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Assessing the Additivity of the Effects of Drugs in Mixtures

Celine Brochot, William Couet, Andrew Gelman, Frederic Yves Bois

INERIS, Verneuil en Halatte, France

A general statistical model to assess the effects of combinations of any number of drugs is presented. The model is applicable to data collected following an experimental protocol called `direct assay'. In such a protocol, drugs are gradually applied until a target response is observed. At that point in time, some measure of effective (e.g., internal) dose is obtained for each agent. The model, developped in a Bayesian framework, takes inter-individual variability, measurement error and dose-response relationship into account. To check the model, data were simulated using a polynomial dose-response model.Synergism simulated by the data was detected and reasonable estimations were obtained for the parameters. An application to a real data set, on pefloxacin and theophylline mixture-induced seizures in rats, is demonstrated. A previous analysis of these data, using an approximate method, had estimated a negative interaction between these compounds. In contrast, we found the effect of mixtures of these two agents to be approximately additive. We attribute our new finding to an improved treatment of measurement error in our model. Two other data sets, on norfloxacin and theophylline and on norfloxacin and pefloxacin induced seizures in rats, were studied. In these cases, our method confirmed previous analyses.