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A new approach to overcome shortcomings with multiple testing of reproduction data in ecotoxicology

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Abstract

In ecotoxicology species reproduction tests and multiple testing of reproduction data are wide spread. While normal approximation of the data is a minor problem often the requirement of variance homogeneity is not fulfilled. Variance homogeneity is necessary to assure the proper application of statistical procedures like pairwise t tests, Dunnett t test, and Williams t test. A Poisson model can solve this issue preserving meaningful results and rendering statistical analysis more reliable. Moreover, sequential application of pairwise statistical “control vs. treatment” tests is a drawback concerning \(\alpha \)-inflation. The closure principle (CP) for hypothesis testing is used to generate a step-wise approach for detection of the No/Lowest Observed Effect Concentration using the computational approach test (CAT). The advantages and disadvantages of the combined CPCAT approach compared to the widely used t tests are pointed out and results of real data and fictitious data analysis are compared revealing the superiority of the Poisson model and CPCAT.

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References

  • Bretz F, Hothorn T, Westfall P et al (2011) Multiple comparisons using R. CRC Press, Boca Raton

    Google Scholar 

  • Carrasco IJ, Chang S-Y (2005) Random monte carlo simulation analysis and risk assessment for ammonia concentrations in wastewater effluent disposal. Stoch Environ Res Risk Assess 19:134–145

    Article  Google Scholar 

  • Chang C-H, Pal N, Lin J-J (2010) A note on comparing several poisson means. Commun Stat Simul Comput 39:1605–1627

    Article  Google Scholar 

  • Chapman PF, Crane M, Wiles J, Noppert F, McIndoe E (1996) Improving the quality of statistics in regulatory ecotoxicity tests. Ecotoxicology 5:169–186

    Article  CAS  Google Scholar 

  • Chiu SN (2010) Parametric bootstrap and approximate tests for two poisson variates. J Stat Comput Simul 80:263–271

    Article  Google Scholar 

  • Chiu SN, Wang L (2009) Homogeneity tests for several poisson populations. Comput Stat Data Anal 53:4266–4278

    Article  Google Scholar 

  • Delignette-Muller ML, Lopes C, Veber P, Charles S (2014) Statistical handling of reproduction data for exposure-response modeling. Environ Sci Technol 48(13):7544–7551

    Article  CAS  Google Scholar 

  • Drew JH, Evans DL, Glen AG, Leemis L (2008) Computational probability: algorithms and applications in the mathematical sciences. Springer, New York

    Google Scholar 

  • Dudley RM (2014) Uniform central limit theorems. Cambridge University Press, Cambridge

    Google Scholar 

  • Dunnett CW (1955) A multiple comparison procedure for comparing several treatments with a control. J Am Stat Assoc 50:1096–1121

    Article  Google Scholar 

  • Dunnett CW (1964) New tables for multiple comparisons with a control. Biometrics 20:482–491

    Article  Google Scholar 

  • Fahd F, Khan F, Hawboldt K, Abbassi R (2014) Developing a novel methodology for ecological risk assessment of thiosalts. Stoch Environ Res Risk Assess 28:383–391

    Article  Google Scholar 

  • Gopi RA, Ayyappan S, Chandrasehar G, Varma KK, Goparaju A (2012) Effect of potassium dichromate on the survival and reproduction of daphnia magna. Bull Environ Pharmacol Life Sci 1:89–94

    Google Scholar 

  • Gupta BC, Guttman I (2014) Statistics and probability with applications for engineers and scientists. Wiley, Hoboken

    Google Scholar 

  • Holm S (1979) A simple sequentially rejective multiple test procedure. Scand J Stat 6:65–70

    Google Scholar 

  • Jonckheere AR (1954) A distribution-free k-sample test against ordered alternatives. Biometrika 41:133–145

    Article  Google Scholar 

  • Krishnamoorthy K, Thomson J (2004) A more powerful test for comparing two poisson means. J Stat Plan Inference 119:23–35

    Article  Google Scholar 

  • Kruskal WH, Wallis WA (1952) Use of ranks in one-criterion variance analysis. J Am Stat Assoc 47:583–621

    Article  Google Scholar 

  • Lee H-K, Yeh Y-Y, Chen W-M (2006) Cancer risk analysis and assessment of trihalomethanes in drinking water. Stoch Environ Res Risk Assess 21:1–13

    Article  CAS  Google Scholar 

  • Lehmann EL, Romano JP (2006) Testing statistical hypotheses. Springer, New York

    Google Scholar 

  • Liu KF-R, Ko C-Y, Fan C, Chen C-W (2013) Incorporating the lcia concept into fuzzy risk assessment as a tool for environmental impact assessment. Stoch Environ Res Risk Assess 27:849–866

    Article  Google Scholar 

  • Marx, C., Mühlbauer, V., Krebs, P. & Kuehn, V. (2015) Species-related risk assessment of antibiotics using the probability distribution of long-term toxicity data as weighting function: a case study. Stoch Environ Res Risk Assess:1–13. doi:10.1007/s00477-015-1026-4

  • Ng HKT, Tang ML (2005) Testing the equality of two poisson means using the rate ratio. Stat Med 24:955–965

    Article  Google Scholar 

  • OECD (1984) Test no. 206: Avian reproduction test. In: OECD guidelines for the testing of chemicals section 2. OECD Publishing, Paris

  • OECD (2004) Test no. 220: Enchytraeid reproduction test. In: OECD guidelines for the testing of chemicals, section 2. OECD Publishing, Paris

  • OECD (2006) Test no. 221: Lemna sp. growth inhabition test. In: OECD guidelines for the testing of chemicals, section 2. OECD Publishing, Paris

  • OECD (2012) Test no. 211: Daphnia magna reproduction test. In: OECD guidelines for the testing of chemicals, section 2. OECD Publishing, Paris

  • Olofsson P (2013) Probabilities: the little numbers that rule our lives. Wiley, Hoboken

    Google Scholar 

  • Panjer HH (1981) Recursive evaluation of a family of compound distributions. ASTIN Bull 12:22–26

    Google Scholar 

  • Przyborowski J, Wilenski H (1940) Homogeneity of results in testing samples from Poisson series. Biometrika 31:313–323

    Google Scholar 

  • Qin Y, Yang Z, Yang W (2011) Ecological risk assessment for water scarcity in Chinas Yellow River Delta Wetland. Stoch Environ Res Risk Assess 25:697–711

    Article  Google Scholar 

  • R Development Core Team (2010) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna

    Google Scholar 

  • Sieratowicz A, Stange D, Schulte-Oehlmann U, Oehlmann J (2011) Reproductive toxicity of bisphenol a and cadmium in Potamopyrgus antipodarum and modulation of bisphenol a effects by different test temperature. Environ Pollut 159:2766–2774

    Article  CAS  Google Scholar 

  • Welch BL (1974) The generalization of ”student’s” problem when several different population variances are involved. Biometrika 34:28–35

    Google Scholar 

  • Williams DA (1971) A test for differences between treatment means when several dose levels. Biometrics 27:103–117

    Article  CAS  Google Scholar 

  • Williams DA (1972) The comparison of several dose levels with a zero dose control. Biometrics 28:519–531

    Article  CAS  Google Scholar 

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Acknowledgments

We thank Jörg Oehlmann (Goethe-University Frankfurt, Germany) for providing detailed information concerning snail reproduction after exposure to Cd (data set 5).

Author information

Authors and Affiliations

  1. Federal Environment Agency, Dessau-Roßlau, Germany

    René Lehmann, Jean Bachmann, Dirk Maletzki & Christian Polleichtner

  2. ToxRat Solutions GmbH, Alsdorf, Germany

    Hans Toni Ratte & Monika Ratte

Authors
  1. René Lehmann
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  2. Jean Bachmann
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  3. Dirk Maletzki
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  4. Christian Polleichtner
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  5. Hans Toni Ratte
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  6. Monika Ratte
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Corresponding author

Correspondence to René Lehmann.

Appendix

Appendix

See Tables 4, 5 and 6.

Table 4 Data sets 1–3: yield of Lemna minor L. reproduction after exposure to 3,5-DCP
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Table 5 Data set 5: cumulative numbers of snail embryos (Potamopyrgus antipodarum) after 4 weeks exposure to Cd
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Table 6 Data sets 6–7: fictitious reproduction data
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1.1 R-Code: CP

1.2 R-Code: CAT

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Lehmann, R., Bachmann, J., Maletzki, D. et al. A new approach to overcome shortcomings with multiple testing of reproduction data in ecotoxicology. Stoch Environ Res Risk Assess 30, 871–882 (2016). https://doi.org/10.1007/s00477-015-1079-4

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