To the Editor:

In a recent Nature Methods Points of Significance piece1, drug combination was used to illustrate the principles of factorial experiments for the analysis of interaction effects. Factorial analysis of variance (ANOVA) can be very misleading in drug combination studies. Drugs follow a nonlinear dose-response pattern, and ANOVA is based on linear modeling. In practical terms, this means that unless the doses chosen in an experiment are in the linear-response range for the drugs, ANOVA might not detect a drug interaction. For example, if one dose for one of the drugs is at saturation response, then the data might seem to show a negative interaction (inhibition) for a drug that in reality has additive effects.

Nonlinearity is a general problem for factorial ANOVA for several types of variables. This can be dealt with in many cases by the use of pilot studies to establish the linear-response range. However, this is often not possible in drug studies, where random effects can cause minor but significant shifts in response curves between experiments, such that the linearity assumption cannot be made. To overcome this, it is best to study drug interactions in experiments that generate response curves for the drugs both individually and in combination in the same experimental replicate. Data from these types of experiments can be used in a variety of appropriate analyses such as isobologram and combination index2, curve shift3 and nonlinear mixed effect4 analyses. An additional advantage of these methods is that they allow for quantification of the strength of the interaction between drugs, which is crucial for practical decision making in drug combination experimental design.

It is important for researchers to be aware of the pitfalls of factorial experimental designs in the study of drug combination. There is a large and growing literature on the interpretation of degrees of drug synergy (positive interaction) using these methods2,3,4,5. Recent advances include the application of nonparametric methods as well as more precise consideration of the specific nonlinear forms of response curves and the relative potency of the two drugs being investigated6. Now that computationally intense methods are available to all with access to a personal computer, there is no reason not to use more robust and informative methods.