R: Log-normal dose-response model

lnormal {drc} | R Documentation

## Log-normal dose-response model

### Description

`lnormal` and the accompanying convenience functions provide a general framework for specifying the mean function of the decreasing or incresing log-normal dose-response model.

### Usage

      lnormal(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"),
      method = c("1", "2", "3", "4"), ssfct = NULL,
      fctName, fctText, loge = FALSE)

      LN.2(upper = 1, fixed = c(NA, NA), names = c("b", "e"), ...)

      LN.3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...)

      LN.3u(upper = 1, fixed = c(NA, NA, NA), names = c("b", "c", "e"), ...)

      LN.4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)

### Arguments

`fixed` | numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed.
`names` | vector of character strings giving the names of the parameters (should not contain ":"). The default is reasonable (see under 'Usage'). The order of the parameters is: b, c, d, e, f (see under 'Details' for the precise meaning of each parameter).
`method` | character string indicating the self starter function to use.
`ssfct` | a self starter function to be used.
`fctName` | character string used internally by convenience functions (optional).
`fctText` | character string used internally by convenience functions (optional).
`loge` | logical indicating whether or not ED50 or log(ED50) should be a parameter in the model. By default ED50 is a model parameter.
`upper` | numeric specifying the upper horizontal asymptote in the convenience function. The default is 1.
`...` | additional arguments to be passed from the convenience functions to `lnormal`.

### Details

For the case where log(ED50), denoted e in the equation below, is a parameter in the model, the mean function is:

f(x) = c + (d-c)(Φ(b(\log(x)-e)))

and the mean function is:

f(x) = c + (d-c)(Φ(b(\log(x)-\log(e))))

in case ED50, which is also denoted e, is a parameter in the model. If the former model is fitted any estimated ED values will need to be back-transformed subsequently in order to obtain effective doses on the original scale.

The mean functions above yield the same models as those described by Bruce and Versteeg (1992), but in a different parameterisations (among other things the natural logarithm is used).

For the case c=0 and d=1, the log-normal model reduces the classic probit model (Finney, 1971) with log dose as explanatory variable (mostly used for quantal data). This special case is available through the convenience function `LN.2`.

The case c=0 is available as the function `LN.3`, whereas the `LN.3u` corresponds to the special case where the upper horizontal asymptote is fixed (default is 1). The full four-parameter model is available through `LN.4`.

### Value

The value returned is a list containing the non-linear function, the self starter function and the parameter names.

### Note

The function is for use with the function `drm`, but typically the convenience functions `link{LN.2}`, `link{LN.3}`, `link{LN.3u}`, and `link{LN.4}` should be used.

### Author(s)

Christian Ritz

### References

Finney, D. J. (1971) Probit analysis, London: Cambridge University Press.

Bruce, R. D. and Versteeg, D. J. (1992) A statistical procedure for modeling continuous toxicity data, Environ. Toxicol. Chem., 11, 1485–1494.

### See Also

The log-logistic model (`llogistic`) is very similar to the log-normal model at least in the middle, but they may differ in the tails and thus provide different estimates of low effect concentrations EC/ED.

Examples are provided in the help pages of the datasets `S.capricornutum`, `P.promelas`, and `M.bahia`.

[Package drc version 3.0-1 Index]