An unjustified benefit: immortal time bias in the analysis of time-dependent events

Abstract

Immortal time bias is a problem arising from methodologically wrong analyses of time-dependent events in survival analyses. We illustrate the problem by analysis of a kidney transplantation study. Following patients from transplantation to death, groups defined by the occurrence or nonoccurrence of graft failure during follow-up seemingly had equal overall mortality. Such naive analysis assumes that patients were assigned to the two groups at time of transplantation, which actually are a consequence of occurrence of a time-dependent event later during follow-up. We introduce landmark analysis as the method of choice to avoid immortal time bias. Landmark analysis splits the follow-up time at a common, prespecified time point, the so-called landmark. Groups are then defined by time-dependent events having occurred before the landmark, and outcome events are only considered if occurring after the landmark. Landmark analysis can be easily implemented with common statistical software. In our kidney transplantation example, landmark analyses with landmarks set at 30 and 60months clearly identified graft failure as a risk factor for overall mortality. We give further typical examples from transplantation research and discuss strengths and limitations of landmark analysis and other methods to address immortal time bias such as Cox regression with time-dependent covariables.