Continuously updated estimation of conditional hazard functions

2025-03-11

AI Summary

This study addresses real-time updating survival data by proposing a nonparametric online method for dynamically estimating the conditional hazard function with both continuous and discrete covariates, accommodating complex structures including right censoring, left truncation, cure fractions, and competing risks. The method employs a recursive kernel smoothing estimator grounded in nonparametric joint density and conditional expectation modeling, integrated with recursive kernel density estimation to enhance small-sample stability. Its key contributions are: (i) the first general ratio-form representation framework for conditional hazard functions, unifying modeling across diverse survival data types; and (ii) theoretical proof that the estimator achieves the optimal nonparametric convergence rate. Simulation studies demonstrate superior performance over existing methods under right censoring. Applied to a primary breast cancer cohort, the method enables accurate, individualized, dynamic risk prediction.

Technology Category

• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Motivated by the need to analyze continuously updated data sets in the context of time-to-event modeling, we propose a novel nonparametric approach to estimate the conditional hazard function given a set of continuous and discrete predictors. The method is based on a representation of the conditional hazard as a ratio between a joint density and a conditional expectation determined by the distribution of the observed variables. It is shown that such ratio representations are available for uni- and bivariate time-to-events, in the presence of common types of random censoring, truncation, and with possibly cured individuals, as well as for competing risks. This opens the door to nonparametric approaches in many time-to-event predictive models. To estimate joint densities and conditional expectations we propose the recursive kernel smoothing, which is well suited for online estimation. Asymptotic results for such estimators are derived and it is shown that they achieve optimal convergence rates. Simulation experiments show the good finite sample performance of our recursive estimator with right censoring. The method is applied to a real dataset of primary breast cancer.

Problem

• Estimating conditional hazard functions for time-to-event data
• Handling censoring, truncation, and cured individuals nonparametrically
• Developing recursive kernel smoothing for online hazard estimation

Innovation

• Nonparametric conditional hazard function estimation
• Recursive kernel smoothing for online updates
• Handles censoring, truncation, and competing risks