Survival Analysis with Longitudinal Covariates Measured with Correlated Error

• Activity Number: 497
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Qiuju Li*+ and Jianxin Pan
• Companies: The University of Manchester and The University of Manchester
• Keywords: proportional hazards model ; longitudinal covariates ; within-subject error ; sufficient statistical method ; modified Cholesky decomposition

Abstract

When covariates in proportional hazards models are time-dependent, given the complete knowledge of true covariates history statistical inferences are analogous to these when covariates are time-independent. Time-dependent covariates, however, are usually measured intermittently and often with error. Longitudinal covariates are generally assumed to be measured with mutually independent error, however, this may not be always true. We study the effects of violation of independent assumption on the parameter estimation. Utilizing the sufficient statistics method proposed by Tsiatis and Davidian (2001), we show through simulation studies that the violation leads to a significant bias which increases with correlation. Generalized least square estimates are developed for the parameters associated with time-dependent covariates to take into account the correlation of within-subject error. Meanwhile, data-driven method based on modified Cholesky decomposition is proposed to make statistical inferences for the within-subject covariances. Numerical studies show that, with good estimates of covariances, the estimation bias can be largely reduced, and so that survival inference can be improved.