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Estimation of ED values using model-averaging

Source: R/maED.R
maED.Rd

Estimates and confidence intervals for ED values are estimated using model-averaging.

Usage

maED(
  object,
  fctList = NULL,
  respLev = c(10, 20, 50),
  interval = c("none", "buckland", "kang"),
  linreg = FALSE,
  clevel = NULL,
  level = 0.95,
  type = c("relative", "absolute"),
  display = TRUE,
  na.rm = FALSE,
  extended = FALSE
)

Arguments

object

an object of class drc.

fctList

a list of non-linear functions to be compared.

respLev

a numeric vector containing the response levels.

interval

character string specifying the type of confidence intervals to be supplied. The default is "none". The choices "buckland" and "kang" are explained in the Details section.

linreg

logical indicating whether or not additionally a simple linear regression model should be fitted.

clevel

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

level

numeric. The confidence level. Must be a single value strictly between 0 and 1. The default is 0.95.

type

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

display

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

na.rm

logical indicating whether or not NA values occurring during model fitting should be excluded from subsequent calculations.

extended

logical specifying whether or not an extended output (including fit summaries) should be returned.

Value

If extended = FALSE, a matrix with two or more columns containing the model-averaged estimates and the corresponding estimated standard errors and, optionally, lower and upper confidence limits. If extended = TRUE, a list with components:

estimates

Matrix of model-averaged ED estimates and intervals.

fits

Matrix of per-model ED estimates and AIC-based weights.

Details

Model-averaging of individual estimates is carried out as described by Buckland et al. (1997) and Kang et al. (2000) using AIC-based weights. The two approaches differ w.r.t. the calculation of confidence intervals: Buckland et al. (1997) provide an approximate variance formula under the assumption of perfectly correlated estimates (so, confidence intervals will tend to be too wide). Kang et al. (2000) use the model weights to calculate confidence limits as weighted means of the confidence limits for the individual fits.

References

Buckland, S. T. and Burnham, K. P. and Augustin, N. H. (1997) Model Selection: An Integral Part of Inference, Biometrics 53, 603–618.

Kang, Seung-Ho and Kodell, Ralph L. and Chen, James J. (2000) Incorporating Model Uncertainties along with Data Uncertainties in Microbial Risk Assessment, Regulatory Toxicology and Pharmacology 32, 68–72.

See also

The function mselect provides a summary of fit statistics for several models fitted to the same data.

Author

Christian Ritz, Hannes Reinwald

Examples

## Fitting an example dose-response model
ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = LL.4())

## Model-averaging with default settings (no confidence intervals)
maED(
  ryegrass.m1,
  list(LL.5(), LN.4(), W1.4(), W2.4(), FPL.4(-1, 1), FPL.4(-2, 3), FPL.4(-0.5, 0.5)),
  c(10, 50, 90)
)
#>                     ED10     ED50     ED90     Weight
#> LL.4            1.463706 3.057955 6.388640 0.14047308
#> LL.5            1.560325 3.023549 7.729713 0.06816147
#> LN.4            1.489188 3.044673 6.224889 0.12248817
#> W1.4            1.405979 3.088964 5.101022 0.03782468
#> W2.4            1.628278 2.996913 7.805803 0.17886712
#> FPL.4(-1,1)     1.540346 3.038790 7.086271 0.18043370
#> FPL.4(-2,3)     1.507055 3.063612 5.836831 0.08869758
#> FPL.4(-0.5,0.5) 1.531613 3.047967 7.204860 0.18305421
#> 
#>      Estimate
#> e:10 1.530770
#> e:50 3.039453
#> e:90 6.891117

## Model-averaging with Buckland confidence intervals
maED(
  ryegrass.m1,
  list(LL.5(), LN.4(), W1.4(), W2.4()),
  c(10, 50, 90),
  interval = "buckland"
)
#>          ED10     ED50     ED90     Weight
#> LL.4 1.463706 3.057955 6.388640 0.25642453
#> LL.5 1.560325 3.023549 7.729713 0.12442435
#> LN.4 1.489188 3.044673 6.224889 0.22359424
#> W1.4 1.405979 3.088964 5.101022 0.06904651
#> W2.4 1.628278 2.996913 7.805803 0.32651037
#> 
#>      Estimate Std. Error    Lower    Upper
#> e:10 1.531174  0.1977800 1.143532 1.918816
#> e:50 3.032914  0.1945023 2.651697 3.414132
#> e:90 6.892701  1.5391238 3.876074 9.909329

## Model-averaging with Kang confidence intervals
maED(
  ryegrass.m1,
  list(LL.5(), LN.4(), W1.4(), W2.4()),
  c(10, 50, 90),
  interval = "kang"
)
#>          ED10     ED50     ED90     Weight
#> LL.4 1.463706 3.057955 6.388640 0.25642453
#> LL.5 1.560325 3.023549 7.729713 0.12442435
#> LN.4 1.489188 3.044673 6.224889 0.22359424
#> W1.4 1.405979 3.088964 5.101022 0.06904651
#> W2.4 1.628278 2.996913 7.805803 0.32651037
#> 
#>      Estimate    Lower    Upper
#> e:10 1.531174 1.155988 1.906360
#> e:50 3.032914 2.631988 3.433841
#> e:90 6.892701 4.241165 9.544238