What's the proper way to determine whether dose response curves +/- another variable (besides dose) are statistically different?
Good call on not using multiple t-tests. The reason being, assuming a 95% confidence interval, each time you run the test you are "allowing" a 5% possibility of making a Type I error - this means that you incorrectly reject the null hypothesis in favour of the alternative hypothesis. If you run one t-test, there's a five percent chance of making an error. If you run two t-tests, there's a ten percent chance of making an error.

Between a regression model, or ANOVA, it does not matter. As the mathematics behind each are pretty much equivalent.

What you really want to look for, is the slopes of both models. If the two models have a statistically significant difference between their slopes, then this is indicating an interaction effect.

Two examples of (some, but not all) possible interaction effects:


Carrier A &amp; B have a similar effect on dose-response at 2mmol. But as the dosage approaches 10mmol, Carrier B causes a dose-response that is nearly double that of Carrier A.
Above 5mmol, Carrier B creates a greater dose-response. Below 5mmol Carrier A creates a greater dose response. At 5mmol the dose-response is nearly equivalent.