A Comparison of Two Factorial Designs, a Complete 3×3 Factorial and a Central Composite Rotatable Design, for Use in Binomial Response Experiments in Aquatic Toxicology

Abstract

Using an amphibian toxicity testing protocol, comparative studies were conducted to assess the predictive precision, degree of similarity of results and efficiency of a central composite rotatable design (CCRD) in relation to a conventional complete 3×3 factorial design. Data were treated with response surface analysis using generalized linear models (glm) and application of profile deviance to generate confidence intervals. Design comparisons were based on studies conducted using the Frog Embryo Teratogenesis Assay—Xenopus (FETAX) protocol to examine the interaction of three toxicants at pH levels ranging from 4.5 to 8.5. Test substances included two commercial herbicide formulations based on glyphosate ([N-phosphonomethyl]glycine) isopropylamine salt (Vision, Rodeo) as well as a polyethoxylated tallow amine surfactant blend (MON 0818), which is a key component of the Vision formulation. The generated models from both the CCRD and the factorial designs produced toxicity estimates similar to each other and to previously published results. Trends were also similar to published results in that the surfactant, MON 0818, was comparatively more toxic than Vision, which was more toxic than Rodeo. Further, all toxicants induced higher mortality under alkaline as opposed to acidic conditions. The CCRD was between 66 and 124% more efficient in the Vision and Rodeo experiments in comparison to the complete 3×3 factorial. Thus, the factorial experiment would have required at least 66% more observations to obtain the same precision. There appeared to be no efficiency gain with the use of the CCRD for MON 0818. The CCRD had tighter confidence intervals in 9 of 12 cases across all test substances. Computer simulations using the experimental data for Vision demonstrated that the LCα estimates generated from the 1,000 simulated data sets were very close to the “true” value for both designs. This was based on small bias and mean squared error calculations. Coverage probabilities in both designs were between 91.6 and 95.6%, close to the nominal coverage of 95%. Efficiency comparisons of the simulated Vision data sets demonstrated that the CCRD was more efficient in 93.3% of the comparisons. We suggest that a CCRD using glm and profile deviance for statistical analyses be considered an effective and efficient alternative in toxicity studies where interactive effects are of interest.