A Structural Description of Biases That Generate Immortal Time

causal diagrams
epidemiology
immortal time
misclassification bias
selection bias
survival analysis
target trial
  • Core Argument: The true source of immortal time bias is the underlying selection or misclassification of subjects, not the period of event-free time itself.
  • Two Mechanisms: The paper structurally describes two ways the bias arises: 1) Selection bias when eligibility is applied after assignment; and 2) Misclassification bias when assignment is defined using post-eligibility data for strategies indistinguishable at baseline.
  • Prevention: The definitive solution is to use Target Trial Emulation to achieve synchronization of eligibility and treatment assignment at the start of follow-up, thereby eliminating the generating biases.
Published

23 January 2026

PubMed: 39494894 DOI: 10.1097/EDE.0000000000001808 Overview generated by: Gemini 2.5 Flash, 26/11/2025

Key Concepts and Goal

Immortal time is defined as an event-free period included in a survival analysis during which a person, by definition, cannot experience the event of interest. The authors argue that the term “immortal time bias” is misleading because the bias is not generated by the time itself, but by the underlying selection or misclassification that creates the immortal time. The primary goal of the paper is to review the two mechanisms that produce immortal time and to propose causal diagrams to represent them.

The ultimate prevention strategy is Target Trial Emulation, which explicitly specifies eligibility and assignment to the treatment strategies and synchronizes them at the start of follow-up. This alignment prevents the selection and misclassification that lead to immortal time.

Mechanism 1: Immortal Time Due to Selection

This mechanism arises when an eligibility criterion is (incorrectly) applied after the start of follow-up (i.e., after treatment assignment).

Study Design Failure

The issue is created when researchers restrict the analysis to individuals who survived or completed a certain period of follow-up after the initial treatment assignment. For example, if follow-up data for the first 3 months are accidentally deleted, or if an observational analysis is restricted to individuals who have completed 3 months of follow-up, the resulting dataset only contains survivors, creating an “immortal” period where all included individuals survived.

Resulting Bias

  • The selection of surviving individuals results in selection bias due to a differential exclusion of the individuals most susceptible to the outcome in each treatment group.
  • If the follow-up is started at the time of treatment assignment but the immortal period is included, the resulting selection bias is often called “immortal time bias.”
  • If the follow-up is started after the immortal period (e.g., using a landmark approach), the resulting bias is sometimes referred to as “prevalent user bias.”

Solution

To prevent this bias, researchers must ensure that all eligibility criteria are defined at time zero so that no selection occurs after treatment assignment. This is naturally achieved by explicitly emulating a target trial based on data for all eligible individuals from the time of treatment assignment.

Mechanism 2: Immortal Time Due to Misclassification

This mechanism occurs when individuals are misclassified into a treatment group that differs from the one they were assigned to, typically because the treatment strategies under study are not distinguishable at time zero.

Study Design Failure

This arises when a treatment strategy includes a grace period or a waiting period (e.g., “start treatment within 3 months” vs. “never start treatment”). If the assignment indicator (\(Z\)) is deleted (or unknown in observational data), researchers might reconstruct an assignment (\(Z^*\)) based on whether the individual actually received treatment during the grace period. This forces individuals who were assigned to treatment but died before starting it to be classified into the “no treatment” group.

Resulting Bias

  • This reconstruction uses information on the outcome (survival until treatment) to define the assignment variable \(Z^*\), which is a violation of the rule that assignment at time zero must not depend on future outcome values.
  • The resulting error is outcome-dependent misclassification, which makes the treated group look artificially “immortal” during the grace period (as anyone who died before treatment is excluded from the \(Z^*\) group).

Solutions

  1. Change the Causal Question: Re-define the comparison to strategies that are distinguishable at time zero (e.g., comparing immediate treatment to no treatment today).
  2. Cloning Followed by Censoring: Create multiple “clones” of each individual for every treatment strategy compatible with their data at baseline. Each clone is censored if they deviate from the assigned strategy. This approach requires inverse-probability weighting to adjust for the induced selection bias.
  3. Plug-in G-Formula: A complex estimation approach requiring the modeling of the joint distribution or iterated conditional expectation of time-varying treatment, outcome, and confounders.

Cautionary Note on Alternative Methods

While landmark analysis and person-time analysis can avoid immortal time, they do not explicitly specify the target trial and do not eliminate the fundamental misalignment of eligibility and assignment. These methods can still be susceptible to bias (like selection bias for landmark analysis) or rely on implausible assumptions (like the constant hazard ratio assumption for person-time analysis).