Kernel meets sieve: transformed hazards models with sparse longitudinal covariates

We study the transformed hazards model with intermittently observed time-dependent covariates for the censored outcome. Existing work assumes the availability of the whole trajectory of the time-dependent covariates, which is not realistic. 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 has favorable performance over existing methods. An application to a COVID-19 study in Wuhan illustrates the practical utility of our method.