Analysis of the Proportional Hazards Model with Sparse Longitudinal Covariates.

TitleAnalysis of the Proportional Hazards Model with Sparse Longitudinal Covariates.
Publication TypeJournal Article
Year of Publication2015
AuthorsCao, Hongyuan, Mathew M. Churpek, Donglin Zeng, and Jason P. Fine
JournalJ Am Stat Assoc
Date Published2015

Regression analysis of censored failure observations via the proportional hazards model permits time-varying covariates which are observed at death times. In practice, such longitudinal covariates are typically sparse and only measured at infrequent and irregularly spaced follow-up times. Full likelihood analyses of joint models for longitudinal and survival data impose stringent modelling assumptions which are difficult to verify in practice and which are complicated both inferentially and computationally. In this article, a simple kernel weighted score function is proposed with minimal assumptions. Two scenarios are considered: half kernel estimation in which observation ceases at the time of the event and full kernel estimation for data where observation may continue after the event, as with recurrent events data. It is established that these estimators are consistent and asymptotically normal. However, they converge at rates which are slower than the parametric rates which may be achieved with fully observed covariates, with the full kernel method achieving an optimal convergence rate which is superior to that of the half kernel method. Simulation results demonstrate that the large sample approximations are adequate for practical use and may yield improved performance relative to last value carried forward approach and joint modelling method. The analysis of the data from a cardiac arrest study demonstrates the utility of the proposed methods.

Alternate JournalJ Am Stat Assoc
Original PublicationAnalysis of the proportional hazards model with sparse longitudinal covariates.
PubMed ID26576066
PubMed Central IDPMC4643320
Grant ListP01 CA142538 / CA / NCI NIH HHS / United States
R01 GM047845 / GM / NIGMS NIH HHS / United States
U01 NS082062 / NS / NINDS NIH HHS / United States