Analysis of Proportional Hazards Model with Sparse Longitudinal Covariates

• Activity Number: 107
• Type: Invited
• Date/Time: Monday, August 1, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Jason Fine*
• Companies: The University of North Carolina at Chapel Hill

Abstract

Regression analysis via the proportional hazards model permits time-varying covariates which are observed at death times. In practice, such covariates are typically measured infrequently and at irregularly spaced times. Last value carried forward imputation may incur substantial bias. Joint models for longitudinal and survival data impose stringent modelling assumptions which are difficult to verify and which are inferentially and computationally complex. We propose simple kernel weighted score functions which downweight imputed covariates according to the distance from the imputation timepoint. Two scenarios are considered: half kernel estimation where observation ceases at the event time and full kernel estimation where observation continues after the event. The estimators are consistent and asymptotically normal under minimal assumptions, but converge at slower than parametric rates for fully observed covariates, with half kernel achieving a superior convergence rate to full kernel. Simulation results demonstrate good performance of the methods with realistic sample sizes. A cardiac arrest dataset illustrates the practical utility of the approach.