Time-to-event data analysis often focuses exclusively on the event, which is the endpoint of some underlying evolving process that is usually overlooked. First-Hitting-Time (FHT) models aim to account for the evolving process itself, and the choice of a suitable stochastic process is therefore crucial. In the literature, FHT models based on a Wiener process with drift are often considered, and a boosting algorithm for such a model has been proposed in recent years. The Wiener process, characterised by Gaussian increments, accommodates non-monotonic trajectories - a useful feature for modelling phenomena with temporary rebounds. However, in many cases, the process of interest is irreversible, making a monotonic process such as a gamma process a more appropriate alternative. As I will show, "the inattentive reader" might mistakenly conclude, based on the survival analysis literature, that lifetimes generated by an underlying gamma process follow an inverse-gamma distribution. Such a reader might even venture to develop a boosting algorithm for an inverse-gamma survival model while believing they are working within the FHT framework. In this talk, I will revisit and correct this previous misconception, presenting a boosting model for the true FHT distribution derived from a gamma process.
Clara Bertinelli Salucci: Modelling time-to-event with underlying gamma processes: Misconceptions, challenges, and solutions
Clara Bertinelli Salucci is a Postdoctoral Fellow at the Department of Mathematics, affiliated with the PLUMBIN' (Physics Learning Using Machines and Bayesian INference) project at the University of Oslo. She completed her PhD in Statistics and Machine Learning at the University of Oslo in April 2024, where she developed statistical and machine learning methods for diagnostics and prognostics of lithium-ion batteries for maritime applications. Currently, she is investigating the role of likelihood ratio test statistics for hypotheses tests in experimental and theoretical particle physics, focusing on deviations from Wilks' theorem in the search for new particles. Her postdoctoral research combines her expertise in statistics with her background in high-energy physics.
