# Comparison of effective dose values

### Description

Comparison of a pair of effective dose values from independent experiments where only the estimates and their standard errors are reported.

### Usage

1 2 |

### Arguments

`est` |
a numeric vector of length 2 containing the two estimated ED values |

`se` |
a numeric vector of length 2 containing the two standard errors |

`log` |
logical indicating whether or not estimates and standard errors are on log scale |

`interval` |
logical indicating whether or not a confidence interval should be returned |

`operator` |
character string taking one of the two values "-" (default) or "/" corresponding to a comparison based on the difference or the ratio. |

`level` |
numeric value giving the confidence level |

`df` |
numeric value specifying the degrees of freedom for the percentile used in the confidence interval (optional) |

### Details

The choice "/" for the argument `operator`

and FALSE for `log`

will result in estimation of a socalled
relative potency (sometimes also called a selectivity index).

The combination TRUE for `log`

and "/" for `operator`

only influences the confidence interval,
that is no ratio is calculated based on logarithm-transformed effective dose values.

By default confidence interval relies on percentiles in the normal distribution.

In case the entire dataset is available the functions `drm`

and (subsequently) `EDcomp`

should be used instead.

### Value

A matrix with the estimated difference or ratio and the associated standard error and the resulting confidence interval (unless not requested).

### Note

The development of the function `comped`

is a side effect of the project on statistical analysis of
toxicity data funded by the Danish EPA ("Statistisk analyse og biologisk tolkning af toksicitetsdata",
MST j.nr. 669-00079).

### Author(s)

Christian Ritz

### References

Wheeler, M. W. and Park, R. M. and Bailer, A. J. (2006)
Comparing median lethal concentration values using confidence interval overlap or ratio tests,
*Environmental Toxicology and Chemistry*, **25**, 1441–1441.

### See Also

The function `ED.drc`

calculates arbitrary effective dose values based on a model fit. The function
`EDcomp`

calculates relative potencies based on arbitrary effective dose values.

### 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 | ```
## Fitting the model
S.alba.m1 <- boxcox(drm(DryMatter~Dose, Herbicide, data=S.alba, fct = LL.4(),
pmodels=data.frame(Herbicide,1,1,Herbicide)), method = "anova")
## Displaying estimated ED values
ED(S.alba.m1, c(10, 90))
## Making comparisons of ED50 in two ways and for both differences and ratios
compParm(S.alba.m1, "e", "/")
comped(c(28.396147, 65.573335), c(1.874598, 5.618945), log=FALSE, operator = "/")
# similar result
compParm(S.alba.m1, "e", "-")
comped(c(28.396147, 65.573335), c(1.874598, 5.618945), log=FALSE, operator = "-")
# similar result
## Making comparisons of ED10 and ED90
comped(c(21.173, 44.718), c(11.87, 8.42), log=FALSE, operator = "/")
comped(c(21.173, 44.718), c(11.87, 8.42), log=FALSE, operator = "/", interval = FALSE)
comped(c(21.173, 44.718), c(11.87, 8.42), log=FALSE, operator = "-")
``` |

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