Kernel meets sieve: transformed hazards models with sparse longitudinal covariates

TL;DR

This paper introduces a robust, kernel-weighted sieve estimation method for transformed hazards models with intermittently observed, time-dependent covariates, addressing practical data limitations in survival analysis.

Contribution

It develops a new kernel-weighted sieve M-estimator for transformed hazards models with sparse longitudinal covariates, providing a rigorous theoretical framework and practical implementation.

Findings

Estimator has desirable asymptotic properties.

Method outperforms existing approaches in simulations.

Applied successfully to COVID-19 data in Wuhan.

Abstract

We study the transformed hazards model with time-dependent covariates observed intermittently for the censored outcome. Existing work assumes the availability of the whole trajectory of the time-dependent covariates, which is unrealistic. We propose to combine kernel-weighted log-likelihood and sieve maximum log-likelihood estimation to conduct statistical inference. The method is robust and easy to implement. We establish the asymptotic properties of the proposed estimator and contribute to a rigorous theoretical framework for general kernel-weighted sieve M-estimators. Numerical studies corroborate our theoretical results and show that the proposed method performs favorably over existing methods. Applying to a COVID-19 study in Wuhan illustrates the practical utility of our method.