Recursive Model for Dose-time Responses in Pharmacological Studies

Abstract

Clinical studies often track dose-response curves of subjects over time. One can easily model dose-response curve at each time point with Hill equation, but such a model fails to capture the temporal evolution of curves. On the other hand, one can use Gompertz equation to model the dose-time curves at each time point without capturing the evolution of time curves across dosage. In this article, we propose a parametric model for dose-time responses that follows Gompertz law in time and approximately follows Hill equation across dose. We derive a recursion relation for dose-response curves over time capturing the temporal evolution. We then specify a regression model connecting the parameters controlling the dose-time responses with individual level proteomic data. The resultant joint model allows us to predict the dose-response curves over time for new individuals. We illustrate the superior performance of our proposed model as compared to the individual models using data from the HMS-LINCS database.