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Applied Longitudinal Data AnalysisModeling Change and Event Occurrence$
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Judith D. Singer and John B. Willett

Print publication date: 2003

Print ISBN-13: 9780195152968

Published to Oxford Scholarship Online: September 2009

DOI: 10.1093/acprof:oso/9780195152968.001.0001

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Extending the Cox Regression Model

Extending the Cox Regression Model

(p.543) 15 Extending the Cox Regression Model
Applied Longitudinal Data Analysis

Judith D. Singer

John B. Willett

Oxford University Press

This chapter begins by describing how to include time-varying predictors in the Cox regression model. It then introduces two methods for relaxing the proportionality assumption. Section 15.2 presents the stratified Cox regression model, which stipulates that while the effects of each predictor are identical across strata, the baseline hazard functions can differ. Section 15.3 presents an alternative strategy that closely mirrors the approach used in discrete time: the inclusion of interactions with time as predictors in the model. Section 15.4 introduces a range of regression diagnostics useful for examining the underlying assumptions of the Cox model. Section 15.5 discusses what to do when modeling “competing risks”—multiple events that compete to terminate an individual's lifetime. Section 15.6 concludes by describing what to do when you have not observed the beginning of time for everyone in your sample and there are so-called late entrants to the risk set.

Keywords:   time-varying predictors, Cox regression models, hazard models time, baseline hazard, discrete time

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