I've performed an experiment in which a cell line was treated with a cocktail of three different compounds (call them A, B, and C). Compound A was used at two concentrations, compound B was used at four concentrations, and concentration C was used at four concentrations. The goal was to see how these different compounds affect cell viability. I'd like to see if each of the compounds independently has an effect, as well as if there are synergistic effects between the compounds. All 32 possible cocktails were examined in triplicate.

I initially ran a 3-way ANOVA on my data to identify main effects, as well as interactions. I started to wonder, though, if it would be better to run three independent ANCOVAs, each time treating one of the compounds as a fixed factor and the other two as covariates. I thought that might better isolate whether or not each compound is affecting viability by controlling for the other two compounds. Then I wondered if it would be best to perform a linear regression since the concentrations for all three compounds are technically continuous, I've simply chosen several discrete concentrations.

Could someone please help me parse my data? Again, the goal is to determine whether or not each of the compounds independently affects viability, as well as whether or not compounds interact with one another to affect viability. If there are differences between concentrations, I'd like to run post-hoc analyses to see which concentrations show differences.