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Mixture Experimental Design
Citation:
Simmons, J., I. Eide, G. Rice, AND P. Feder. Mixture Experimental Design. Chapter 13, Chemical Mixtures and Combined Chemical and Nonchemical Stressors. Springer International Publishing AG, Cham (ZG), Switzerland, , 335-366, (2018). https://doi.org/10.1007/978-3-319-56234-6_13
Impact/Purpose:
The chapter is intended to foster mixture experiments that are well designed, properly powered, appropriately conducted, analyzed and interpreted, i.e. the ‘right’ experiment. Key considerations for appropriate experimental design development are provided and illustrated with examples. The reader will be better prepared to conduct meaningful mixtures research. The ‘right’ experiment is one that is tailored to address the question being asked. Careful and clear articulation of both the effects to be examined and the null and alternative hypotheses are cruicial. The optimal design will vary based on the purpose of the experiment; in turn, the the purpose of the experiment drives the elements of the null and alternative hypotheses. The experimental design should optimize the accuracy and precision of the values being estimated; the optimal design depends on the values being estimated and the ‘true’ nature of the underlying dose-response relationship, i.e. the shape of the underlying dose-response curve(s) and variability. The total number of experimental units is important as is the number of dose groups, the selection of doses and the allocation of experimental units witin dose groups. Developing the analysis plan is important as the most elegant design will not be successful if the analysis is not appropriate; conversely a superior analysis strategy will flounder if the data collected are not suitable for that type of analysis. Consideration of power in advance of conducting the experiment is vital. The importance of advance power analysis increases as investigators move into the low effect/low-dose region of dose-response curves. Different designs are likely to be required dependent on the complexity of the dose-response trend, the complexity of the interactions and whether the focus is on detection of a greater-than-additive, less-than-additive or a dose-dependent interaction. A pilot experiment provides highly useful data to use in planning the more definitive experiment, including: determination of the sources and degree of variability; the selection of an appropriate design, power calculations; dose selectiondecisions; the allocation of experimental units per dose group; and, optimization of experimental design. The experimental design and the analysis should always match the question being asked.
Description:
There is a general consensus, based on a number of surveys and analytic efforts, that mixture study designs have historically been lacking. Although there has been considerable progress over the past decades, further improvement is necessary both in the development and application of experimental designs to yield data suitable for quantitative analytic methods and in the implementation of appropriate statistical analyses. This chapter reviews the state of the science with regard to the experimental and statistical quality of mixtures studies. The importance of properly powering mixtures experiments is emphasized, in particular when the focus is on the low-dose/low-effect region. Issues with powering defined mixture and complex mixture experiments are explored. Some designs that have proven useful in mixtures experimentation are reviewed, including full and fractional factorial designs and statistical mixture designs such as the isobologram and the fixed ratio ray. General considerations are provided that will aid in development of both experimental design and analysis strategies that address the question(s) being asked.
