Stat 505 - Environmental Statistics - References for part 2
Analysis of toxicological data
General Books / Book Chapters
Finney, D.J. 1971. Probit Analysis, 3rd ed. Cambridge University Press.
Finney, D.J. 1978. Statistical Methods in Biological Assay, 3rd ed. Griffin and Company.
Both Finney books are classic treatments of the use and interpretation of studies with responses that are yes/no. Overview of the classic methods, usually involving least squares
regression on transformed proportions, to estimate dose-response curves. Lots of discussion
of concepts, including tolerance distributions.
Gaddum, J.H. 1953. Bioassays and mathematics. Pharmacological Review 5:87-134.
Lengthy classic paper on dose-response estimation. Sections on quantal effects apply to our
discussions. Quantal responses are responses where you observe yes / no on each individual.
Hosmer, D.W. and Lemeshow, S. 1989. Applied Logistic Regression Wiley.
I believe a 2nd ed. is now available. Intermediate level text on logistic regression. Does not
discuss overdispersion (at least 1st ed. doesn’t).
Kendall, R.J. and Lacher, T.E. Jr. 1994. Wildlife Toxicology and Population Modeling: Integrated Studies of Agroecosystems Lewis Publishers.
Papers originally presented at an invited conference on toxicology science and policy. Source
of a couple of the assigned readings.
McCulloch, C.E. and Searle, S.R. 2001. Generalized, Linear, and Mixed Models. Wiley.
Compact treatment of properties of overdispersed binomial data. My approach to overdispersion based on section 2.6
Morgan, B. J.T. 1996. Statistics in Toxicology. Oxford. Univ. Press
A collection of papers as a memorial for David Williams, who worked in tox statistics. Papers
in three areas: design of tox. expts, estimating LC50, and overdispersion. Source of one of
the assigned readings.
Newman, M.C. 2013. Quantitative Ecotoxicology, 2nd ed.. CRC Press
Compilation of methods, written for non-statisticians. Chapter 4, discusses LC50 estimation;
pp 197-199 discuss NOEC and related quantities.
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Benchmark Dose and NOEC
Allen, B. C., Kavlock, R.J., Kimmel, C.A. and Faustman, E.M. 1994. Dost-reponse assessment for developmental toxicity: II. Comparison of generic benchmark dose estimates with
NOAELs. Fundamental and Applied Toxicology 23:487-495.
Allen, B. C., Kavlock, R.J., Kimmel, C.A. and Faustman, E.M. 1994. Dost-reponse assessment
for developmental toxicity: III. Statistical Models. Fundamental and Applied Toxicology
23:496-509.
Crump, K. 1984. A new method for determining allowable daily intakes. Fundamental and
Applied Toxicology 4: 854-871.
Original paper on the Benchmark Dose method.
Crump, K., Allen B. and Faustman, E. 1995. The Use of the Benchmark Dose Approach in
Health Risk Assessment. US EPA, Risk Assessment Forum. EPA/630/R-94/007
US EPA. 2012. Benchmark Dose Technical Guidance. Online at:
http://www.epa.gov/raf/publications/benchmarkdose.htm.
“This guidance document addresses the computation of the BMDs and benchmark concentrations and their confidence limits; data requirements; dose-response analysis, and recommendations for reporting the results.”
Leisenring W, and Ryan L 1992. Statistical properties of the NOAEL. Regulatory Toxicology
and Pharmacology 15:161-171
Statistical critique of NOEC.
Mantel, N. and Schneiderman, M.A. 1975. Estimating “safe” levels, a hazardous undertaking.
Cancer Research 35:1379-1386.
West RW, and Kodell RL. 2005. Changepoint alternatives to the NOAEL. Journal of Agricultural Biological and Environmental Statistics 10:197-211
Estimating LC50 Most of the general books above cover LC50 estimation in detail.
Hamilton, M.A. 1991. Estimation of the typical lethal dose in acute toxicity studies. pp 61-88
in Krewski, D. and Franklin, C. (eds.) Statistics in Toxicology. Gordon Breach Science
Publishers.
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Stephan, C.E. 1977. Methods for calculating an LC50 . pp 65-84 in Mayer, F.L. and Hamelink,
J.L. (eds.) Aquatic Toxicology and Hazard Evaluation ASTM STP 634. American Society
for Testing and Materials.
“Standard” procedure for estimating LC50 . Recommends methods that produce ci’s as well
as estimates and paying attention to practical considerations in addition to statistical.
Overdispersion
Kupper, L., Portier, C., Hogan, M., Yamatoto, E. 1986. The impact of litter effects on doseresponse modeling in teratology. Biometrics 42:85-98.
Ryan, L.M. 1992. Quantitative risk assessment for developmental toxicity. Biometrics 48:163174.
Extrapolation to entire communities
Wagner, C. and Lokke H. 1991. Estimation of ecotoxicological protection levels from NOEC
toxicity data. Water Res. 25:1237-1242.
Given tox information on a subset of species from a community what can be said about
effect on all species?
Smith, E. P. and Cairns, J. Jr. 1993. Extrapolation methods for setting ecological standards
for water quality: statistical and ecological concerns. Ecotoxicology 2:203-219.
Hormesis: concepts
Calabrese, E.J. 2005. Historical blunders: how toxicology got the dose-response relationship
half right. Cell Mol Biol (Noisy-le-grand) 14:643-654.
Calabrese, E.J. 2008. Hormesis: Why it is Important to Toxicology and Toxicologists. Environ
Toxicol Chem. 27:1451-1474
Calabrese E, Stanek EJ, Nascarella M, et al. 2008. Hormesis Predicts Low-Dose Responses
Better Than Threshold Models. International Journal of Toxicology 27:369-378
Calabrese, E.J. and Baldwin, L.A. 2003. Hormesis: the dose-response revolution. Annual
Review of Pharmacology and Toxicology 43:175-97.
Calabrese EJ. 2009. Getting the dose-response wrong: why hormesis became marginalized and
the threshold model accepted. Archives of Toxicology 83:227-247.
My comment: Ed Calabrese is a persistent advocate of hormesis.
Hanekamp, J.C. 2007. Hormesis in precautionary regulatory culture: models preferences and
the advancement of science. Human and Expt. Tox. 26:855-873.
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Hormesis: basic models
Brain, P. and Cousens, R. 1989. An equation to describe dose responses where there is stimulation of growth at low doses. Weed Research 29:93-96.
Cedergreen, N., Ritz, C., and Streibiq, J.C. 2005. Improved empirical models describing hormesis. Env. Tox. and Chem. 24: 3316-3172.
Deng, C., Graham, R., and Shukla, R. 2001. Detecting and Estimating Hormesis Using a
Model-Based Approach. Human and Ecol. Risk Assessment 7:849-866.
Schabenberger, O. and Birch, J.B. 2001. Statistical dose-response models with hormetic effects.
Intl J. Human and Ecol. Risk Assess. 7:891-908.
Schabenberger, O. and Pierce, F.J. 2000. Contemporary Statistical Models for the Plant and Soil
Sciences, CRC Press pp 275 - 278 discusses a way to construct general models for hormetic
effects by combining two models.
Van Ewijk, P.H. and Hoekstra, J.A. 1993. Calculation of the EC50 and its confidence interval
when subtoxic stimulus is present. Ecotoxicol. and Environmental Safety 25:25-32.
Miscellaneous discussions of other issues
Hothorn, L. A., Lin, K.K., Hamada, C., and Rebel, W. 1997. Recommendations for biostatistics
of repeated toxicity studies. Drug Information Journal 31: 327-334.
Recommendations from an international consensus committee on studies using repeated
doses of toxicant. Concepts, not details.
Krewski, D., Leroux, B.G., and Zhu, Y. 1996. Statistical analysis of toxicological experiments
on carcenogenicity, mutagenicity, and developmental toxicity. Chapter 21 in Armitage, P.
and David, H.A. Advances in Biometry. New York: Wiley
Review of a very extensive literature. Each of the three sections (on carcenogenicity, mutagenicity, and dev. tox. presents mathematical models, trend tests (does response increase
with dose) and dose-response models.
Mudholkar, G.S. and George, E.O. 1978. A remark on the shape of the logistic distribution.
Biometrika 65:667-8
shows the similarity between a logistic distribution and T distribution with 9 d.f.
Ryan L. 2003. Epidemiologically based environmental risk assessment Statistical Science 18:466480
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