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

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 epidemiologic studies. However, it remains unclear how immortal time arises and what the structures of bias from immortal time are. Here, we use an example "Do Nobel Prize winners live longer than less recognized scientists?" to illustrate that immortal time arises from using postbaseline information to define exposure or eligibility. We use time-varying directed acyclic graphs (DAGs) to present the structures of bias from immortal time as the key sources of bias, that is confounding and selection bias. We explain that excluding immortal time from the follow-up does not fully address the bias, and that the presence of competing risks can worsen the bias. We also discuss how the structures of bias from immortal time are shared by different study designs in pharmacoepidemiology and provide solutions, where possible, to address the bias.