Optimal experimental designs for estimating the drug combination index in toxicology

An interactive tool for designing efficient toxicology experiments

The design of dose-response experiments is an important part of toxicology research. Efficient design of these experiments requires choosing optimal doses and assigning the correct number of subjects to those doses under a given criterion. Optimal design theory provides the tools to find the most efficient experimental designs in terms of cost and statistical efficiency. However, the mathematical details can be distracting and make these designs inaccessible to many toxicologists. To facilitate use of these designs, we present an easy to use web-app for finding two types of optimal designs for models commonly used in toxicology. We include tools for checking the optimality of a given design and for assessing efficiency of any user-supplied design. Using state-of-the-art nature-inspired metaheuristic algorithms, the web-app allows the user to quickly find optimal designs for estimating model parameters or the benchmark dose.

Applications of statistical experimental designs to improve statistical inference in weed management

In a balanced design, researchers allocate the same number of units across all treatment groups. It has been believed as a rule of thumb among some researchers in agriculture. Sometimes, an unbalanced design outperforms a balanced design. Given a specific parameter of interest, researchers can design an experiment by unevenly distributing experimental units to increase statistical information about the parameter of interest. An additional way of improving an experiment is an adaptive design (e.g., spending the total sample size in multiple steps). It is helpful to have some knowledge about the parameter of interest to design an experiment. In the initial phase of an experiment, a researcher may spend a portion of the total sample size to learn about the parameter of interest. In the later phase, the remaining portion of the sample size can be distributed in order to gain more information about the parameter of interest. Though such ideas have existed in statistical literature, they have not been applied broadly in agricultural studies. In this article, we used simulations to demonstrate the superiority of the experimental designs over the balanced designs under three practical situations: comparing two groups, studying a dose-response relationship with right-censored data, and studying a synergetic effect of two treatments. The simulations showed that an objective-specific design provides smaller error in parameter estimation and higher statistical power in hypothesis testing when compared to a balanced design. We also conducted an adaptive experimental design applied to a dose-response study with right-censored data to quantify the effect of ethanol on weed control. Retrospective simulations supported the benefit of this adaptive design as well. All researchers face different practical situations, and appropriate experimental designs will help utilize available resources efficiently.

Modeling dose-response functions for combination treatments with log-logistic or Weibull functions

Dose-response curves of new substances in toxicology and related areas are commonly fitted using log-logistic functions. In more advanced studies, an additional interest is often how these substances will behave when applied in combination with a second substance. Here, an essential question for both design and analysis of these combination experiments is whether the resulting dose-response function will still be a member of the class of log-logistic functions, and, if so, what function parameters will result for the combined substances. Different scenarios might be considered in regard to whether a true interaction between the substances is expected, or whether the combination will simply be additive. In this paper, it is shown that the resulting function will in general not be a log-logistic function, but can be approximated very closely with one. Parameters for this approximation can be predicted from the parameters of both ingredients. Furthermore, some simple interaction structures can still be represented with a single log-logistic function. The approach can also be applied to Weibull-type dose-response functions, and similar results are obtained. Finally, the results were applied to a real data set obtained from cell culture experiments involving two cancer treatments, and the dose-response curve of a combination treatment was predicted from the properties of the singular substances.

Parametric modeling and optimal experimental designs for estimating isobolograms for drug interactions in toxicology

In toxicology and related areas, interaction effects between two substances are commonly expressed through a combination index [Formula: see text] evaluated separately at different effect levels and mixture ratios. Often, these indices are combined into a graphical representation, the isobologram. Instead of estimating the combination indices at the experimental mixture ratios only, we propose a simple parametric model for estimating the underlying interaction function. We integrate this approach into a joint model where both the parameters of the dose-response functions of the singular substances and the interaction parameters can be estimated simultaneously. As an additional benefit, this concept allows to determine optimal statistical designs for combination studies optimizing the estimation of the interaction function as a whole. From an optimal design perspective, finding the interaction parameters generally corresponds to a [Formula: see text]-optimality resp. [Formula: see text]-optimality design problem, while estimation of all underlying dose response parameters corresponds to a [Formula: see text]-optimality design problem. We show how optimal designs can be obtained in either case as well as how combination designs providing reasonable performance in regard to both criteria can be determined by putting a constraint on the efficiency in regard to one of the criteria and optimizing for the other. As all designs require prior information about model parameter values, which may be unreliable in practice, the effect of misspecifications is investigated as well.