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Since the famous paper written by Kaplan and Meier in 1958, survival analysis has become one of the most important fields in statistics. Nowadays it is one of the most important statistical tools in analyzing epidemiological and clinical…
Sellke and Siegmund (1983) developed the Brownian approximation to the Cox partial likelihood score as a process of calendar time, laying the foundation for group sequential analysis of survival studies. We extend their results to cover…
This paper explores foundational and applied aspects of survival analysis, using fall risk assessment as a case study. It revisits key time-related probability distributions and statistical methods, including logistic regression, Poisson…
We provide a novel approach and an exploratory study for modelling life event choices and occurrence from a probabilistic perspective through causal discovery and survival analysis. Our approach is formulated as a bi-level problem. In the…
Modeling the evolution of a financial index as a stochastic process is a problem awaiting a full, satisfactory solution since it was first formulated by Bachelier in 1900. Here it is shown that the scaling with time of the return…
In this paper, we explore a method for treating survival analysis as a classification problem. The method uses a "stacking" idea that collects the features and outcomes of the survival data in a large data frame, and then treats it as a…
We consider Bayesian hierarchical models for survival analysis, where the survival times are modeled through an underlying diffusion process which determines the hazard rate. We show how these models can be efficiently treated by means of…
In the development of stochastic integration and the theory of semimartingales, Markov processes have been a constant source of inspiration. Despite this historical interweaving, it turned out that semimartingales should be considered the…
The notion of an individual random sequence goes back to von Mises. We describe the evolution of this notion, especially the use of martingales (suggested by Ville), and the development of algorithmic information theory in 1960s and 1970s…
This work bridges the gap between staggered adoption designs and survival analysis to estimate causal effects in settings with time-varying treatments, addressing a fundamental challenge in medical research exemplified by the Stanford Heart…
The mean residual life function is a key functional for a survival distribution. It has a practically useful interpretation as the expected remaining lifetime given survival up to a particular time point, and it also characterizes the…
Computing in the life sciences has undergone a transformative evolution, from early computational models in the 1950s to the applications of artificial intelligence (AI) and machine learning (ML) seen today. This paper highlights key…
In the context of survival analysis, Marshall and Olkin (1997) introduced families of distributions by adding a scalar parameter to a given survival function, parameterized or not. In that paper, we generalize their approach. We show how it…
Organizations interact with the environment and with other organizations, and these interactions constitute an important way of learning and evolution. To overcome the problems that they face during their existence, organizations must…
Survival analysis is one of the most important fields of statistics in medicine and the biological sciences. In addition, the computational advances in the last decades have favoured the use of Bayesian methods in this context, providing a…
Survival analysis is an integral part of the statistical toolbox. However, while most domains of classical statistics have embraced deep learning, survival analysis only recently gained some minor attention from the deep learning community.…
Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state…
The influx of deep learning (DL) techniques into the field of survival analysis in recent years has led to substantial methodological progress; for instance, learning from unstructured or high-dimensional data such as images, text or omics…
We introduce a semi-parametric Bayesian model for survival analysis. The model is centred on a parametric baseline hazard, and uses a Gaussian process to model variations away from it nonparametrically, as well as dependence on covariates.…
In recent years, the growing availability of biomedical datasets featuring numerous longitudinal covariates has motivated the development of several multi-step methods for the dynamic prediction of survival outcomes. These methods employ…