Dose Response Data Analysis using the 4 Parameter Logistic (4pl) Model

Models the relationship between dose levels and responses in a pharmacological experiment using the 4 Parameter Logistic model. Traditional packages on dose-response modelling such as 'drc' and 'nplr' often draw errors due to convergence failure especially when data have outliers or non-logistic shapes. This package provides robust estimation methods that are less affected by outliers and other initialization methods that work well for data lacking logistic shapes. We provide the bounds on the parameters of the 4PL model that prevent parameter estimates from diverging or converging to zero and base their justification in a statistical principle. These methods are used as remedies to convergence failure problems. Gadagkar, S. R. and Call, G. B. (2015) Ritz, C. and Baty, F. and Streibig, J. C. and Gerhard, D. (2015) .

output: md_document: variant: markdown_github

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The package dr4pl (Dose Response 4 Parameter Logisitic model) specializes in applying the 4 Parameter Logistic (4PL) model. The 4PL model has been recognized as a major tool to analyze the relationship between a dose and a response in pharmacological experiments. The package dr4pl may be used to model increasing and decreasing curves. The goal of dr4pl is to bring a statistical method which is capable of handeling specific error cases of which other statistical packages produce errors. Examples of Dose Response datasets that will produce errors in other packages may be accessed by name once dr4pl is loaded and these data sets are under the names of drc_error_1, drc_error_2, drc_error_3, and drc_error_4. Along with these error data sets, this package also supplies 13 standard example data sets for the 4PL model under the name sample_data_1, sampel_data_2, etc. The package dr4pl also alows for the user to decide how their theta variable is approximated. The user may choose the default logistic model or use Mead's Method. Additionally, the user may decide between four loss functions to minimize: Squared, Absolute, Huber, or Tukey's biweight. Please attempt each of the loss functions and choose the best fit from plotting the dr4pl object.


You can install dr4pl from github with:

# install.packages("devtools")


This is a basic example which shows you how to solve a common problem. This example may be used with drc_error_1, drc_error_2, drc_error_3, and drc_error_4:

## basic example code, datasets
## example requires the drc and dr4pl package to be loaded
#> Loading required package: MASS
#> 'drc' has been loaded.
#> Please cite R and 'drc' if used for a publication,
#> for references type 'citation()' and 'citation('drc')'.
#> Attaching package: 'drc'
#> The following objects are masked from 'package:stats':
#>     gaussian, getInitial
a <- drc::drm(drc_error_1$Response~drc_error_1$Dose, fct = LL.4())
#> Error in drmOpt(opfct, opdfct1, startVecSc, optMethod, constrained, warnVal, : Convergence failed
#> Error in plot(a): object 'a' not found
## basic example code
## example requires the dr4pl package to be loaded
b <- dr4pl(drc_error_1$Response~drc_error_1$Dose, method.init = "logistic", method.robust = "Tukey") 
#> Warning: Transformation introduced infinite values in continuous x-axis
#> Warning: Transformation introduced infinite values in continuous x-axis

plot of chunk example_solution

#> $call
#> dr4pl.formula(formula = drc_error_1$Response ~ drc_error_1$Dose, 
#>     method.init = "logistic", method.robust = "Tukey")
#> $coefficients
#>                 Estimate       StdErr       t.value p.value
#> UpperLimit  7.913355e+04 2.538637e-01  3.117166e+05       0
#> IC50        4.258701e-13 3.054816e-04  1.394094e-09       1
#> Slope      -7.370728e-02 2.481119e-06 -2.970728e+04       0
#> LowerLimit -8.393064e+03 6.511088e-01 -1.289042e+04       0
#> attr(,"class")
#> [1] "summary.dr4pl"


output: md_document

dr4pl 1.1.6

dr4pl function now allows 'data' argument when using 'dose' and 'response' arguments. See dr4pl examples.

dr4pl 1.1.7

print.summary.dr4pl function no long provides t-statistics and p-values but now prints 95% confidence intervals instead. Consolidated Vignettes.

dr4pl 1.1.8

Following proper semantic versioning.

Reference manual

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1.1.11 by Justin T. Landis, a year ago

Report a bug at

Browse source code at

Authors: Justin T. Landis [aut, cre] , Hyowon An [aut] , Aubrey G. Bailey [aut] , Dirk P. Dittmer [aut] , James S. Marron [aut]

Documentation:   PDF Manual  

GPL (>= 2) license

Imports ggplot2, Matrix, matrixcalc, tensor, Rdpack

Suggests drc, devtools, roxygen2, testthat, knitr, rmarkdown

Imported by Biotech.

See at CRAN