Speaker: Dr F. Javier Rubio, University College London

Abstract. The hazard function represents one of the main quantities of interest in the analysis of survival data. I will present a general approach for modelling the dynamics of the hazard function using systems of autonomous ordinary differential equations (ODEs). This modelling approach can be used to provide qualitative and quantitative analyses of the evolution of the hazard function over time. Our proposal capitalises on the extensive literature of ODEs which, in particular, allow for establishing basic rules or laws on the dynamics of the hazard function via the use of autonomous ODEs. We show how to implement the proposed modelling framework in cases where there is an analytic solution to the system of ODEs or where an ODE solver is required to obtain a numerical solution. Although I will focus on the use of a Bayesian modelling approach, the proposed methodology can also be coupled with maximum likelihood estimation. I will present a case study using real data to illustrate the use of the proposed approach and to highlight the interpretability of the corresponding models. I will conclude with a discussion on potential extensions of our work and strategies to include covariates into our framework.

This will be a free hybrid seminar. To register to attend virtually, please click here: https://us02web.zoom.us/meeting/register/tZYlce-spjIqHdQ4PYgBuSHSUSDRmLBAJQ5n