A Measure for Assessing Functions of Time-Varying Effects in Survival Analysis

Anika Buchholz¹, Willi Sauerbrei¹, Patrick Royston²

¹Center for Medical Biometry and Medical Informatics, Medical Center - University of Freiburg, Freiburg, Germany.
²MRC Clinical Trials Unit at University College London, London, UK.

DOI: 10.4236/ojs.2014.411092                

Abstract

A standard approach for analyses of survival data is the Cox proportional hazards model. It assumes that covariate effects are constant over time, i.e. that the hazards are proportional. With longer follow-up times, though, the effect of a variable often gets weaker and the proportional hazards (PH) assumption is violated. In the last years, several approaches have been proposed to detect and model such time-varying effects. However, comparison and evaluation of the various approaches is difficult. A suitable measure is needed that quantifies the difference between time-varying effects and enables judgement about which method is best, i.e. which estimate is closest to the true effect. In this paper we adapt a measure proposed for the area between smoothed curves of exposure to time-varying effects. This measure is based on the weighted area between curves of time-varying effects relative to the area under a reference function that represents the true effect. We introduce several weighting schemes and demonstrate the application and performance of this new measure in a real-life data set and a simulation study.

Keywords

Cox Model, Measure of Distance, Survival Analysis, Time-Varying Effects

Conflicts of Interest

The authors declare no conflicts of interest.

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