Immortal time bias in observational studies of time-to-event outcomes

PurposeThe purpose of the study is to show, through simulation and example, the magnitude and direction of immortal time bias when an inappropriate analysis is used.Materials and methodsWe compare 4 methods of analysis for observational studies of time-to-event outcomes: logistic regression, standard Cox model, landmark analysis, and time-dependent Cox model using an example data set of patients critically ill with influenza and a simulation study.ResultsFor the example data set, logistic regression, standard Cox model, and landmark analysis all showed some evidence that treatment with oseltamivir provides protection from mortality in patients critically ill with influenza. However, when the time-dependent nature of treatment exposure is taken account of using a time-dependent Cox model, there is no longer evidence of a protective effect of treatment. The simulation study showed that, under various scenarios, the time-dependent Cox model consistently provides unbiased treatment effect estimates, whereas standard Cox model leads to bias in favor of treatment. Logistic regression and landmark analysis may also lead to bias.ConclusionsTo minimize the risk of immortal time bias in observational studies of survival outcomes, we strongly suggest time-dependent exposures be included as time-dependent variables in hazard-based analyses.