Estimating equation for E-max dose-response model

Implements the hyperbolic E-max (Hill) model: $$R_i = \theta_0 + \frac{\theta_{max} D_i}{\theta_{50} + D_i}$$

Usage

ee_emax(theta, dose, response, loss = NULL, k = NULL)

Arguments

theta

Numeric vector of length 3: zero-dose response (e0), maximum change in response (emax), ED50. emax is the change the response approaches as the dose grows without bound, not the response itself, so the asymptote is e0 + emax.

dose

Numeric vector of n dose values.

response

Numeric vector of n response values.

loss

Optional character string for robust loss function. Default NULL (no robust loss). See robust_loss_functions().

k

Optional numeric tuning parameter for robust loss.

Value

A 3-by-n matrix, with rows named e0, emax, and ed50.

See also

ee_emax_ed() for the effective dose at a given level, which is stacked with this equation to give it a sandwich standard error.

Examples

# Dose-response of a herbicide on ryegrass root length. The response falls
# with dose, so the maximum change in response is initialized negative.
psi <- function(theta) {
  ee_emax(theta, dose = inderjit$dose, response = inderjit$response)
}

m <- m_estimate(stacked_equations = psi, init = c(8, -8, 2))

# Zero-dose response, maximum change in response, and ED50
coef(m)
#>        e0      emax      ed50 
#>  8.215129 -9.820041  4.574524