A Statistical Approach to the Construction and Analysis of Isobolograms

Current statistical procedures used in the construction of isobolograms do not use recent advances in mathematical statistics. The variability in the experimental data is either ignored or incompletely accounted for in the analyses. The decision procedures currently used to characterize the type of interaction between two agents do not permit the determination of the level of statistical significance associated with a given conclusion. Furthermore, the often formidable sample size is not exploited in the current isobologram methodology. Statistical techniques exist that may be used to construct isobolograms and decision procedures with a reliable level of significance. An isobologram is a contour of constant response of the underlying dose-response surface. Consequently, response surface methods (RSM) are useful in the estimation and analysis of isobolograms. The interaction between ethanol and chloral hydrate in female ICR mice was evaluated using the RSM approach by fitting the logistic model to quantal data. The loss of righting reflex was quantitated in mice 30 min after coadministration of the two drugs, injected IP on a body weight basis (mg/kg). The study consisted of 39 groups with 6 animals per group. Analysis of our data supports the conclusion of synergy between the drugs as reported by others; however, our results were obtained with a significantly smaller number of animals. These studies also demonstrate that response surface modeling can be used for determining additivity, synergism, and antagonism at a given preselected level of significance.