  In biomedical applications it is often necessary to estimate a physiological
response to a treatment consisting of multiple components, and learn the
separate effects of the components in addition to the joint effect. Here, we
extend existing probabilistic nonparametric approaches to explicitly address
this problem. We also develop a new convolution-based model for composite
treatment-response curves that is more biologically interpretable. We validate
our models by estimating the impact of carbohydrate and fat in meals on blood
glucose. By differentiating treatment components, incorporating their dosages,
and sharing statistical information across patients via a hierarchical
multi-output Gaussian process, our method improves prediction accuracy over
existing approaches, and allows us to interpret the different effects of
carbohydrates and fat on the overall glucose response.
