Recursive model for dose-time responses in pharmacological studies

Clinical studies often track dose-response curves of subjects over time. One can easily model the dose-response curve at each time point with Hill equation, but such a model fails to capture the temporal evolution of the curves. On the other hand, one can use Gompertz equation to model the temporal behaviors at each dose 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 Hill equation across dose approximately. We derive a recursion relation for dose-response curves over time capturing the temporal evolution and 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 have compared the efficacy of our proposed Recursive Hybrid model with individual dose-response predictive models at desired time points. We note that our proposed model exhibits a superior performance compared to the individual ones for both synthetic data and actual pharmacological data. For the desired dose-time varying genetic characterization and drug response values, we have used the HMS-LINCS database and demonstrated the effectiveness of our model for all available anticancer compounds.