Construct a Simultaneous Confidence Interval for Linear Time-Varying Coefficients in Cox Proportional Hazard Model

• Activity Number: 697
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Shizue Izumi* and Tetsuji Tonda and Kenichi Satoh
• Companies: Oita University and Prefectural University of Hiroshima and Hiroshima University
• Keywords: Survival time data ; Cox proportional hazard model ; Time dependent covariate ; Time varying coefficient ; Simultaneous confidence interval

Abstract

We propose a simple method to construct a simultaneous confidence interval for linear time varying coefficients in Cox proportional hazard model. Here we consider the intervals for both time-independent and time varying coefficients. For the linear time varying coefficients we estimate the interactions of time and covariate as time-dependent covariate in an extended Cox proportional model in which a linear varying coefficient is incorporated. Second we construct the estimate of time varying coefficient and compute its simultaneous confidence interval on either an infinite or a finite time interval using a traditional multivariate data analytical method. We demonstrate our proposed method using an example data set, and the results show that a simultaneous confidence interval is wider than a pointwise confidence interval. Our proposal promises researchers to give an additional easy approach to deal with time-dependent covariates in the survival time data analyses.