Evaluation of combination chemotherapy: Integration of nonlinear regression, curve shift, isobologram, and combination index analyses

Isobologram and combination index (CI) analyses are the two most popular methods for evaluating drug interactions in combination cancer chemotherapy. As the commonly used CI-based software program uses linear regression, our first objective was to evaluate the effects of logarithmic data transformation on data analysis and conclusions. Monte-Carlo simulations were conducted with experimentally relevant parameter values to generate error containing effect or concentration-effect data of single agents and combinations. The simulated data were then analyzed with linear and nonlinear regression. The results showed that data transformation reduced the accuracy and precision of the regression-derived IC50 curve shape parameter and CI values. Furthermore, as neither isobologram nor CI analyses provide output of concentration-effect curves for investigator evaluation, our second objective was to develop a method and the associated computer program/algorithm to (a) normalize drug concentrations in IC50 equivalents and thereby enable simultaneous presentation of the curves for single agents and combinations in a single plot for visual inspection of potential curve shifts, (b) analyze concentration-effect data with nonlinear regression, and (c) use the curve shift analysis simultaneously with isobologram and CI analyses. The applicability of this method was shown with experimentally obtained data for single agent doxorubicin and suramin and their combinations in cultured tumor cells. In summary, this method, by incorporating nonlinear regression and curve shift analysis, although retaining the attractive features of isobologram and CI analyses, reduced the potential errors introduced by logarithmic data transformation, enabled visual inspection of data variability and goodness of fit of regression analysis, and simultaneously provided information on the extent of drug interaction at different combination ratios/concentrations and at different effect levels.