Illustrating the structures of bias from immortal time using directed acyclic graphs

Background Immortal time is a period of follow-up during which death or the study outcome cannot occur by design. Bias from immortal time has been increasingly recognized in epidemiological studies. However, the fundamental causes and structures of bias from immortal time have not been explained systematically. Methods We use an example ‘Does winning a Nobel Prize prolong lifespan?’ for illustration. We illustrate how immortal time arises and present structures of bias from immortal time using directed acyclic graphs that specify time-varying variables. We further explore the structures of bias with the exclusion of immortal time and with the presence of competing risks. We discuss how these structures are shared by different study designs in pharmacoepidemiology and provide solutions, where possible, to address the bias. Results The fundamental cause of immortal time is misalignment of exposure allocation and eligibility. Specifically, immortal time arises from using post-eligibility information to define exposure or using post-exposure information to define eligibility. The structures of bias from immortal time are confounding by survival until exposure allocation or selection bias from selecting on survival until eligibility. Excluding immortal time from follow-up does not fully address this confounding or selection bias, and the presence of competing risks can worsen the bias. Bias from immortal time may be avoided by aligning baseline, exposure allocation and eligibility, and by excluding individuals with prior exposure. Conclusions Understanding bias from immortal time in terms of confounding or selection bias helps researchers identify and thereby avoid or ameliorate this bias.