base_GIA {loewesadditivity}

Estimate GIA according to the base model

Description

Estimate GIA according to the base model

Usage

base_GIA(model_params, dose_A, dose_B, fn_list = NULL)

Arguments

model_params

named vector of parameters to be used in function. Specifically, the named parameters must be "beta_A", "beta_B", "gamma_A", "gamma_B", "tau_1", and "tau_2". See details for more info.

dose_A

numeric vector of doses (e.g. mg/mL) of dose_A

dose_B

numeric vector of doses (e.g. mg/mL) of dose_B

fn_list

NULL

Value

estimated GIA for each combination of dose A and dose B

Details

The equation is given in full as follows. The GIA (%) is given a as a function of the model parameters and the doses A_i and B_i, respectively. The doses scaled by the respective ED50s \beta_A and \beta_B are denoted by A_i^* and B_i^*, respectively. The parameters \gamma_A and \gamma_B are shape parameters. The parameters \tau_1 and \tau_2 are interaction parameters. Finally, \lambda_i is a weighted combination of dose A and dose B.

GIA_i = 100\%(1 - e^{-\psi_i})

\psi_i = \log(2)u_i^{v_i}

u_i = A^*_i + B_i^* + \tau_1 A^*_i B^*_i

v_i = \lambda_i \gamma_A + (1-\lambda_i) \gamma_B + \tau_1 \tau_2\lambda_i (1 - \lambda_i) \gamma_A \gamma_B

\lambda_i = \frac{A_i^*}{A_i^* + B_i^*}

A_i^* = A_i / \beta_A

B_i^* = B_i / \beta_B

Examples

model_params <- c("beta_A" = 1, "beta_B" = 2, "gamma_A" = .5,
"gamma_B" = .6,  "tau_1" = 1, "tau_2" = 0)
dose_A <- c(0, 1, 0)
dose_B <- c(0, 0, 1)
base_GIA(model_params, dose_A, dose_B)