Selecting the best design for nonstandard toxicology experiments

Although many experiments in environmental toxicology use standard statistical experimental designs, there are situations that arise where no such standard design is natural or applicable because of logistical constraints. For example, the layout of a laboratory may suggest that each shelf serve as a block, with the number of experimental units per shelf either greater than or less than the number of treatments in a way that precludes the use of a typical block design. In such cases, an effective and powerful alternative is to employ optimal experimental design principles, a strategy that produces designs with precise statistical estimates. Here, a D-optimal design was generated for an experiment in environmental toxicology that has 2 factors, 16 treatments, and constraints similar to those described above. After initial consideration of a randomized complete block design and an intuitive cyclic design, it was decided to compare a D-optimal design and a slightly more complicated version of the cyclic design. Simulations were conducted generating random responses under a variety of scenarios that reflect conditions motivated by a similar toxicology study, and the designs were evaluated via D-efficiency as well as by a power analysis. The cyclic design performed well compared to the D-optimal design.