A methodology for finding optimal dosage levels in multi-drug treatment interactions

The aim of this paper is to demonstrate a methodology for finding optimal dosage levels in multi-drug treatment interactions and, at the same time, to analyse the synergetic effect which may occur with the combination of drugs. It includes a method for getting non-zero optimal dosage values for the drugs used in the treatment and a confidence region for those values. The analysis is based on survival data, to which a variant of the Cox multi-regression is applied, modelled by a quadratic function and followed by a test of model fitting, based on residual analysis. If the fit is adequate, the method allows predictions to be made for the best dosage levels. The therapeutic effect can be read for all possible drug dosages combinations from contour plots of constant response, which display the full results of the entire analysis.