To test the anticancer effect of combining two drugs targeting different biological pathways, the popular way to show synergistic effect of drug combination is a heat map or surface plot based on the percent excess the Bliss prediction using the average response measures at each combination dose. Such graphs, however, are inefficient in the drug screening process and it does not give a statistical inference on synergistic effect. To make a statistically rigorous and robust conclusion for drug combination effect, we present a two-stage Bliss independence response surface model to estimate an overall interaction index (τ) with 95% confidence interval (CI). By taking into all data points account, the overall τ with 95% CI can be applied to determine if the drug combination effect is synergistic overall. Using some example data, the two-stage model was compared to a couple of classic models following Bliss rule. The data analysis results obtained from our model reflect the pattern shown from other models. The application of overall τ helps investigators to make decision easier and accelerate the preclinical drug screening.