Maximum mean response

Estimates the maximum mean response and the dose at which it occurs, using a bisection method to locate the peak of the fitted dose-response curve. This function is only implemented for the built-in model functions of class braincousens and cedergreen, which are capable of exhibiting hormesis (i.e., a non-monotone response with a stimulatory effect at low doses).

Usage

MAX(object, lower = 0.001, upper = 1000, pool = TRUE)

Arguments

object

an object of class drc, fitted using drm with a hormesis model such as CRS.4c or BC.4.

lower

numeric. Lower bound of the interval used by the bisection method to search for the dose at maximum response. Must be strictly smaller than upper and should be set below the expected dose at maximum response. Defaults to 1e-3.

upper

numeric. Upper bound of the interval used by the bisection method to search for the dose at maximum response. Must be strictly larger than lower and should be set above the expected dose at maximum response. Defaults to 1000.

pool

logical. If TRUE (default), curves are pooled when computing the variance-covariance matrix. Otherwise they are not. This argument only works for models with independently fitted curves as specified in drm. Note: currently the variance-covariance matrix is retrieved for internal consistency but standard errors are not yet reported in the output.

Value

Invisibly returns a numeric matrix with one row per curve in the data set and two columns:

Dose

The dose at which the maximum mean response occurs, found via bisection within [lower, upper].

Response

The estimated maximum mean response at that dose.

Row names correspond to curve identifiers. If the computation fails for a given curve, the corresponding row will contain NA values and a warning is issued. The matrix is also printed to the console via printCoefmat.

Details

The function numerically locates the dose \(d^*\) that maximises the fitted dose-response curve over the search interval [lower, upper]: $$d^* = \arg\max_{d} f(d, \hat{\theta})$$ where \(f\) is the fitted dose-response function and \(\hat{\theta}\) is the vector of estimated parameters. The search is performed using a bisection approach defined internally by the model's maxfct component.

It is the user's responsibility to ensure that the true maximum lies within [lower, upper]. If the maximum falls outside this interval, the function will silently return a boundary value and a warning is issued.

References

Cedergreen, N., Ritz, C., and Streibig, J. C. (2005) Improved empirical models describing hormesis, Environmental Toxicology and Chemistry 24, 3166–3172.

Author

Christian Ritz. Issues fixed and documentation enhanced by Hannes Reinwald.

Examples

## Fitting a Cedergreen-Ritz-Streibig model
lettuce.m1 <- drm(weight ~ conc, data = lettuce, fct = CRS.4c())

## Finding the maximum mean response and the corresponding dose
MAX(lettuce.m1)
#>     Dose Response
#> 1 0.2546   1.1787

## Custom search interval
MAX(lettuce.m1, lower = 1e-5, upper = 500)
#>      Dose Response
#> 1 0.25461   1.1787

## Capture the result matrix
result <- MAX(lettuce.m1)
#>     Dose Response
#> 1 0.2546   1.1787
result["Dose"]
#> [1] NA