Interaction Index and Different Methods for Determining Drug Interaction in Combination Therapy

Melding a New 3-Dimensional Agarose Colony Assay with the E(max) Model to Determine the Effects of Drug Combinations on Cancer Cells

The goal of our study was two-fold: (i) develop a robust 3D colony assay methodology to interrogate drug combinations using GelCount and (ii) to develop 2-drug combinations that might be useful in the clinic for the treatment of high-grade gliomas. We used three glioma cell lines (U251MG, SNB19, and LNZ308) and two adenocarcinoma cell lines (MiaPaCa and SW480) grown as colonies in a two-tiered agarose cultures. We evaluated two-drug combinations of difluoromethylornithine (DFMO), carboplatin, vorinostat (SAHA), and docetaxel. To analyze for antitumor efficacy we used GelCount to measure the area under the curve for tumor colony volumes (microm(2) x OD) in each plate. The non-linear dose-response E(max) model and the interaction index based on the Loewe additivity are applied to calculate two-drug synergy, additive, and antagonistic interactions. For glioblastoma cell lines, (i) carboplatin followed by DFMO was synergistic or additive in 2/3 cell lines, (ii) carboplatin before SAHA was synergistic in 1 cell line, (iii) carboplatin before docetaxel was synergistic in 2/3 cell lines and partially additive in the third, (iv) SAHA before docetaxel was synergistic in 1/3 cell lines, (v) docetaxel before DFMO was additive or partially active in 3/3 cell lines, and (vi) DFMO plus SAHA was inactive regardless of order. In the MiaPaCA cell line, synergy occurred when DFMO followed carboplatin and, at short exposure times, when SAHA was combined with carboplatin (regardless of order). In the SW480 cell line synergy occurred only in short exposures for carboplatin followed by docetaxel; additive and mixed partial effects were also seen with DFMO plus carboplatin or docetaxel (regardless of order), carboplatin before DFMO, carboplatin before SAHA, and docetaxel before carboplatin. In conclusion, by applying the Gelcount automated counting and sizing of colonies and the use of E(max) and Loewe models to define drug interactions, we can reliably define drug combination efficacy as a function of log dose and duration of drug exposure.

Confidence Intervals of Interaction Index for Assessing Multiple Drug Interaction

Studies of interactions among biologically active agents have become increasingly important in many branches of biomedical research. We consider that the Loewe additivity model is one of the best general reference models for defining drug interactions. Based on the Loewe additivity model, synergy occurs when the interaction index is less than one, and antagonism occurs when interaction index is greater than one. Starting from the Loewe additivity model and the marginal dose-effect curve for each drug involved in a combination, we first present a procedure to estimate the interaction index and its associated confidence interval at a combination dose with observed effects. Following Chou and Talalay's method for assessing drug interaction based on the plot of interaction indices versus effects for combination doses at a fixed ray, we then construct a pointwise (1-alpha)x100% confidence bound for the curve of interaction indices versus effects. We found that these methods work better on the logarithm transformed scale than on the untransformed scale of the interaction index. We provide simulations and case studies to illustrate the performances of these two procedures, and present their pros and cons. We also provide S-Plus/R code to facilitate the implementation of these two procedures.

A semiparametric response surface model for assessing drug interaction

When multiple drugs are administered simultaneously, investigators are often interested in assessing whether the drug combinations are synergistic, additive, or antagonistic. Existing response surface models are not adequate to capture the complex patterns of drug interactions. We propose a two-component semiparametric response surface model with a parametric function to describe the additive effect of a combination dose and a nonparametric function to capture the departure from the additive effect. The nonparametric function is estimated using the technique developed in thin plate splines, and the pointwise bootstrap confidence interval for this function is constructed. The proposed semiparametric model offers an effective way of formulating the additive effect while allowing the flexibility of modeling a departure from additivity. Example and simulations are given to illustrate that the proposed model provides an excellent estimation for different patterns of interactions between two drugs.