Non-parametric synergy modeling of chemical compounds with Gaussian processes

Understanding the synergetic and antagonistic effects of combinations of drugs and toxins is vital for many applications, including treatment of multifactorial diseases and ecotoxicological monitoring. Synergy is usually assessed by comparing the response of drug combinations to a predicted non-interactive response from reference (null) models. Possible choices of null models are Loewe additivity, Bliss independence and the recently rediscovered Hand model. A different approach is taken by the MuSyC model, which directly fits a generalization of the Hill model to the data. All of these models, however, fit the dose-response relationship with a parametric model.

We propose the Hand-GP model, a non-parametric model based on the combination of the Hand model with Gaussian processes. We introduce a new logarithmic squared exponential kernel for the Gaussian process which captures the logarithmic dependence of response on dose. From the monotherapeutic response and the Hand principle, we construct a null reference response and synergy is assessed from the difference between this null reference and the Gaussian process fitted response. Statistical significance of the difference is assessed from the confidence intervals of the Gaussian process fits. We evaluate performance of our model on a simulated data set from Greco, two simulated data sets of our own design and two benchmark data sets from Chou and Talalay. We compare the Hand-GP model to standard synergy models and show that our model performs better on these data sets. We also compare our model to the MuSyC model as an example of a recent method on these five data sets and on two-drug combination screens: Mott et al. anti-malarial screen and O'Neil et al. anti-cancer screen. We identify cases in which the HandGP model is preferred and cases in which the MuSyC model is preferred.

The Hand-GP model is a flexible model to capture synergy. Its non-parametric and probabilistic nature allows it to model a wide variety of response patterns.