Related papers: Threshold Regression for Survival Analysis: Modeli…
We conducted a systematic comparison of statistical methods used for the analysis of time-to-event outcomes under various proportional and nonproportional hazard (NPH) scenarios. Our study used data from recently published oncology trials…
Many clinical studies require the follow-up of patients over time. This is challenging: apart from frequently observed drop-out, there are often also organizational and financial challenges, which can lead to reduced data collection and, in…
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…
Hazard ratios are ubiquitously used in time to event analysis to quantify treatment effects. Although hazard ratios are invaluable for hypothesis testing, other measures of association, both relative and absolute, may be used to fully…
In recent years, model collapse has become a critical issue in language model training, making it essential to understand the underlying mechanisms driving this phenomenon. In this paper, we investigate recursive parametric model training…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
First passage phenomena arise across physics, biology, and finance when stochastic processes first reach a threshold, triggering downstream events. Examples include the irreversible exit from a domain, a biochemical reaction, a financial…
In this paper, we focus on the hitting times of a stochastic epidemic model presented by \cite{Gray}. Under the help of the auxiliary stopping times, we investigate the asymptotic limits of the hitting times by the variations of calculus…
We consider the non-equilibrium dynamics of disordered systems as defined by a master equation involving transition rates between configurations (detailed balance is not assumed). To compute the important dynamical time scales in…
The classical approach to analyze time-to-event data, e.g. in clinical trials, is to fit Kaplan-Meier curves yielding the treatment effect as the hazard ratio between treatment groups. Afterwards commonly a log-rank test is performed in…
In this work, we investigate the population dynamics of tumor cells under therapeutic pressure. Although drug treatment initially induces a reduction in tumor burden, treatment failure frequently occurs over time due to the emergence of…
In this study, spatial stochastic and logistic model (SSLM) describing dynamics of a population of a certain species was analysed. The behaviour of the extinction threshold as a function of model parameters was studied. More specifically,…
We propose a semiparametric model to study the effect of covariates on the distribution of a censored event time while making minimal assumptions about the censoring mechanism. The result is a partially identified model, in the sense that…
We study first-hitting times in Differential Evolution (DE) through a conditional hazard frame work. Instead of analyzing convergence via Markov-chain transition kernels or drift arguments, we ex press the survival probability of a…
Interesting theoretical problems of target search or threshold crossing, formally known as {\it first passage}, often arise in both diffusive transport problems as well as problems of chemical reaction kinetics. We study three systems…
The size of a website's active user base directly affects its value. Thus, it is important to monitor and influence a user's likelihood to return to a site. Essential to this is predicting when a user will return. Current state of the art…
How long does it take a random walker to reach a given target point? This quantity, known as a first passage time (FPT), has led to a growing number of theoretical investigations over the last decade1. The importance of FPTs originates from…
We propose a multi-threshold change plane regression model which naturally partitions the observed subjects into subgroups with different covariate effects. The underlying grouping variable is a linear function of covariates and thus…
The modeling of time-to-event data, also known as survival analysis, requires specialized methods that can deal with censoring and truncation, time-varying features and effects, and that extend to settings with multiple competing events.…
Prognostic models in survival analysis are aimed at understanding the relationship between patients' covariates and the distribution of survival time. Traditionally, semi-parametric models, such as the Cox model, have been assumed. These…