Statistics in Toxicology Using R: 1st Edition (Hardback) book cover

Statistics in Toxicology Using R

1st Edition

By Ludwig A. Hothorn

Chapman and Hall/CRC

234 pages | 98 B/W Illus.

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The apparent contradiction between statistical significance and biological relevance has diminished the value of statistical methods as a whole in toxicology. Moreover, recommendations for statistical analysis are imprecise in most toxicological guidelines. Addressing these dilemmas, Statistics in Toxicology Using R explains the statistical analysis of selected experimental data in toxicology and presents assay-specific suggestions, such as for the in vitro micronucleus assay.

Mostly focusing on hypothesis testing, the book covers standardized bioassays for chemicals, drugs, and environmental pollutants. It is organized according to selected toxicological assays, including:

  • Short-term repeated toxicity studies
  • Long-term carcinogenicity assays
  • Studies on reproductive toxicity
  • Mutagenicity assays
  • Toxicokinetic studies

The book also discusses proof of safety (particularly in ecotoxicological assays), toxicogenomics, the analysis of interlaboratory studies and the modeling of dose-response relationships for risk assessment. For each toxicological problem, the author describes the statistics involved, matching data example, R code, and outcomes and their interpretation. This approach allows you to select a certain bioassay, identify the specific data structure, run the R code with the data example, understand the test outcome and interpretation, and replace the data set with your own data and run again.


"The field of toxicology raises all sorts of statistical issues. This book is a practical guide to an important subset of those issues, those that are addressable by comparison of response means for two or more dose treatments. … The material in the book is organized in a way that is useful both for someone interested in general principles and someone interested in a specific type of toxicological study. …Unlike many books of the "using R" flavor that focus on one R package, this book illustrates the use of functions from many different packages. Compilations at the end of the book list 24 packages used for statistical analyses, five packages used for data manipulation or graphics, and another 11 packages that provide datasets. … This book will be useful to many applied statisticians, not just those working with toxicological data. The principles and methods discussed here are relevant formany types of studies. In particular, if you are interested in multiple testing or evaluating monotonic trends, you will find a wealth of methods, examples, and R code here."

—Philip M. Dixon, Iowa State University, in The American Statistician, July 2017

"This book has the potential to become the go-to text for those working at the intersection of statistics and toxicology…The book is very thorough in its coverage of toxicological tests, how to carry them out and how to interpret them in R, with over 400 references…Use is made of a wide array of R packages, from coin to WinProb, most of which appear in CRAN. The key package SiTuR, which provides access to the example data and selected functions in the book, is available on Github."

— Alice Richardson, ANU College of Medicine, Australia, in International Statistical Review, April 2017

"The book presents a wealth of hands-on examples, explanations, methods, insights, and references on how statistical analysis in toxicology may be approached from a modern, 21st-century point of view, discarding or at least devaluing some long-standing but quite useless concepts and methods along the way. … The versatile R packages ‘multcomp’ and ‘coin’ are key players in this approach throughout the book as demonstrated in the many concrete R examples throughout the book. As far as I know, no similar book is currently available. It should be extremely useful for applied statisticians and toxicologists alike."

Christian Ritz, University of Copenhagen, Denmark

Table of Contents


Evaluation of short-term repeated toxicity studies

Selected statistical problems

Proof of hazard using two-sample comparisons

Simultaneous comparisons versus a negative control

Proof of hazard using simultaneous comparisons versus a negative control

Trend tests

Reference values

Analysis of complex designs

Proof of safety

Evaluation of long-term carcinogenicity assays


Analysis of mortality

Analysis of crude tumor rates

Mortality-adjusted tumor rates with cause-of-death information

Mortality-adjusted tumor rates without cause-of-death information

More complex analyzes

Evaluation of mutagenicity assays

What is specific in the analysis of mutagenicity assays?

Evaluation of the Ames assay as an example for dose-response shapes with possible downturn effects

Evaluation of the micronucleus assay as an example for nonparametric tests in small sample size design

Evaluation of the SHE assay using trend tests on proportions

Evaluation of the in vivo micronucleus assay as an example of the analysis of proportions taking overdispersion into account

Evaluation of the in vivo micronucleus assay as an example of the analysis of counts taking overdispersion into account

Evaluation of HET-MN assay for an example of transformed count data

Evaluation of cell transformation assay for an example of near-to-zero counts in the control

Evaluation of the LLNA as an example for k-fold rule

Evaluation of the HET-MN assay using historical control data

Evaluation of a micronucleus assay taking the positive control into account

Evaluation of the Comet assay as an example for mixing distribution

Evaluation of the in vitro micronucleus assay as an example for comparing cell distributions

Evaluation of reproductive toxicity assays

The statistical problems

Evaluation of the continuous endpoint pup weight

Evaluation of proportions

Analysis of different-scaled multiple endpoints

Analysis of female-specific endpoints

Behavioral tests

Ecotoxicology: Test on significant toxicity

Proof of safety

Two-sample ratio-to-control tests

Ratio-to-control tests for several concentrations

Modeling of dose-response relationships

Models to estimate the EDxx

Benchmark dose estimation

Is model selection toward LOAEL an alternative?

Further methods



Evaluation of interlaboratory studies


Appendix: R details

About the Author

Ludwig A. Hothorn is a professor in the Institute of Biostatistics at the Leibniz University of Hannover. Dr. Hothorn has published more than 130 papers in peer-reviewed journals and contributed numerous book chapters. His research interests include computational statistics using R as well as the application of statistical methods in biology, agriculture, medicine, life sciences, toxicology, pharmacology, and quantitative genetics.

About the Series

Chapman & Hall/CRC The R Series

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General
MEDICAL / Toxicology