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We derive optimal designs to estimate efficacy and toxicity in active controlled dose-finding trials when the bivariate continuous outcomes are described using nonlinear regression models. We determine upper bounds on the required number of different doses and provide conditions under which the boundary points of the design space are included in the optimal design. We provide an analytical description of minimally supported optimal designs and show that they do not depend on the correlation between the bivariate outcomes.

Concentration-dependent cytotoxicity experiments are frequently used in toxicology. Although it has been reported that an adequate choice of concentrations improves the quality of the statistical inference substantially, a recent literature review of three major toxicological journals has shown that the corresponding methods are rarely used in toxicological practice. In this study the performance of different sets of concentrations, also called designs, are analyzed, while the overall goal is to promote the advantages of optimal design procedures and to present a user-friendly guideline for planning new cytotoxicity concentration-response experiments. We compare the frequently used log-equidistant design to a Bayesian design, which is constructed by methods of optimum design theory. Using both a dense data set of concentration-cytotoxicity data of valproic acid (VPA) and regular assay data of 104 substances, the performance of the different designs is analyzed in two scenarios, where detailed previous knowledge on VPA is available or not. The results show that it is critical to apply a specific design strategy to determine optimal concentrations for cytotoxicity testing. In particular, the Bayesian design technique with and without incorporating pre-existing knowledge of a specific test substance resulted in a more precise statistical inference than the other used designs. Finally, we present a guideline for upcoming experiments and an accessible user-friendly Shiny app (see http://shiny.statistik.tu-dortmund.de:8080/app/occe )., Competing Interests: Declarations. Conflict of interest: The authors declare that they have no conflict of interest. Ethical approval: Not applicable. Consent to participate: Not applicable. Consent for publication: Not applicable. Code availability: The corresponding Shiny app can be found online openly accessible at http://shiny.statistik.tu-dortmund.de:8080/app/occe ., (© 2024. The Author(s).)

Background: An important problem in toxicology in the context of gene expression data is the simultaneous inference of a large number of concentration-response relationships. The quality of the inference substantially depends on the choice of design of the experiments, in particular, on the set of different concentrations, at which observations are taken for the different genes under consideration. As this set has to be the same for all genes, the efficient planning of such experiments is very challenging. We address this problem by determining efficient designs for the simultaneous inference of a large number of concentration-response models. For that purpose, we both construct a D-optimality criterion for simultaneous inference and a K-means procedure which clusters the support points of the locally D-optimal designs of the individual models., Results: We show that a planning of experiments that addresses the simultaneous inference of a large number of concentration-response relationships yields a substantially more accurate statistical analysis. In particular, we compare the performance of the constructed designs to the ones of other commonly used designs in terms of D-efficiencies and in terms of the quality of the resulting model fits using a real data example dealing with valproic acid. For the quality comparison we perform an extensive simulation study., Conclusions: The design maximizing the D-optimality criterion for simultaneous inference improves the inference of the different concentration-response relationships substantially. The design based on the K-means procedure also performs well, whereas a log-equidistant design, which was also included in the analysis, performs poorly in terms of the quality of the simultaneous inference. Based on our findings, the D-optimal design for simultaneous inference should be used for upcoming analyses dealing with high-dimensional gene expression data., (© 2023. BioMed Central Ltd., part of Springer Nature.)

The analysis of dose-response, concentration-response, and time-response relationships is a central component of toxicological research. A major decision with respect to the statistical analysis is whether to consider only the actually measured concentrations or to assume an underlying (parametric) model that allows extrapolation. Recent research suggests the application of modelling approaches for various types of toxicological assays. However, there is a discrepancy between the state of the art in statistical methodological research and published analyses in the toxicological literature. The extent of this gap is quantified in this work using an extensive literature review that considered all dose-response analyses published in three major toxicological journals in 2021. The aspects of the review include biological considerations (type of assay and of exposure), statistical design considerations (number of measured conditions, design, and sample sizes), and statistical analysis considerations (display, analysis goal, statistical testing or modelling method, and alert concentration). Based on the results of this review and the critical assessment of three selected issues in the context of statistical research, concrete guidance for planning, execution, and analysis of dose-response studies from a statistical viewpoint is proposed., (© 2023. The Author(s).)

The determination of alert concentrations, where a pre-specified threshold of the response variable is exceeded, is an important goal of concentration-response studies. The traditional approach is based on investigating the measured concentrations and attaining statistical significance of the alert concentration by using a multiple t-test procedure. In this paper, we propose a new model-based method to identify alert concentrations, based on fitting a concentration-response curve and constructing a simultaneous confidence band for the difference of the response of a concentration compared to the control. In order to obtain these confidence bands, we use a bootstrap approach which can be applied to any functional form of the concentration-response curve. This particularly offers the possibility to investigate also those situations where the concentration-response relationship is not monotone and, moreover, to detect alerts at concentrations which were not measured during the study, providing a highly flexible framework for the problem at hand., (© 2021 The Authors. Biometrics published by Wiley Periodicals LLC on behalf of International Biometric Society.)

A key objective of Phase II dose finding studies in clinical drug development is to adequately characterize the dose response relationship of a new drug. An important decision is then on the choice of a suitable dose response function to support dose selection for the subsequent Phase III studies. In this paper, we compare different approaches for model selection and model averaging using mathematical properties as well as simulations. We review and illustrate asymptotic properties of model selection criteria and investigate their behavior when changing the sample size but keeping the effect size constant. In a simulation study, we investigate how the various approaches perform in realistically chosen settings. Finally, the different methods are illustrated with a recently conducted Phase II dose finding study in patients with chronic obstructive pulmonary disease. Copyright © 2016 John Wiley & Sons, Ltd., (Copyright © 2016 John Wiley & Sons, Ltd.)

We consider the optimal design problem for a comparison of two regression curves, which is used to establish the similarity between the dose response relationships of two groups. An optimal pair of designs minimizes the width of the confidence band for the difference between the two regression functions. Optimal design theory (equivalence theorems, efficiency bounds) is developed for this non standard design problem and for some commonly used dose response models optimal designs are found explicitly. The results are illustrated in several examples modeling dose response relationships. It is demonstrated that the optimal pair of designs for the comparison of the regression curves is not the pair of the optimal designs for the individual models. In particular it is shown that the use of the optimal designs proposed in this paper instead of commonly used "non-optimal" designs yields a reduction of the width of the confidence band by more than 50%.