Extension of the Isobolographic Approach to Interactions Studies Between More than Two Drugs: Illustration with the Convulsant Interaction between Pefloxacin, Norfloxacin, and Theophylline in Rats

Abstract

This work proposes a model to characterize the additivity or the nonadditivity of combinations of more than two agents. Using a Bayesian framework, we modeled the variability between experimental subjects, the errors that occurred during data collection, and the relationship between effects and concentrations of agents at the effect site. The model was used to characterize the additivity (or non-additivity) of norfloxacin, pefloxacin, and theophylline in causing maximal seizures in male Sprague Dawley rats. Animals received the drugs separately or in various combinations. Drug infusion was stopped at the onset of maximal seizures, and cerebrospinal fluid samples were collected for determination of drug concentration by high-performance liquid chromatography. The model was fitted to concentration data using Markov Chain Monte Carlo techniques. Results showed that induction of seizures by mixtures of theophylline and pefloxacin were additive. Seizure induction by mixtures of norfloxacin and pefloxacin or norfloxacin and theophylline were not additive and, given the model, these drugs interacted negatively. There was no triple interaction effect between the drugs. This study demonstrates the ease with which mixtures of more than two drugs can be analyzed with the proposed model. © 2004 Wiley-Liss, Inc. and the American Pharmacists Association