Experimental designs for mixtures of chemicals along fixed ratio rays.

Abstract

Experimental design is important when studying mixtures/combinations of chemicals. The traditional approach for studying mixtures/combinations of multiple chemicals involves response surface methodology, often supported by factorial designs. Although such an approach permits the investigation of both the effects of individual chemicals and their interactions, the number of design points needed to study the chemical mixtures becomes prohibitive when the number of compounds increases. Fixed ratio ray designs have been developed to reduce the amount of experimental effort when interest can be restricted to a specific ray. We focus on the design and analysis issues involved in studying mixtures/combinations of compounds along fixed ratio rays of the compounds. To obtain the inference regarding the interactions among the compounds, we show that the only data required are those along the fixed ratio ray.

Concentration-Dependent Synergy and Antagonism within a Triple Antifungal Drug Combination againstAspergillusSpecies: Analysis by a New Response Surface Model

“…Finally, since combination studies with three of more drugs are laborious, time-consuming, and expensive, optimal experimental designs for mixtures can be employed in order to determine the parameters of the new model using the fewest possible data points (21). However, one should acknowledge the complexity of the new model, the use of multiple statistical diagnostic tests to ensure the goodness of fit, and the possibility that some pharmacodynamic interactions may be better described by higher-or lower-order polynomials (27).…”

Ds-optimal designs for studying combinations of chemicals using multiple fixed-ratio ray experiments

“…; x cðkÞ define a vector of doses at a given mixture point along the kth ray and t ¼ P c i¼1 x iðkÞ define total dose. When ray designs are considered, total dose is the independent variable along the mixing rays and the amount of the ith compound in the mixture along the kth ray is given by a iðkÞ t. Following Meadows et al (2002), the additivity (i.e. no interaction) model along the kth fixed-ratio ray can be expressed as gð addðkÞ Þ ¼ 0 þ 1 a 1ðkÞ t þ 2 a 2ðkÞ t þ Á Á Á þ c a cðkÞ t ¼ 0 þ ð 1 a 1ðkÞ þ 2 a 2ðkÞ þ Á Á Á þ c a cðkÞ Þt…”

“…The significance of higher-order terms in the polynomial approximation of the doseresponse relationship, expressed as a function of the total dose, indicates departure from additivity. Meadows et al (2002) showed that with this approach, only mixture data along a fixed-ratio ray are necessary for detecting departure from additivity. Casey (2003) extended these results to detect departure from additivity across multiple fixed-ratio rays in the presence or absence of single chemical data.…”

“…Recent advances in the statistical modeling of mixture data have moved the field from the analysis of binary combinations to analysis of multiple chemicals using response surfaces or ray designs. Meadows et al (2002) and Casey (2003) and are summarized in Section 2. Thus, the objective of this article is to provide methodology to determine at what dose levels and in what proportion of the total sample size observations should be taken for studies of mixture rays.…”

Combined Treatment of Pancreatic Cancer with Mithramycin A and Tolfenamic Acid Promotes Sp1 Degradation and Synergistic Antitumor Activity—Response

“…The interaction index has been discussed by several authors, such as Berenbaum (9), Tallarida (14), and Meadows and colleagues (15). The definition of the interaction index coincides with Chou and Talalay's definition of the combination index for mutually exclusive drugs, published in 1984 (16).…”