`ED`

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

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, ...)
``` |

`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. |

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, ...).

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).

Christian Ritz

`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.

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)
``` |

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