Dose-response analysis can be carried out using multi-purpose commercial statistical software, but except for a few special cases the analysis easily becomes cumbersome as relevant, non-standard output requires manual programming. The extension package drc for the statistical environment R provides a flexible and versatile infrastructure for dose-response analyses in general. The present version of the package, reflecting extensions and modifications over the last decade, provides a user-friendly interface to specify the model assumptions about the dose-response relationship and comes with a number of extractors for summarizing fitted models and carrying out inference on derived parameters. The aim of the present paper is to provide an overview of state-of-the-art dose-response analysis, both in terms of general concepts that have evolved and matured over the years and by means of concrete examples.

We describe an add-on package for the language and environment R which allows simultaneous fitting of several non-linear regression models. The focus is on analysis of dose response curves, but the functionality is applicable to arbitrary non-linear regression models. Features of the package is illustrated in examples.

Advances in statistical software allow statistical methods for nonlinear regression analysis of dose-response curves to be carried out conveniently by non-statisticians. One such statistical software is the program R with the drc extension package. The drc package can: (1) simultaneously fit multiple dose-response curves; (2) compare curve parameters for significant differences; (3) calculate any point along the curve at the response level of interest, commonly known as an effective dose (e.g., ED30, ED50, ED90), and determine its significance; and (4) generate graphs for publications or presentations. We believe that the drc package has advantages that include: the ability to relatively simply and quickly compare multiple curves and select ED-levels easily along the curve with relevant statistics; the package is free of charge and does not require licensing fees, and the size of the package is only 70 MB. Therefore, our objectives are to: (1) provide a review of a few common issues in dose-response-curve fitting, and (2) facilitate the use of up-to-date statistical techniques for analysis of dose-response curves with this software. The methods described can be utilized to evaluate chemical and non-chemical weed control options. Benefits to the practitioners and academics are also presented.

During the past two decades, the phenomenon of hormesis has gained increased recognition. To promote research in hormesis, a sound statistical quantification of important parameters, such as the level and significance of the increase in response and the range of concentration where it occurs, is strongly needed. Here, we present an improved statistical model to describe hormetic dose-response curves and test for the presence of hormesis. Using the delta method and freely available software, any percentage effect dose or concentration can be derived with its associated standard errors. Likewise, the maximal response can be extracted and the growth stimulation calculated. The new model was tested on macrophyte data from multiple-species experiments and on laboratory data of Lemna minor. For the 51 curves tested, significant hormesis was detected in 18 curves, and for another 17 curves, the hormesis model described that data better than the logistic model did. The increase in response ranged from 5 to 109%. The growth stimulation occurred at an average dose somewhere between zero and concentrations corresponding to approximately 20 to 25% of the median effective concentration (EC50). Testing the same data with the hormesis model proposed by Brain and Cousens in 1989, we found no significant hormesis. Consequently, the new model is shown to be far more robust than previous models, both in terms of variation in data and in terms of describing hormetic effects ranging from small effects of a 10% increase in response up to effects of an almost 100% increase in response.

Resume: ZusammenfassungOne of the most commonly used techniques to assess the efficacy of herbicides is to apply lo the principle of bioassays. A bioassay is defined as an experiment for estimating the potency of a herbicide by analysis of the reaction that follows its application to living organisms. The analysis of variance is central to most applications of statistical methods in the analysis of experiments. This is true for bioassay. but perhaps the fundamental importance of regression and related concepts is here particularly apparent. The purpose of this presentation is (o quantify herbicidal effects of applying non-linear regression models to herbicide bioassays. and to demonstrate how some general hypotheses about the mode of action of ihe assayed herbicides can be incorporated into the regression models. The validity of herbicide bioassay data is discussed in view of the general principles used in bioassay in other biological sciences. Essai d'efficacite biologique des herbicidesUne des principalcs methodes utilisces pour estimer Tefficacite des herbicides est la mise en place d'essais biologiques. Un essai biologique est defini comme une experimentation pour estimer le potentiel d'un herbicide par la moyenne des reactions qui suivenl son application sur les organismes vivants. L'analyse de la variance est a la base dc la plupart des methodes statisliqucs utilisees dans !es experimentations. Ceci est vrai pour les essais biologiques. mais peut etre que ["importance fondamentale de la regression et des concepts afferenis est ici particulierement cvidente. En vue de quantifier les resultiils d'un essai biologique herbicide, il est important de pouvoir ctablir une courbe reponse qui decrit I'evenlai! des doses dans sa totalite de I'effecacitc nulle aux faibles doses a la destruction lotale aux hautes doses. Le but de cette communication esl la quantification dc I'efficacite herbicide en appliquant des modeles de regression non lincaircs aux essais biologiques et de demontrer comment certaines hypotheses generales sur le mode d'action des herbicides essayes peuvent etre integrecs dans les modeles de regression. La validitc des donnees issues des essais herbicides biologiques est discutee par rapport aux principaux generaux des essais biologiques. Herhizid-Bio testsZu den meistgebrauchten Techniken zur Bestimmung der herbiziden Wirksamkeit gehdren Biotests, bei denen die Wirkung eines Herbizids anhand der Reaktion eines lebenden Organismus bestimmt wird. FCir die Analyse von Vcrsuchsergebnis.scn wird die Varianzanalyse als haufigste stalistischc Mcthode verwendct. Dies irifft auch fiir Biotests zu, aber vcrmutlich ist die fundamentale Bedeutung der Regressionsanalyse und vcrwandler Verrechnungsmoglichkeiten hier besonders deutlich. Um einen Herbizid-Biotest vollstiindigzu quantifizieren, miissen Dosis-Wirkungs-Kurvcn angewandt werden. die den gesamlen Bereich von ganzlich fehlender Reaktion bei nicdrigen Dosen bis zur vollslandigcn Abtotung durch hohe Dosen abdeckcn. In der vorgestelltcn Untersuchung wird die...