Time varying effects in survival analysis: a novel data-driven method for drift identification and variable selection

In this paper we address the problem of survival models when high-dimensional panel data are available. We discuss two related issues: The first one concerns the issue of variable selection and the second one deals with the stability over time of such a selection, since presence of time dimension in survival data requires explicit treatment of evolving socio-economic context. We show how graphical models can serve two purposes. First they serve as the input for a first algorithm to to assess the temporal stability of the data: Secondly, allow the deployment of a second algorithm which partially automates the process of variable selection, while retaining the option to incorporate domain expertise in the process of empirical model-building. To put our proposed methodology to the test, we utilize a dataset comprising Italian firms funded in 2009 and we study the survival of these entities over the period of 10 years. In addition to revealing significant volatility in the set of variables explaining firm exit over the years, our novel methodology enables us to offer a more nuanced perspective than the conventional one regarding the critical roles played by traditional variables such as industrial sector, geographical location, and innovativeness in firm survival.