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Core Functions

Main functions for dose-response analysis

drm()
Fitting dose-response models
ED()
Estimating effective doses
EDcomp()
Comparison of relative potencies between dose-response curves
compParm()
Comparison of parameters
mselect()
Dose-response model selection
drmc()
Sets control arguments

Model Functions

Available dose-response model families

LL.2() l2()
Two-parameter log-logistic function
LL.3() l3()
Three-parameter log-logistic function
LL.3u() l3u()
Three-parameter log-logistic function with upper limit fixed
LL.4() l4()
Four-parameter log-logistic function
LL.5() l5()
Five-parameter log-logistic function
LL2.2()
Two-Parameter Log-Logistic Model with log(ED50) as Parameter
LL2.3()
Three-Parameter Log-Logistic Model with log(ED50) and Lower Limit at 0
LL2.3u()
Three-Parameter Log-Logistic Model with log(ED50) and Fixed Upper Limit
LL2.4()
Four-Parameter Log-Logistic Model with log(ED50) as Parameter
LL2.5()
Five-Parameter Generalised Log-Logistic Model with log(ED50) as Parameter
W1.2() w2()
Two-parameter Weibull type 1 model
W1.3() w3()
Three-parameter Weibull type 1 model
W1.3u()
Three-parameter Weibull type 1 model with upper limit fixed
W1.4() w4()
Four-parameter Weibull type 1 model
W2.2()
Two-parameter Weibull (type 2) model
W2.3()
Three-parameter Weibull (type 2) model
W2.3u()
Three-parameter Weibull (type 2) model with upper limit fixed
W2.4()
Four-parameter Weibull (type 2) model
W2x.3()
Three-parameter Weibull type 2 model with lag time
W2x.4()
Four-parameter Weibull type 2 model with lag time
G.2()
Two-parameter Gompertz model
G.3()
Three-parameter Gompertz model
G.3u()
Three-parameter Gompertz model with upper limit fixed
G.4()
Four-parameter Gompertz model
G.aparine
Herbicide applied to Galium aparine
GiantKelp
Measurements of germination tubes for Giant Kelp
LN.2()
Two-parameter log-normal dose-response model
LN.3()
Three-parameter log-normal dose-response model
LN.3u()
Three-parameter log-normal model with upper limit fixed
LN.4()
Four-parameter log-normal dose-response model
BC.4()
Four-parameter Brain-Cousens hormesis model
BC.5()
Five-parameter Brain-Cousens hormesis model
CRS.4a() deprecated
Cedergreen-Ritz-Streibig Model with Lower Limit Fixed at 0 and Alpha = 1 (Deprecated)
CRS.4b() deprecated
Cedergreen-Ritz-Streibig Model with Lower Limit Fixed at 0 and Alpha = 0.5 (Deprecated)
CRS.4c() deprecated
Cedergreen-Ritz-Streibig Model with Lower Limit Fixed at 0 and Alpha = 0.25 (Deprecated)
CRS.5()
Wrapper for 5-parameter Cedergreen-Ritz-Streibig Model
CRS.5a() deprecated
Cedergreen-Ritz-Streibig Five-Parameter Model with Alpha = 1 (Deprecated)
CRS.5b() deprecated
Cedergreen-Ritz-Streibig Five-Parameter Model with Alpha = 0.5 (Deprecated)
CRS.5c() deprecated
Cedergreen-Ritz-Streibig Five-Parameter Model with Alpha = 0.25 (Deprecated)
CRS.6()
Generalised Cedergreen-Ritz-Streibig Model for Hormesis
UCRS.4a()
U-shaped CRS model with lower limit 0 (alpha=1)
UCRS.4b()
U-shaped CRS model with lower limit 0 (alpha=0.5)
UCRS.4c()
U-shaped CRS model with lower limit 0 (alpha=0.25)
UCRS.5a()
U-shaped CRS five-parameter model (alpha=1)
UCRS.5b()
U-shaped CRS five-parameter model (alpha=0.5)
UCRS.5c()
U-shaped CRS five-parameter model (alpha=0.25)
NEC.2()
Two-parameter NEC model
NEC.3()
Three-parameter NEC model
NEC.4()
Four-parameter NEC model
L.3()
Three-parameter logistic model
L.4()
Four-parameter logistic model
L.5()
Five-parameter generalized logistic model
AR.2()
Two-parameter asymptotic regression model
AR.3()
Three-parameter shifted asymptotic regression model
EXD.2()
Two-parameter exponential decay model
EXD.3()
Three-parameter exponential decay model
MM.2()
Two-parameter Michaelis-Menten function
MM.3()
Three-parameter Michaelis-Menten function
FPL.4()
Four-parameter fractional polynomial-logistic model
ml3a() deprecated
Alias for CRS.4a (Deprecated)
ml3b() deprecated
Alias for CRS.4b (Deprecated)
ml3c() deprecated
Alias for CRS.4c (Deprecated)
ml4a() deprecated
Alias for CRS.5a (Deprecated)
ml4b() deprecated
Alias for CRS.5b (Deprecated)
ml4c() deprecated
Alias for CRS.5c (Deprecated)
uml3a()
Alias for UCRS.4a
uml3b()
Alias for UCRS.4b
uml3c()
Alias for UCRS.4c
uml4a()
Alias for UCRS.5a
uml4b()
Alias for UCRS.5b
uml4c()
Alias for UCRS.5c
bcl3()
Alias for BC.4
bcl4()
Alias for BC.5
baro5()
The Baroreflex Five-Parameter Dose-Response Model
braincousens()
The Brain-Cousens hormesis models
cedergreen()
Cedergreen-Ritz-Streibig Model
ucedergreen()
U-shaped Cedergreen-Ritz-Streibig model
fplogistic()
Fractional polynomial-logistic dose-response model
gammadr()
Gamma Dose-Response Model
gaussian()
Normal (Gaussian) biphasic dose-response model
gompertz()
Gompertz dose-response or growth curve model
gompertzd()
Derivative of the Gompertz function
lgaussian()
Log-normal (log-Gaussian) biphasic dose-response model
llogistic()
The log-logistic function
llogistic2()
Five-Parameter Log-Logistic Model with log(ED50) as Parameter
lnormal()
Log-normal dose-response model
logistic()
The general asymmetric five-parameter logistic model
threephase()
Three-Phase Dose-Response Model
twophase()
Two-Phase Dose-Response Model
weibull1()
The four-parameter Weibull type 1 model
weibull2()
The four-parameter Weibull (type 2) model
weibull2x()
Five-parameter Weibull type 2 model with lag time
yieldLoss()
Calculating yield loss parameters
arandaordaz()
Asymptotic Regression Model

Effective Dose Estimation

Functions for estimating effective doses and comparisons

ED(<drc>)
Estimating effective doses
ED_robust()
Robust Calculation of Effective Doses (ED)
CIcomp()
Classical combination index for effective doses
CIcompX()
Calculation of combination index for binary mixtures
comped()
Comparison of effective dose values
maED()
Estimation of ED values using model-averaging
maED_robust()
Robust Calculation of Model-Averaged Effective Doses
isobole()
Creating isobolograms
NEC()
No Effect Concentration (NEC) dose-response model
MAX()
Maximum mean response
PR()
Expected or predicted response
relpot()
Relative potency function

Diagnostics and Model Selection

Model diagnostics and helper functions

modelFit()
Assessing the model fit
Rsq()
R-squared for dose-response models
rss()
Residual sum of squares for dose-response models
rdrm()
Simulating a dose-response curve
anova(<drc>)
ANOVA for dose-response model fits
lin.test()
Lack-of-fit test for the mean structure based on cumulated residuals
mr.test()
Mizon-Richard test for dose-response models
neill.test()
Neill's lack-of-fit test for dose-response models
noEffect()
Testing if there is a dose effect at all
backfit()
Calculation of backfit values from a fitted dose-response model
boxcox(<drc>)
Transform-both-sides Box-Cox transformation
searchdrc()
Search through a range of initial parameter values to obtain convergence
simDR()
Simulating ED values under various scenarios
simFct()
Simulation of dose-response data and ED estimation
plotFACI()
Plot combination index as a function of fraction affected
getInitial()
Showing starting values used
getMeanFunctions()
Display available dose-response models

S3 Methods

Methods for drc model objects

coef(<drc>)
Extract Model Coefficients
confint(<drc>)
Confidence Intervals for Model Parameters
cooks.distance(<drc>)
Cook's distance for nonlinear dose-response models
estfun(<drc>)
Estimating function for the sandwich estimator
fitted(<drc>)
Extract fitted values from model
hatvalues(<drc>)
Model diagnostics for nonlinear dose-response models
logLik(<drc>)
Extracting the log likelihood
plot(<drc>)
Plotting fitted dose-response curves
predict(<drc>)
Prediction
print(<drc>)
Printing key features
print(<summary.drc>)
Printing summary of non-linear model fits
residuals(<drc>)
Extracting residuals from the fitted dose-response model
summary(<drc>)
Summarising non-linear model fits
update(<drc>)
Updating and re-fitting a model
vcov(<drc>)
Calculating variance-covariance matrix for objects of class 'drc'
bread(<drc>)
Bread for the sandwich estimator

Datasets

Example datasets for dose-response analysis

acidiq
Acifluorfen and diquat tested on Lemna minor.
aconiazide
Weight change in rats after exposure to a medical drug
acute.inh
Acute inhalation
algae
Volume of algae as function of increasing concentrations of a herbicide
arbovirus
arbovirus
auxins
Effect of technical grade and commercially formulated auxin herbicides
barley
Barley
bees
bees
blackgrass
Seedling Emergence of Blackgrass (Alopecurus myosuroides)
broccoli
The Effects of Drought Stress on Leaf Development in a Brassica oleracea population
C.dubia
Offsprings resulting from a toxicity test
CadmiumDaphnia
Cadmium Daphnia Data
carbendazim
Damage of lymphocyte cells
chickweed
Germination of common chickweed (Stellaria media)
chlorac
chlorac
chlordan
Chlordan
ctb
CellTiter-Blue Cell Viability Assay Data
Cyp17
Cyp17 expression data
Daphnia
Daphnia
daphnids
Daphnia test
decontaminants
Performance of decontaminants used in the culturing of a micro-organism
deguelin
Deguelin applied to chrysanthemum aphis
earthworms
Earthworm toxicity test
echovirus
Infections as response to exposure with Echovirus 12
Eryngium.sparganophyllum
Germination of Eryngium sparganophyllum
etmotc
Effect of erythromycin on mixed sewage microorganisms
finney71
Example from Finney (1971)
fluoranthene
Death of fathead minnow larvae after exposure to fluoranthene
germination
Germination of three crops
GiantKelp
Measurements of germination tubes for Giant Kelp
glymet
Glyphosate and metsulfuron-methyl tested on algae.
guthion
guthion
H.virescens
Mortality of tobacco budworms
heartrate
Heart rate baroreflexes for rabbits
leaflength
Leaf length of barley
lemna
Lemna
lepidium
Dose-response profile of degradation of agrochemical using lepidium
lettuce
Hormesis in lettuce plants
liver.tumor
Liver tumor incidence
M.bahia
Effect of an effluent on the growth of mysid shrimp
mdra
3T3 mouse fibroblasts and NRU assay
mecter
Mechlorprop and terbythylazine tested on Lemna minor
metals
Data from heavy metal mixture experiments
methionine
Weight gain for different methionine sources
mixture()
Fitting binary mixture models
multi2()
Multistage Dose-Response Model with Quadratic Terms
nasturtium
Dose-response profile of degradation of agrochemical using nasturtium
nfa
Network Formation Assay Data
nicotine
nicotine
O.mykiss
Test data from a 21 day fish test
P.promelas
Effect of sodium pentachlorophenate on growth of fathead minnow
RScompetition
Competition between two biotypes
red.fescue
Red fescue
ryegrass
Effect of ferulic acid on growth of ryegrass
ryegrass2
Ryegrass
S.alba
Potency of two herbicides
S.alba.comp
Potency of two herbicides
S.capricornutum
Effect of cadmium on growth of green alga
secalonic
Root length measurements
selenium
Data from toxicology experiments with selenium
spinach
Inhibition of photosynthesis
TCDD
Liver tumor incidence
terbuthylazin
The effect of terbuthylazin on growth rate
ursa()
Universal Response Surface Approach (URSA) for Drug Interaction
vinclozolin
Vinclozolin from AR in vitro assay