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

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 a-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.

Statistical analysis of no observed effect concentrations or levels in eco-toxicological assays with overdispersed count endpoints

“…Corresponding R-code is included in the Appendix III for the examples and can be easily adapted to other data situations. (1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L), .Label = c("Control", "D188", "D375", "D750", "Positive" ), class = "factor"), animal = c (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,22,23,24), MN = c(4, 2, 4, 2, 2, 3, 5, 7, 2, 0, 5, 6, 1, 4, 2, 2, 4, 1, 1, 0, 26, 28, 22, 37, 29)), .Names = c("group", "animal", "MN"), row.names = c(NA, 25L), class = "data.frame") ## ----datDapnhia, echo=FALSE, result='asis', warning=FALSE------------------------------------daphnia <structure(list('Concentration ' = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.56, 1.56, 1.56, 1.56, 1.56, 1.56, 1.56, 1.56, 1.56, 1.56, 3.12, 3.12, 3.12, 3.12, 3.12, 3.12, 3.12, 3.12, 3.12, 3.12, 6.25, 6.25, 6.25, 6.25, 6.25, 6.25, 6.25, 6.25, 6.25, 6. 25, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25), Adults = c (1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,…”

“…Recently the use the closure principle computational approach test (CPCAT) assuming the Poisson distribution was proposed [23] for the analysis of count data, e.g. reproduction data in (eco-) toxicology.…”

The Minimum Detectable Difference (MDD) Concept for Establishing Trust in Nonsignificant Results: A Critical Review

“…Each experiment can thus be analyzed by a single t test. We note that there are more appropriate ways to deal with the analysis of count data (see, for example, Szöcs and Schäfer 2015; Lehmann et al 2016), but we chose the commonly used log‐transformation because it allows us to continue using the t test and because this procedure is frequently used in this context (Brock et al 2015). The results can be expected to generalize to situations in which several pesticide concentrations are tested against the control, for example, via a Williams or Dunnett's test, which control for multiple testing (Williams 1972; Kennedy et al 1999; de Jong et al 2006; European Food Safety Authority PPR Panel 2013; Brock et al 2015), as well as via other statistical tests.…”

The CPCAT as a novel tool to overcome the shortcomings of NOEC/LOEC statistics in ecotoxicology: a simulation study to evaluate the statistical power

“…Species reproduction considerably affects population dynamics and ecology. As such, the new closure principle computational approach test (CPCAT) was proposed for the evaluation of discrete reproduction data [2]. Numbers of new Lemna fronds ( Lemna minor L. ), numbers of juvenile Daphnids ( Daphnia magna ), and numbers of fish eggs laid are popular examples of reproduction count data.…”

“…Recently, a Poisson distribution together with CPCAT was used to test for differences in mean reproduction of different species [2]. Poisson distribution is known as the law of rare events [6].…”