On Estimating the Relationship between Longitudinal Measurements and Time-to-Event Data Using a Simple Two-Stage Procedure
Article first published online: 17 SEP 2010
© 2009, The International Biometric Society
Volume 66, Issue 3, pages 983–987, September 2010
How to Cite
Albert, P. S. and Shih, J. H. (2010), On Estimating the Relationship between Longitudinal Measurements and Time-to-Event Data Using a Simple Two-Stage Procedure. Biometrics, 66: 983–987. doi: 10.1111/j.1541-0420.2009.01324_1.x
- Issue published online: 17 SEP 2010
- Article first published online: 17 SEP 2010
- Received September 2008. Revised January 2009. Accepted February 2009.
- Informative dropout;
- Joint model;
- Regression calibration;
- Two-stage models
SummaryYe, Lin, and Taylor (2008, Biometrics 64, 1238–1246) proposed a joint model for longitudinal measurements and time-to-event data in which the longitudinal measurements are modeled with a semiparametric mixed model to allow for the complex patterns in longitudinal biomarker data. They proposed a two-stage regression calibration approach that is simpler to implement than a joint modeling approach. In the first stage of their approach, the mixed model is fit without regard to the time-to-event data. In the second stage, the posterior expectation of an individual's random effects from the mixed-model are included as covariates in a Cox model. Although Ye et al. (2008) acknowledged that their regression calibration approach may cause a bias due to the problem of informative dropout and measurement error, they argued that the bias is small relative to alternative methods. In this article, we show that this bias may be substantial. We show how to alleviate much of this bias with an alternative regression calibration approach that can be applied for both discrete and continuous time-to-event data. Through simulations, the proposed approach is shown to have substantially less bias than the regression calibration approach proposed by Ye et al. (2008). In agreement with the methodology proposed by Ye et al. (2008), an advantage of our proposed approach over joint modeling is that it can be implemented with standard statistical software and does not require complex estimation techniques.