  In cancer translational research, increasing effort is devoted to the study
of the combined effect of two drugs when they are administered simultaneously.
In this paper, we introduce a new approach to estimate the part of the effect
of the two drugs due to the interaction of the compounds, i.e. which is due to
synergistic or antagonistic effects of the two drugs, compared to a reference
value representing the condition when the combined compounds do not interact,
called zero-interaction. We describe an in-vitro cell viability experiment as a
random experiment, by interpreting cell viability as the probability of a cell
in the experiment to be viable after treatment, and including information
related to different exposure conditions. We propose a flexible Bayesian spline
regression framework for modelling the viability surface of two drugs combined
as a function of the concentrations. Since the proposed approach is based on a
statistical model, it allows to include replicates of the experiments, to
evaluate the uncertainty of the estimates, and to perform prediction. We test
the model fit and prediction performance on a simulation study, and on an
ovarian cancer cell dataset. Posterior estimates of the zero-interaction level
and of the synergy term, obtained via adaptive MCMC algorithms, are used to
compute interpretable measures of efficacy of the combined experiment,
including relative volume under the surface (rVUS) measures to summarise the
zero-interaction and synergy terms and a bi-variate alternative to the
well-known EC50 measure.
