Drug Combinations and Dose-Response Matrices

When doing experiments (usually referred to as high-throughput screens) with drug combinations,5 specific dosages for each drug are tested and the combined effect is measured. The results are usually represented in a matrix form, where the \(a_{i,j}\) element is the combined response, while the labeling/name of the \(i\)-row is the concentration of the first drug and the labeling of the \(j\)-column is the concentration of the second drug. From such a representation you can generate the surface response model and perform analyses using that 3D representation, which search for combinations of doses that produce larger combination effects (Chou and Talalay 1984). Another method plots the combination response vs the combined dosages of the two drugs (could be the sum of the doses for example), such that the description of the drug combination as synergistic or antagonistic is based on visual comparison between the single drug-response curves and the combined one, as is done in the CImbinator tool (Flobak et al. 2017).

Most methodologies use a (mathematical) model that describes/calculates a response/effect threshold, which distinguishes synergy from non-synergy. Thus, comparing each observed response with that threshold, we get a different synergy score value for each element of the dose-response matrix and then we can average these values (or use another method6) to get a single value for the whole dose-response matrix – a summary interaction score that tells us if the combination was synergistic or not in the end. The models that describe how to define those thresholds (for each combination data point in the dose-response matrix for example) are discussed in the next section.

  1. referring to combinations, we will mean 2 drugs for the rest of the text↩︎

  2. Huge story here, should you take the average of the matrix, the average of a specific sub-matrix, the minimum, the median, a value that optimizes an expression, etc. I have seen most of these methods around papers. If you are looking for some examples, take a look at the ExcessHSA, beta (\(\beta\)), gamma (\(\gamma\)) and summary delta (\(\Delta\)) scores at the SI of (“High-throughput combinatorial screening identifies drugs that cooperate with ibrutinib to kill activated B-cell-like diffuse large B-cell lymphoma cells.” 2014) and (Yadav et al. 2015)↩︎