# Estimating effective doses

### Description

`ED`

estimates effective doses (ECp/EDp/ICp) for given reponse levels.

### Usage

1 2 3 4 5 6 | ```
## S3 method for class 'drc'
ED(object, respLev, interval = c("none", "delta", "fls", "tfls"),
clevel = NULL, level = ifelse(!(interval == "none"), 0.95, NULL),
reference = c("control", "upper"), type = c("relative", "absolute"), lref, uref,
bound = TRUE, od = FALSE, vcov. = vcov, display = TRUE, pool = TRUE, logBase = NULL,
multcomp = FALSE, ...)
``` |

### Arguments

`object` |
an object of class 'drc'. |

`respLev` |
a numeric vector containing the response levels. |

`interval` |
character string specifying the type of confidence intervals to be supplied. The default is "none".
Use "delta" for asymptotics-based confidence intervals (using the delta method and the t-distribution).
Use "fls" for from logarithm scale based confidence intervals (in case the parameter in the model is log(ED50) as for
the |

`clevel` |
character string specifying the curve id in case on estimates for a specific curve or compound is requested. By default estimates are shown for all curves. |

`level` |
numeric. The level for the confidence intervals. The default is 0.95. |

`reference` |
character string. Is the upper limit or the control level the reference? |

`type` |
character string. Whether the specified response levels are absolute or relative (default). |

`lref` |
numeric value specifying the lower limit to serve as reference. |

`uref` |
numeric value specifying the upper limit to serve as reference (e.g., 100%). |

`bound` |
logical. If TRUE only ED values between 0 and 100% are allowed. FALSE is useful for hormesis models. |

`od` |
logical. If TRUE adjustment for over-dispersion is used. |

`vcov.` |
function providing the variance-covariance matrix. |

`display` |
logical. If TRUE results are displayed. Otherwise they are not (useful in simulations). |

`pool` |
logical. If TRUE curves are pooled. Otherwise they are not. This argument only works for models with independently fitted curves as specified in |

`logBase` |
numeric. The base of the logarithm in case logarithm transformed dose values are used. |

`multcomp` |
logical to switch on output for use with the package multcomp (which needs to be activated first). Default is FALSE (corresponding to the original output). |

`...` |
see the details section below. |

### Details

For hormesis models (`braincousens`

and `cedergreen`

), the additional
arguments `lower`

and `upper`

may be supplied. These arguments specify the lower and upper limits
of the bisection method used to find the ED values. The lower and upper limits need to be smaller/larger
than the EDx level to be calculated. The default limits are 0.001 and 1000 for `braincousens`

and
0.0001 and 10000 for `cedergreen`

and `ucedergreen`

, but this may need to be modified
(for `cedergreen`

the upper limit may need to be increased and for `ucedergreen`

the lower limit may need to be increased). Note that the lower limit should not be set to 0 (use instead
something like 1e-3, 1e-6, ...).

### Value

An invisible matrix containing the shown matrix with two or more columns, containing the estimates
and the corresponding estimated standard errors and possibly lower and upper confidence limits.
Or, alternatively, a list with elements that may be plugged directly into `parm`

in the package *multcomp* (in case the argument `multcomp`

is TRUE).

### Author(s)

Christian Ritz

### See Also

`backfit`

, `isobole`

, and `maED`

use `ED`

for specific calculations involving estimated ED values.

The related function `EDcomp`

may be used for estimating differences and ratios of ED values,
whereas `compParm`

may be used to compare other model parameters.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 | ```
## Fitting 4-parameter log-logistic model
ryegrass.m1 <- drm(ryegrass, fct = LL.4())
## Calculating EC/ED values
ED(ryegrass.m1, c(10, 50, 90))
## first column: the estimates of ED10, ED50 and ED90
## second column: the corresponding estimated standard errors
### How to use the argument 'ci'
## Also displaying 95% confidence intervals
ED(ryegrass.m1, c(10, 50, 90), interval = "delta")
## Comparing delta method and back-transformed
## confidence intervals for ED values
## Fitting 4-parameter log-logistic
## in different parameterisation (using LL2.4)
ryegrass.m2 <- drm(ryegrass, fct = LL2.4())
ED(ryegrass.m1, c(10, 50, 90), interval = "fls")
ED(ryegrass.m2, c(10, 50, 90), interval = "delta")
### How to use the argument 'bound'
## Fitting the Brain-Cousens model
lettuce.m1 <- drm(weight ~ conc,
data = lettuce, fct = BC.4())
### Calculating ED[-10]
# This does not work
#ED(lettuce.m1, -10)
## Now it does work
ED(lettuce.m1, -10, bound = FALSE) # works
ED(lettuce.m1, -20, bound = FALSE) # works
## The following does not work for another reason: ED[-30] does not exist
#ED(lettuce.m1, -30, bound = FALSE)
``` |