On the Statistical Limitations of Landmark Analysis for Addressing Immortal Time Bias

Landmark analysis establishes a fixed "landmark" time, including only individuals who remain event-free up to that point and classifying survivors according to their treatment status at the landmark. By restarting follow-up from this time, the method aims to create comparable groups presumed free from immortal time bias. Despite its simplicity and widespread use, landmark analysis has notable limitations. Under potential outcomes and piecewise proportional hazards, we derived closed-form results for naive, exclusion, and landmark analyses and evaluated them via simulations. We found that landmark estimates fail to recover the target causal effect because the reference group mixes "never-treated" and "late-treated" subjects. This mixture attenuates the effect size, generally biasing estimates toward the null, with the magnitude of bias depending on the true effect, treatment rate, and event rate, except under the null hypothesis. In addition, landmark analysis suffers a substantial loss of statistical power due to the exclusion of early events and the attenuation of effect estimates. Indeed, the attenuation alone can make landmark analysis perform considerably worse in power than a randomized trial with equal group sizes. Without clinical context, a small treatment effect observed in a landmark analysis may reflect bias rather than a true null effect. Therefore, caution is warranted when using landmark analysis to address immortal time bias, and time-dependent regression models provide a more robust alternative.