parv=c(10^-6,10^-6,1,3,1,0,0,100,100,100))
# BRAID antagonism
act <- evalBRAIDrsm(conc1,conc2,parv=c(10^-6,10^-6,1.5,1.5,1,-1,0,100,100,100))
# delta-BRAID synergy
act <- evalBRAIDrsm(conc1,conc2,parv=c(10^-6,10^-6,1.5,1.5,1.75,0,0,100,100,100))
# Differing final effects
act <- evalBRAIDrsm(conc1,conc2,parv=c(10^-6,10^-6,1.5,1.5,1,0,0,75,100,100))