Continuously updated estimation of conditional hazard functions

The article delves into the continuous estimation of conditional hazard functions in time-to-event analysis, a critical area with applications in biostatistics, engineering, labor economics, finance, insurance, and demography. It addresses the main challenge in this field: the incomplete observation of the time-to-event variable due to mechanisms like censoring and truncation. The text introduces a novel representation of the conditional hazard function as a ratio between the joint density and a conditional expectation, which can be applied in various contexts, including left or right random censoring, truncation, and models with a cure fraction. The authors propose recursive kernel estimators for the numerator and denominator of this hazard representation, which are easy to implement and update, and achieve optimal rates of convergence. The article also discusses the application of these methods to large datasets and online estimation, highlighting their practical relevance. Through simulations and real data analysis, the authors demonstrate the effectiveness of their approach, particularly in scenarios where classical parametric models may not be suitable. The findings underscore the importance of nonparametric methods in time-to-event analysis, offering professionals a robust tool for accurate hazard function estimation.