Quantifying Synergistic Drug Interactions

To demonstrate the performance of the ZIP-based delta scoring, we considered a recent cancer drug screen study involving ibrutinib in combination with 466 compounds for the activated B-cell-like subtype (ABC) of diffuse large B-cell lymphoma (DLBCL) [14] (link). Ibrutinib is a small molecule targeting Bruton's tyrosine kinase (BTK) approved for the treatment of mantle cell lymphoma and chronic lymphocytic leukemia [16] (link). In this study, a high-throughput drug combination screening was used to identify other compounds that can synergistically interact with ibrutinib to improve its anticancer efficacy and circumvent drug resistance. For each drug pair, a 6 × 6 dose–response matrix design was utilized, where the drug effect was measured as percentage of cell viability using TMD8 cancer cell line. The raw combination data was provided by the authors via personal communication, but can now be downloaded from https://tripod.nih.gov/matrix-client/rest/matrix/export/241. We transformed the original percentage viability data into the percentage inhibition data before applying the drug combination analysis to be compatible with the mathematical formulation defined in the Methods section.
We ran the ZIP model on the drug combination data and calculated a summary delta score Δ for each drug pair by taking the average of all the delta scores over its dose combinations, i.e., $\Delta =\frac{1}{n}{\displaystyle \sum _{i=1}^n\delta }\text{,}$ where n is the number of dose combinations and n = 25 for a 6 × 6 dose–response matrix (monotherapy responses were removed). We compared the summary delta scores with the other scores derived from the HSA-, Bliss- and Loewe-based models. For HSA and Bliss, there were existing scores implemented in the original study [14] (link), which were based on the following methods: 1) NumExcess is the number of wells in the dose matrix that produced higher effect than both of the individual drug effects; 2) ExcessHSA is the sum of differences between the combination effect and the expected HSA effect; 3) MedianExcess is the median of the HSA excess; 4) ExcessCRX is an extension of the HSA model that was adjusted by dilution factors; 5) LS3 × 3 is the ExcessHSA applied to a 3 × 3 block showing the best HSA synergy in the dose matrix; 6) Beta (β) is the interaction parameter minimizing the deviance from the Bliss independence model over all dose combinations defined as $\underset{\beta }{argmin}\left({\displaystyle \sum {\left(1-y_c-\beta \left(1-y_1\right)\left(1-y_2\right)\right)}^2}\right)$ ; and 7) Gamma (γ) is a combination of HSA and Bliss models minimizing $\underset{\gamma }{argmin}\left({\displaystyle \sum {\left(1-y_c-\gamma max\left(1-y_1,1-y_2\right)\right)}^2}\right)\text{.}$ For the Loewe-based models, we calculated the two common interaction indices CI (Eq. (8)) and alpha(a) (Eq. (9)). The CI was calculated using an R package SYNERGY [13] (link) and the alpha score was estimated using the R package drc[12] .