Kernel Meets Sieve: Transformed Hazards Models with Sparse Longitudinal Covariates

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 combining 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 competing methods. The analysis of a dataset from a COVID-19 study in Wuhan identifies clinical predictors that otherwise cannot be obtained using existing methods. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.