gms | German Medical Science

Kongress Medizin und Gesellschaft 2007

17. bis 21.09.2007, Augsburg

Why and how time-dependent bias leads to biased estimation of effect

Meeting Abstract

  • Jan Beyersmann - IMBI, Freiburg
  • Martin Wolkewitz - IMBI, Freiburg
  • Martin Schumacher - IMBI, Freiburg

Kongress Medizin und Gesellschaft 2007. Augsburg, 17.-21.09.2007. Düsseldorf: German Medical Science GMS Publishing House; 2007. Doc07gmds033

The electronic version of this article is the complete one and can be found online at:

Published: September 6, 2007

© 2007 Beyersmann et al.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( You are free: to Share – to copy, distribute and transmit the work, provided the original author and source are credited.



Background: Time-dependent covariates are usually not known at time origin. Examples for hospital patients include usage of invasive devices and occurrence of complications. Still, such information is often analysed as if known at baseline [1]. Van Walraven et al. [1] also claimed that such inadequate analyses will result in an biased estimate of the hazard ratio, e.g. from a Cox analysis. More precisely, they stated that if there is no effect on the hazard ratio, the inadequate analysis will show a decrease; if there is an increasing effect, the inadequate analysis will show an at least less pronounced increase; if there is a decreasing effect, the inadequate analysis will show an even greater decrease. In this talk, we show that this is actually the case, using simple algebraic rules only.

Methods: We will be able to illustrate this phenomenon in an evident way by employing a very intuitive, but much underused correspondence between time-dependent covariates and multistate models. Exemplary plots and analyses are provided for intensive care unit data.

Results: Time-dependent bias leads to the alleged effect. In intensive care, the prolonging effect of hospital infection on the discharge hazard is overestimated.

Discussion: Multistate models provide an intuitive tool to understand time-dependent covariates. Handling of their timing is essential; ignoring the temporal dynamics leads to erroneous results.


Van Walraven C, Davis D, Forster A, Wells G. Time-dependent bias was common in survival analyses published in leading clinical journals. J Clin Epi. 2004;57:672-82.