Identifying and Estimating a Non-Constant Hazard Ratio with Time-Varying Covariates Using Cox Regression Models

• Activity Number: 421
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Miranda Kroehl*+ and Brittni Frederiksen and Jill Norris and Anna Baron
• Companies: Colorado School of Public Health and Colorado School of Public Health and Colorado School of Public Health and Univ of Colorado Denver
• Keywords: Cox regression ; time-varying covariate ; proportional hazards ; time-dependent covariate

Abstract

In epidemiologic studies, the association between a risk factor and the development of disease is often measured by a hazard ratio estimated from a Cox regression model. While it is common for a risk factor to be a fixed covariate measured at baseline, it is sometimes desirable to estimate the effect of a covariate that changes with time, such as dietary intake. Cox regression models have been extended to accommodate such variables, using the same estimation and testing procedures as for fixed covariates. In a fixed covariate model, it is possible to evaluate whether the effect of the risk factor remains constant with follow-up time by testing for proportional hazards. Furthermore, if the effect is not constant, there exists a variety of methods to estimate the hazard ratio as a function of time. However, little work has been done to address how to identify and estimate a non-constant hazard ratio for time-varying covariates. In this paper, we will explore the application of some common methods for evaluating the proportional hazards assumption to time-varying covariates and examine ways to model and estimate a non-constant hazard in these settings.