Collins MD et al. (2022), A model-based approach to designing development...

ECB-ART-50569

Arch Toxicol 2022 Mar 01;963:919-932. doi: 10.1007/s00204-021-03201-1.

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A model-based approach to designing developmental toxicology experiments using sea urchin embryos.

Collins MD , Cui EH , Hyun SW , Wong WK .

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The key aim of this paper is to suggest a more quantitative approach to designing a dose-response experiment, and more specifically, a concentration-response experiment. The work proposes a departure from the traditional experimental design to determine a dose-response relationship in a developmental toxicology study. It is proposed that a model-based approach to determine a dose-response relationship can provide the most accurate statistical inference for the underlying parameters of interest, which may be estimating one or more model parameters or pre-specified functions of the model parameters, such as lethal dose, at maximal efficiency. When the design criterion or criteria can be determined at the onset, there are demonstrated efficiency gains using a more carefully selected model-based optimal design as opposed to an ad-hoc empirical design. As an illustration, a model-based approach was theoretically used to construct efficient designs for inference in a developmental toxicity study of sea urchin embryos exposed to trimethoprim. This study compares and contrasts the results obtained using model-based optimal designs versus an ad-hoc empirical design.

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	Fig. 1. Density of beta distribution with parameters α and β
	Fig. 2. Development of sea urchin embryos. A Shows two sea urchin embryos/plutei that were exposed to 100 µM trimethoprim from 1 to 24 hpf and observed at 66 hpf. The pre-pluteus on the left has the phenotype described as early embryonic developmental arrest/death (EDA/D), and the pluteus on the right is phenotypically normal for this time of development. B This embryo was exposed to 180 µM trimethoprim from 1 to 24 hpf and observed at 72 hpf and has aboral radialization that is difficult to observe, because there is a problem getting the spicules in focus simultaneously due to the depth of field issues. Nevertheless, there are spicules located at approximately positions of the clock of 8, 9, 10, 11, 1, 3, and 4. C The pluteus shown is a control that was given vehicle (DMSO) from 1 to 24 hpf and then observed at 72 hpf. This photograph shows a single skeletal spicule in the foreground and a second spicule that is less focused but meets the first spicule on the aboral (left) region of the embryo
	Fig. 3. Response curves from the six sets of the parameter values for each endpoint. The black solid curve represents the response curve from the MLEs as nominal values and the red curves are from the five additional parameter sets. a Early embryonic developmental arrest/death (Arrest) versus concentration (Dose) relationship. b Aboral radialization versus concentration (Dose) relationship
	Fig. 4. D-efficiencies of the various designs relative to the locally D-optimal designs with MLEs as nominal values for estimating model parameters across the six sets of nominal parameter values for both endpoints. RD stands for the ξRD, O1 and O2 stand for ad-hoc empirical implemented designs, ξo1 and ξo2, respectively, and U4, U8, and U11 stand for the uniform designs U4, U8, and U11, respectively
	Fig. 5. C-efficiencies of various designs relative to the locally c-optimal designs with MLEs as nominal values for estimating the LC10 and LC20 across the six sets of nominal parameter values for the arrest/death rates as the first endpoint. RDc10 and RDc20 stand for the robust optimal designs, O1 stands for the ad-hoc empirical design ξo1 used for the study, and U4, U8, and U11 are the uniform designs U4, U8, and U11, respectively. The notation O2 stands for the ad-hoc empirical design ξo2 obtained from O1 but on a restricted design space
	Fig. 6. C-efficiencies of various designs relative to the locally c-optimal designs with MLEs as nominal values for estimating the LC25 and LC50 across the six sets of nominal parameter values for aboral radialization as the second endpoint. RDc25 and RDc50 stand for the robust optimal designs, O2 stands for the ad-hoc empirical design ξo2 used for the study, and U4, U8, and U11 are the uniform designs U4, U8, and U11, respectively. The notation O1 stands for the ad-hoc empirical design ξo1 implemented in the study to obtain the responses over the full dose range of interest

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