Fig. 1: Overview to the proposed approach.
a The drug combination data and associated monotherapy responses are used to fit a parametric surface on each dose-response matrix. The BRAID surface model uses the Hill equations of the two drugs, as well as two interaction parameters to model different types of response surfaces. b Illustration of surface normalisation resulting in different similarities. The surfaces S1 and S2 are computed with κ = 0 (neutral), and S2 and S4 with κ = −1.5 (extreme antagonism) and κ = 25 (extreme synergism), respectively. c Finally, a surface-valued prediction problem is formulated and solved with the output kernel learning-style approach, where the output data is mapped with the help of a suitable kernel \({k}_{y}:{\mathcal{Y}}\times {\mathcal{Y}}\to {\mathbb{R}}\) to RKHS \({{\mathcal{H}}}_{{\mathcal{Y}}}\) (ϕy is the associated feature map: \({k}_{y}({y}_{1},{y}_{2})={\langle {\phi }_{y}({y}_{1}),{\phi }_{y}({y}_{2})\rangle }_{{{\mathcal{H}}}_{{\mathcal{Y}}}}\)).
